From d7e1dd7d0214730a8c2b1933dd14efe90c38e364 Mon Sep 17 00:00:00 2001 From: matthieuaussal Date: Tue, 11 Jul 2017 14:20:09 +0200 Subject: [PATCH] 17.07.11 --- nonRegressionTest/nrtAlgebra.m | 577 + nonRegressionTest/nrtCube.m | 246 + nonRegressionTest/nrtDisk.m | 250 + nonRegressionTest/nrtFemConvergence.m | 85 + nonRegressionTest/nrtSparseLU.m | 105 + openFem/fem.m | 107 + openFem/femDiff.m | 60 + openFem/femDof.m | 46 + openFem/femGreenKernel.m | 91 + openFem/femHmatrix.m | 170 + openFem/femHmatrixParallel.m | 214 + openFem/femLagrangePn.m | 437 + openFem/femRegularize.m | 283 + openHmx/hmx.m | 221 + openHmx/hmxACA.m | 149 + openHmx/hmxBuilder.m | 140 + openHmx/hmxChol.m | 65 + openHmx/hmxCtranspose.m | 63 + openHmx/hmxDouble.m | 54 + openHmx/hmxFull.m | 52 + openHmx/hmxFusion.m | 97 + openHmx/hmxInv.m | 73 + openHmx/hmxLU.m | 99 + openHmx/hmxLdl.m | 86 + openHmx/hmxMtimes.m | 197 + openHmx/hmxPlus.m | 224 + openHmx/hmxQRSVD.m | 48 + openHmx/hmxRSVD.m | 69 + openHmx/hmxSherMorr.m | 74 + openHmx/hmxSingle.m | 54 + openHmx/hmxSolveLower.m | 139 + openHmx/hmxSolveUpper.m | 185 + openHmx/hmxSparse.m | 52 + openHmx/hmxSpy.m | 82 + openHmx/hmxSubdivide.m | 44 + openHmx/hmxTimes.m | 70 + openHmx/hmxTranspose.m | 63 + openMsh/msh.m | 154 + openMsh/mshBoundary.m | 48 + openMsh/mshCenter.m | 34 + openMsh/mshClean.m | 37 + openMsh/mshCube.m | 38 + openMsh/mshDisk.m | 56 + openMsh/mshEdge.m | 66 + openMsh/mshFace.m | 57 + openMsh/mshIntegral.m | 347 + openMsh/mshNdvolume.m | 65 + openMsh/mshPlot.m | 80 + openMsh/mshQuadrature.m | 69 + openMsh/mshReadPly.m | 480 + openMsh/mshReadVtk.m | 92 + openMsh/mshReference.m | 142 + openMsh/mshSemiAnalyticInt.m | 109 + openMsh/mshSphere.m | 40 + openMsh/mshSquare.m | 42 + problems/cavityModeNeumann.m | 191 + problems/cubeEigenValues.m | 129 + problems/diskEigenValues.m | 122 + problems/meshes/Oxz_1e4.ply | 29612 +++++++++++++++++++++++ problems/meshes/unitCubeCavity_1e3.ply | 2916 +++ problems/sphereScattering.m | 66 + problems/sphereScatteringD.m | 227 + problems/sphereScatteringDt.m | 238 + problems/sphereScatteringN.m | 249 + problems/sphereScatteringS.m | 211 + 65 files changed, 40988 insertions(+) create mode 100644 nonRegressionTest/nrtAlgebra.m create mode 100644 nonRegressionTest/nrtCube.m create mode 100644 nonRegressionTest/nrtDisk.m create mode 100644 nonRegressionTest/nrtFemConvergence.m create mode 100644 nonRegressionTest/nrtSparseLU.m create mode 100644 openFem/fem.m create mode 100644 openFem/femDiff.m create mode 100644 openFem/femDof.m create mode 100644 openFem/femGreenKernel.m create mode 100644 openFem/femHmatrix.m create mode 100644 openFem/femHmatrixParallel.m create mode 100644 openFem/femLagrangePn.m create mode 100644 openFem/femRegularize.m create mode 100644 openHmx/hmx.m create mode 100644 openHmx/hmxACA.m create mode 100644 openHmx/hmxBuilder.m create mode 100644 openHmx/hmxChol.m create mode 100644 openHmx/hmxCtranspose.m create mode 100644 openHmx/hmxDouble.m create mode 100644 openHmx/hmxFull.m create mode 100644 openHmx/hmxFusion.m create mode 100644 openHmx/hmxInv.m create mode 100644 openHmx/hmxLU.m create mode 100644 openHmx/hmxLdl.m create mode 100644 openHmx/hmxMtimes.m create mode 100644 openHmx/hmxPlus.m create mode 100644 openHmx/hmxQRSVD.m create mode 100644 openHmx/hmxRSVD.m create mode 100644 openHmx/hmxSherMorr.m create mode 100644 openHmx/hmxSingle.m create mode 100644 openHmx/hmxSolveLower.m create mode 100644 openHmx/hmxSolveUpper.m create mode 100644 openHmx/hmxSparse.m create mode 100644 openHmx/hmxSpy.m create mode 100644 openHmx/hmxSubdivide.m create mode 100644 openHmx/hmxTimes.m create mode 100644 openHmx/hmxTranspose.m create mode 100644 openMsh/msh.m create mode 100644 openMsh/mshBoundary.m create mode 100644 openMsh/mshCenter.m create mode 100644 openMsh/mshClean.m create mode 100644 openMsh/mshCube.m create mode 100644 openMsh/mshDisk.m create mode 100644 openMsh/mshEdge.m create mode 100644 openMsh/mshFace.m create mode 100644 openMsh/mshIntegral.m create mode 100644 openMsh/mshNdvolume.m create mode 100644 openMsh/mshPlot.m create mode 100644 openMsh/mshQuadrature.m create mode 100644 openMsh/mshReadPly.m create mode 100644 openMsh/mshReadVtk.m create mode 100644 openMsh/mshReference.m create mode 100644 openMsh/mshSemiAnalyticInt.m create mode 100644 openMsh/mshSphere.m create mode 100644 openMsh/mshSquare.m create mode 100644 problems/cavityModeNeumann.m create mode 100644 problems/cubeEigenValues.m create mode 100644 problems/diskEigenValues.m create mode 100644 problems/meshes/Oxz_1e4.ply create mode 100644 problems/meshes/unitCubeCavity_1e3.ply create mode 100644 problems/sphereScattering.m create mode 100644 problems/sphereScatteringD.m create mode 100644 problems/sphereScatteringDt.m create mode 100644 problems/sphereScatteringN.m create mode 100644 problems/sphereScatteringS.m diff --git a/nonRegressionTest/nrtAlgebra.m b/nonRegressionTest/nrtAlgebra.m new file mode 100644 index 0000000..c5afc81 --- /dev/null +++ b/nonRegressionTest/nrtAlgebra.m @@ -0,0 +1,577 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. Refer to \ \| |/ / | +%| each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Build and algebra for H-Matrix structure | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openHmx') + +% Data type +type = 'double'; + +% Accuracy +tol = 1e-3 + +% Wave number or frequency (Hz) +k = 5 +f = (k*340)/(2*pi); + +% Particles receptors X (sphere) +Nx = 1e3; +[x,y,z] = sphere(ceil(sqrt(Nx))); +X = unique([x(:),y(:),z(:)],'rows'); +Nx = size(X,1) +if strcmp(type,'single') + X = single(X); +end + +% Particles transmitters Y (=X or not) +Ny = Nx; +Y = X; +% Ny = 2e3 +% Y = -1+2*rand(Ny,3); +if strcmp(type,'single') + X = single(X); +end + +% Green kernel -> exp(1i*k*r)/r +rxy = @(X,Y) sqrt( (X(:,1)-Y(:,1)).^2 + (X(:,2)-Y(:,2)).^2 + (X(:,3)-Y(:,3)).^2 ); +green = @(X,Y) exp(1i*k*rxy(X,Y))./(rxy(X,Y) + 1/(1i*k)); + +% Particles charges (multiples) +V = (-1+2*rand(Ny,2,type)) + (-1+2i*rand(Ny,2,type)); + +% Spatial representation of particles +figure +plot3(X(:,1),X(:,2),X(:,3),'*b',Y(:,1),Y(:,2),Y(:,3),'*r') +axis equal + + +%%% Full matrix computation +disp('~~~~~~~~~~~~~ EXACT MATRIX AS REFERENCE~~~~~~~~~~~~~') +tic +M = zeros(Nx,Ny,type); +for i = 1:Nx + M(i,:) = green(X(i,:),Y).'; +end +MV = M * V; +toc + +tic +un = ones(Nx,1); +I = spdiags([-un 2*un -un], [-Nx/2,0,Nx/2] , Nx, Ny); +IV = I*double(V); +toc +spy(I) +disp(' ') + + +%%% H-Matrix computation +disp('~~~~~~~~~~~~~ H-MATRIX ~~~~~~~~~~~~~') +tic +Mh = hmx(X,Y,green,tol); +toc + +tic +Mh2 = hmx(X,Y,M,tol); +toc + +tic +Ih = hmx(double(X),double(Y),I,tol); +toc + +disp(' ') + + +%%% H-Matrix structure +disp('~~~~~~~~~~~~~ SPY STRUCTURE ~~~~~~~~~~~~~') +tic +figure +spy(Mh); +toc + +tic +figure +spy(Mh2); +toc + +tic +figure +spy(Ih); +toc + +disp(' ') + + +%%% Full conversion +disp('~~~~~~~~~~~~~ FULL CONVERSION ~~~~~~~~~~~~~') +tic +sol = full(Mh); +toc +ref = M; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +sol = full(Mh2); +toc +ref = M; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +sol = full(Ih); +toc +ref = full(I); +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% Sparse conversion +disp('~~~~~~~~~~~~~ SPARSE CONVERSION ~~~~~~~~~~~~~') +tic +sol = sparse(double(Mh)); +toc +ref = double(M); +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +sol = sparse(Ih); +toc +ref = I; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% Transposition +disp('~~~~~~~~~~~~~ TRANSPOSITION ~~~~~~~~~~~~~') +tic +tmp = Mh.'; +toc +sol = full(tmp); +ref = M.'; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +tmp = Ih.'; +toc +sol = full(tmp); +ref = I.'; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% Conjugate transposition +disp('~~~~~~~~~~~~~ CTRANSPOSITION ~~~~~~~~~~~~~') +tic +tmp = Mh'; +toc +sol = full(tmp); +ref = M'; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +tmp = Ih'; +toc +sol = full(tmp); +ref = I'; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% H-Matrix right product +disp('~~~~~~~~~~~~~ H-MATRIX * MATRIX ~~~~~~~~~~~~~') +tic +sol = Mh * V; +toc +ref = MV; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +sol = Ih * double(V); +toc +ref = IV; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +sol = double(Mh) * I.'; +toc +ref = double(M) * I.'; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +sol = Ih * I.'; +toc +ref = I * I.'; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% Left product H-Matrix +disp('~~~~~~~~~~~~~ FULL MATRIX * H-MATRIX ~~~~~~~~~~~~~') +tmp = Mh.'; +tic +sol = V.' * tmp; +toc +ref = MV.'; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% Scalar product +disp('~~~~~~~~~~~~~ SCALAR PRODUCT ~~~~~~~~~~~~~') +tic +tmp = (sqrt(2) .* Mh .* pi); +toc +sol = tmp * V; +ref = sqrt(2) * pi * MV; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +tmp = (sqrt(2) .* Ih .* pi); +toc +sol = tmp * double(V); +ref = sqrt(2) * pi * IV; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% Uminus +disp('~~~~~~~~~~~~~ UMINUS ~~~~~~~~~~~~~') +tic +tmp = - Mh; +toc +sol = tmp * V; +ref = - MV; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% Full Addition +disp('~~~~~~~~~~~~~ FULL ADDITION/SUBSTRACTION ~~~~~~~~~~~~~') +tic +tmp = 2*M + Mh - M; +toc +sol = tmp * V; +ref = 2*MV; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +tmp = 2*M + Ih - M; +toc +sol = tmp * V; +ref = MV + IV; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% Full Addition +disp('~~~~~~~~~~~~~ SPARSE ADDITION/SUBSTRACTION ~~~~~~~~~~~~~') +tic +tmp = 2*I + Mh - I; +toc +sol = tmp * V; +ref = MV+IV; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +tmp = 2*I + Ih - I; +toc +sol = tmp * double(V); +ref = 2*IV; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% H-Matrix addition +disp('~~~~~~~~~~~~~ H-MATRIX ADDITION/SUBSTRACTION ~~~~~~~~~~~~~') +tic +tmp = 2.*Mh + Mh - Mh; +toc +sol = tmp * V; +ref = 2*MV; +norm(ref-sol,'inf')/norm(ref,'inf') +figure +spy(tmp) + +tic +tmp = 2.*Ih + Mh - Ih; +toc +sol = tmp * V; +ref = MV + IV; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +tmp = 2.*Mh + Ih - Mh; +toc +sol = tmp * V; +ref = MV + IV; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +tmp = 2.*Ih + Ih - Ih; +toc +sol = tmp * double(V); +ref = 2*IV; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% H-Matrix product +disp('~~~~~~~~~~~~~ H-MATRIX PRODUCT ~~~~~~~~~~~~~') +tic +tmp = Mh * Mh.'; +toc +sol = full(tmp); +ref = M * M.'; +norm(ref-sol,'inf')/norm(ref,'inf') +figure +spy(tmp) + +tic +tmp = Ih.' * double(Mh); +toc +sol = full(tmp); +ref = I.' * double(M); +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +tmp = double(Mh) * Ih.'; +toc +sol = full(tmp); +ref = double(M) * I.'; +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +tmp = Ih * Ih.'; +toc +sol = sparse(tmp); +ref = I * I.'; +norm(ref-sol,'inf')/norm(ref,'inf') +figure +spy(tmp) + +disp(' ') + + +%%% H-Matrix inversion +disp('~~~~~~~~~~~~~ INVERSION ~~~~~~~~~~~~~') +Mh = Mh + sqrt(Nx).*speye(Nx); +M = M + sqrt(Nx).*eye(Nx,type); + +tic +tmp = inv(Mh); +toc +tic +ref = inv(M); +toc +sol = full(tmp); +norm(ref-sol,'inf')/norm(ref,'inf') +figure +spy(tmp) + +tic +tmp = inv(Ih); +toc +tic +ref = inv(I); +toc +sol = full(tmp); +norm(ref-sol,'inf')/norm(ref,'inf') +figure +spy(tmp) + +disp(' ') + + +%%% H-Matrix cholesky +disp('~~~~~~~~~~~~~ CHOLESKY FACTORISATION ~~~~~~~~~~~~~') +tic +Uh = chol(Ih); +toc +sol = sparse(Uh'*Uh); +tic +U = chol(I); +toc +sol2 = U'*U; +ref = I; +norm(ref-sol,'inf')/norm(ref,'inf') +norm(ref-sol2,'inf')/norm(ref,'inf') +figure +spy(Uh) + +disp(' ') + + +%%% H-Matrix LDLt +disp('~~~~~~~~~~~~~ LDLt FACTORISATION ~~~~~~~~~~~~~') +tic +[Lh,Dh] = ldl(Ih); +toc +sol = sparse(Lh*Dh*Lh'); +tic +[L,D,P] = ldl(I); +L = P*L; +toc +sol2 = L*D*L'; +ref = I; +norm(ref-sol,'inf')/norm(ref,'inf') +norm(ref-sol2,'inf')/norm(ref,'inf') +figure +spy(Lh) + +disp(' ') + + +%%% H-Matrix LU +disp('~~~~~~~~~~~~~ LU FACTORISATION ~~~~~~~~~~~~~') +tic +[Lh,Uh] = lu(Mh); +toc +tmp = full(Mh); +tic +[L,U] = lu(tmp); +toc +sol = full(Lh*Uh); +sol2 = L*U; +ref = M; +norm(ref-sol,'inf')/norm(ref,'inf') +norm(ref-sol2,'inf')/norm(ref,'inf') +figure +spy(Lh) +figure +spy(Uh) + +tic +[Lh,Uh] = lu(Ih); +toc +sol = full(Lh*Uh); +tic +[L,U] = lu(I); +toc +sol2 = L*U; +ref = I; +norm(ref-sol,'inf')/norm(ref,'inf') +norm(ref-sol2,'inf')/norm(ref,'inf') +figure +spy(Lh) +figure +spy(Uh) + +disp(' ') + + +%%% Shermann-morrisonn conversion +disp('~~~~~~~~~~~~~ SHERMANN MORRISON CONVERSION ~~~~~~~~~~~~~') +tic +[Sh,A,B] = hmxSherMorr(Mh); +toc +sol = full(Sh) + A*B; +ref = M; +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% H-Matrix \ +disp('~~~~~~~~~~~~~ LU SOLVER ~~~~~~~~~~~~~') +tic +sol = Mh \ V; +toc +tic +ref = M \ V; +toc +norm(ref-sol,'inf')/norm(ref,'inf') + +tic +sol = Ih \ double(V); +toc +tic +ref = I \ double(V); +toc +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% Shermann-morrisonn solver +disp('~~~~~~~~~~~~~ SHERMANN MORRISON SOLVER ~~~~~~~~~~~~~') + +tic +[Lh,Uh] = lu(Sh); +toc + +tic +rk = size(A,2); +Sm1 = Uh \ (Lh \ [A,V]); +Sm1A = Sm1(:,1:rk); +Sm1V = Sm1(:,rk+1:end); +toc + +tic +Mk = eye(rk) + B*(Sm1A); +Mkm1V = Mk \ (B * Sm1V); +toc + +tic +sol = Sm1V - Uh \ (Lh \ ( A * Mkm1V)); +toc +ref = M \ V; + +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% ITERATIVE SOLVER +disp('~~~~~~~~~~~~~ ITERATIVE SOLVER ~~~~~~~~~~~~~') +tic +sol = zeros(Nx,size(V,2),type); +for i = 1:size(V,2) + sol(:,i) = gmres(Mh,V(:,i),[],tol,100); +end +toc +ref = zeros(Nx,size(V,2),type); +for i = 1:size(V,2) + ref(:,i) = gmres(M,V(:,i),[],tol,100); +end +toc +norm(ref-sol,'inf')/norm(ref,'inf') + +disp(' ') + + +%%% END +disp('Done, thanks for use.') + diff --git a/nonRegressionTest/nrtCube.m b/nonRegressionTest/nrtCube.m new file mode 100644 index 0000000..d1f3e7a --- /dev/null +++ b/nonRegressionTest/nrtCube.m @@ -0,0 +1,246 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. You can \ \| |/ / | +%| refer to each library part each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Tetrahedron geometry and finite element validation | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openFem') +addpath('../openMsh') +addpath('../openHmx') + +% Parameters +Nvtx = 2e2; +L = [1 0.25 0.25]; +tol = 1e-3; + +%%%%%%%%%%%%%%% GEOMETRY %%%%%%%%%%%%%%% +disp('=========== GEOMETRY ============') + +% Create mesh disk +mesh = mshCube(Nvtx,L); + +% Graphical representation +plot(mesh); +axis equal; +title('Mesh representation') +xlabel('X'); ylabel('Y'); zlabel('Z'); +alpha(0.01) +hold on + +% Centers +Xctr = mesh.ctr; +meshc = msh(Xctr,(1:length(Xctr))'); +if Nvtx < 1e3 + plot(meshc,'*b') +end + +% Submeshing +Ip = find(Xctr(:,1)>0); +meshp = mesh.sub(Ip); +if Nvtx < 1e3 + plot(meshp,1) + alpha(0.2) +end + +% Faces +[fce2vtx,elt2fce] = mesh.fce; +tmp = elt2fce(Ip,:); +tmp = unique(tmp); +meshf = msh(mesh.vtx,fce2vtx(tmp,:)); +if Nvtx < 1e3 + plot(meshf,0.5) + alpha(0.1) +end + +% Edges +[edg2vtx,elt2edg] = mesh.edg; +tmp = elt2edg(Ip,:); +tmp = unique(tmp); +meshe = msh(mesh.vtx,edg2vtx(tmp,:)); +if Nvtx < 1e3 + plot(meshe,'.-r') +end + +% Free boundaries +bnd2vtx = mesh.bnd; +meshb = msh(mesh.vtx,bnd2vtx); +if Nvtx < 1e3 + plot(meshb,3) + alpha(0.3) +end + +% Surface +A = mesh.ndv; +abs(sum(A) - prod(L))/prod(L) +P = meshb.ndv; +Pref = 2*(L(1)*L(2) + L(1)*L(3) + L(2)*L(3)); +abs(sum(P) - Pref)/Pref + +% Boundary normals +pts = meshb.ctr; +vct = meshb.nrm; +if Nvtx < 1e3 + quiver3(pts(:,1),pts(:,2),pts(:,3),vct(:,1),vct(:,2),vct(:,3),'k'); +end + +% Volume quadrature +mesh.gss = 4; +[Xqud,W] = mesh.qud; +if Nvtx < 1e3 + plot3(Xqud(:,1),Xqud(:,2),Xqud(:,3),'xm') +end +abs(sum(W) - prod(L))/prod(L) + +% Surface quadrature +meshb.gss = 3; +[xqud,w] = meshb.qud; +if Nvtx < 1e3 + plot3(xqud(:,1),xqud(:,2),xqud(:,3),'xm') +% alpha(0.99) +end +abs(sum(w) - Pref)/Pref + +% Finite element dof +u = fem('P1'); +v = fem('P1'); +Xdof = v.dof(mesh); +if Nvtx < 1e3 + plot3(Xdof(:,1),Xdof(:,2),Xdof(:,3),'ob') +end + + +%%%%%%%%%%%%%%% SINGLE INTEGRATION %%%%%%%%%%%%%%% +disp('=========== SINGLE INTEGRATION ============') + +% Numerical function +Id = @(X) ones(size(X,1),1); + +%------------------------------------- + +% \int_{mesh(x)} f(x) dx +I = integral(mesh,Id); +abs(I-prod(L))/prod(L) + +%------------------------------------- + +% \int_{mesh(x)} f(x) psi(x) dx +I = integral(mesh,Id,v); +abs(sum(I,2) - prod(L))/prod(L) + +% \int_{bnd(x)} f(x) psi(x) dx +I = integral(meshb,Id,v); +P = v.sub(meshb,mesh); +I = I * P; +Pref = 2*(L(1)*L(2) + L(1)*L(3) + L(2)*L(3)); +abs(sum(I,2) - Pref)/Pref + +%------------------------------------- + +% \int_{mesh(x)} psi(x)' f(x) dx +I = integral(mesh,u,Id); +abs(sum(I,1) - prod(L))/prod(L) + +%------------------------------------- + +% \int_{mesh(x)} psi(x)' psi(x) dx +I = integral(mesh,u,v); +abs(sum(sum(I,1),2) - prod(L))/prod(L) + +% \int_{mesh(x)} grad(psi)(x)' grad(psi(x)) dx +I = integral(mesh,grad(u),grad(v)); +sum(sum(I,1),2) + +%------------------------------------- + +% \int_{mesh(x)} psi(x)' f(x) psi(x) dx +I = integral(mesh,u,Id,v); +abs(sum(sum(I,1),2) - prod(L))/prod(L) + +% \int_{mesh(x)} grad(psi(x))' f(x) grad(psi(x)) dx +I = integral(mesh,grad(u),Id,grad(v)); +sum(sum(I,1),2) + + +%%%%%%%%%%%%%%% DOUBLE INTEGRATION %%%%%%%%%%%%%%% +disp('=========== DOUBLE INTEGRATION ============') + +% Numerical function +Id = @(X,Y) (X(:,1)==Y(:,1)) .* (X(:,2)==Y(:,2)) .* (X(:,3)==Y(:,3)); + +% \int_{mesh(y)} f(x,y) psi(y) dy +I = integral(mesh.qud,mesh,Id,v); +abs(sum(sum(I,1),2) - prod(L))/prod(L) + +%------------------------------------- + +% \int_{mesh(x)} psi(x)' f(x,y) dx +I = integral(mesh,mesh.qud,u,Id); +abs(sum(sum(I,1),2) - prod(L))/prod(L) + +%------------------------------------- + +% \int_{mesh(x)} \int_{mesh(y)} psi(x)' f(x,y) psi(y) dx +I = integral(mesh,mesh,u,Id,v); + +% \int_{mesh(x)} \int_{mesh(y)} grad(psi(x))' f(x,y) grad(psi(y)) dx +I = integral(mesh,mesh,grad(u),Id,grad(v)); +sum(sum(I,1),2) + + +%%%%%%%%%%%%%%% H-MATRIX INTEGRATION %%%%%%%%%%%%%%% +disp('=========== H-MATRIX INTEGRATION ============') + +% Numerical function +G = @(X,Y) 1./(4*pi) * femGreenKernel(X,Y,'[exp(ikr)/r]',5); + +% \int_{mesh(y)} G(x,y) psi(y) dy +sol = integral(mesh.ctr,mesh,G,v,tol); +ref = integral(mesh.ctr,mesh,G,v); +norm(full(sol)-ref)./norm(ref) + +%------------------------------------- + +% \int_{mesh(x)} psi(x)' G(x,y) dx +sol = integral(mesh,mesh.ctr,u,G,tol); +ref = integral(mesh,mesh.ctr,u,G); +norm(full(sol)-ref)./norm(ref) + +%------------------------------------- + +% \int_{mesh(x)} \int_{mesh(y)} psi(x)' G(x,y) psi(y) dx dy +sol = integral(mesh,mesh,u,G,v,tol); +ref = integral(mesh,mesh,u,G,v); +norm(full(sol)-ref)./norm(ref) + +% \int_{d_mesh(x)} \int_{d_mesh(y)} grad(psi(x))' G(x,y) grad(psi(y)) dx +sol = integral(meshb,meshb,nxgrad(u),G,nxgrad(v),tol); +ref = integral(meshb,meshb,nxgrad(u),G,nxgrad(v)); +norm(full(sol)-ref)./norm(ref) + + +disp('Done, thanks for use.') + + + diff --git a/nonRegressionTest/nrtDisk.m b/nonRegressionTest/nrtDisk.m new file mode 100644 index 0000000..830cb49 --- /dev/null +++ b/nonRegressionTest/nrtDisk.m @@ -0,0 +1,250 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. You can \ \| |/ / | +%| refer to each library part each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Triangles geometry and finite element validation | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openFem') +addpath('../openMsh') +addpath('../openHmx') + +% Parameters +Nvtx = 1e2; +tol = 1e-3; + + +%%%%%%%%%%%%%%% GEOMETRY %%%%%%%%%%%%%%% +disp('=========== GEOMETRY ============') + +% Create mesh disk +mesh = mshDisk(Nvtx,1); + +% Graphical representation +plot(mesh); +axis equal; +title('Mesh representation') +xlabel('X'); ylabel('Y'); zlabel('Z'); +alpha(0.99) +hold on + +% Centers +Xctr = mesh.ctr; +meshc = msh(Xctr,(1:length(Xctr))'); +if Nvtx < 1e3 + plot(meshc,'*b') +end + +% Submeshing +Ip = find(sum(Xctr>0,2)==2); +meshp = mesh.sub(Ip); +if Nvtx < 1e3 + plot(meshp,1) + alpha(0.5) +end + +% Edges +[edg2vtx,elt2edg] = mesh.edg; +tmp = elt2edg(Ip,:); +tmp = unique(tmp); +meshe = msh(mesh.vtx,edg2vtx(tmp,:)); +if Nvtx < 1e3 + plot(meshe,'.-r') +end + +% Free boundaries +bnd2vtx = mesh.bnd; +meshb = msh(mesh.vtx,bnd2vtx); +if Nvtx < 1e3 + plot(meshb,'o-b') +end + +% Surface +A = mesh.ndv; +abs(sum(A) - pi)/pi +P = meshb.ndv; +abs(sum(P) - 2*pi)/(2*pi) + +% Normals +pts = mesh.ctr; +vct = mesh.nrm; +if Nvtx < 1e3 + quiver3(pts(:,1),pts(:,2),pts(:,3),vct(:,1),vct(:,2),vct(:,3),'k'); +end + +% Edges normals +Nu = mesh.nrmEdg; +if Nvtx < 1e3 + for i = 1:3 + pts = mesh.vtx(mesh.elt(Ip,i),:); + vct = Nu{i}(Ip,:); + quiver3(pts(:,1),pts(:,2),pts(:,3),vct(:,1),vct(:,2),vct(:,3),'g'); + end +end + +% Surface quadrature +mesh.gss = 3; +[Xqud,W] = mesh.qud; +if Nvtx < 1e3 + plot3(Xqud(:,1),Xqud(:,2),Xqud(:,3),'xm') + alpha(0.99) +end +abs(sum(W) - pi)/pi + +% Circum quadrature +meshb.gss = 1; +[xqud,w] = meshb.qud; +if Nvtx < 1e3 + plot3(xqud(:,1),xqud(:,2),xqud(:,3),'xm') + alpha(0.99) +end +abs(sum(w) - 2*pi)/(2*pi) + +% Quadrature normals +pts = Xqud; +vct = mesh.nrmQud; +if Nvtx < 1e3 + quiver3(pts(:,1),pts(:,2),pts(:,3),vct(:,1),vct(:,2),vct(:,3),'m'); +end + +% Finite element dof +u = fem('P1'); +v = fem('P1'); +Xdof = v.dof(mesh); +if Nvtx < 1e3 + plot3(Xdof(:,1),Xdof(:,2),Xdof(:,3),'ob') +end + + +%%%%%%%%%%%%%%% SINGLE INTEGRATION %%%%%%%%%%%%%%% +disp('=========== SINGLE INTEGRATION ============') + +% Numerical function +Id = @(X) ones(size(X,1),1); + +%------------------------------------- + +% \int_{mesh(x)} f(x) dx +I = integral(mesh,Id); +abs(I-pi)/pi + +%------------------------------------- + +% \int_{mesh(x)} f(x) psi(x) dx +I = integral(mesh,Id,v); +abs(sum(I,2) - pi)/pi + +% \int_{bnd(x)} f(x) psi(x) dx +I = integral(meshb,Id,v); +P = v.sub(meshb,mesh); +I = I * P; +abs(sum(I,2) - 2*pi)/(2*pi) + +%------------------------------------- + +% \int_{mesh(x)} psi(x)' f(x) dx +I = integral(mesh,u,Id); +abs(sum(I,1) - pi)/pi + +%------------------------------------- + +% \int_{mesh(x)} psi(x)' psi(x) dx +I = integral(mesh,u,v); +abs(sum(sum(I,1),2) - pi)/pi + +% \int_{mesh(x)} grad(psi)(x)' grad(psi(x)) dx +I = integral(mesh,grad(u),grad(v)); +sum(sum(I,1),2) + +%------------------------------------- + +% \int_{mesh(x)} psi(x)' f(x) psi(x) dx +I = integral(mesh,u,Id,v); +abs(sum(sum(I,1),2) - pi)/pi + +% \int_{mesh(x)} grad(psi(x))' f(x) grad(psi(x)) dx +I = integral(mesh,grad(u),Id,grad(v)); +sum(sum(I,1),2) + + +%%%%%%%%%%%%%%% DOUBLE INTEGRATION %%%%%%%%%%%%%%% +disp('=========== DOUBLE INTEGRATION ============') + +% Numerical function +Id = @(X,Y) (X(:,1)==Y(:,1)) .* (X(:,2)==Y(:,2)) ; + +% \int_{mesh(y)} f(x,y) psi(y) dy +I = integral(mesh.qud,mesh,Id,v); +abs(sum(sum(I,1),2) - pi)/pi + +%------------------------------------- + +% \int_{mesh(x)} psi(x)' f(x,y) dx +I = integral(mesh,mesh.qud,u,Id); +abs(sum(sum(I,1),2) - pi)/pi + +%------------------------------------- + +% \int_{mesh(x)} \int_{mesh(y)} psi(x)' f(x,y) psi(y) dx +I = integral(mesh,mesh,u,Id,v); + +% \int_{mesh(x)} \int_{mesh(y)} grad(psi(x))' f(x,y) grad(psi(y)) dx +I = integral(mesh,mesh,grad(u),Id,grad(v)); +sum(sum(I,1),2) + + +%%%%%%%%%%%%%%% H-MATRIX INTEGRATION %%%%%%%%%%%%%%% +disp('=========== H-MATRIX INTEGRATION ============') + +% Numerical function +G = @(X,Y) 1./(4*pi) * femGreenKernel(X,Y,'[exp(ikr)/r]',5); + +% \int_{mesh(y)} G(x,y) psi(y) dy +sol = integral(mesh.ctr,mesh,G,v,tol); +ref = integral(mesh.ctr,mesh,G,v); +norm(full(sol)-ref)./norm(ref) + +%------------------------------------- + +% \int_{mesh(x)} psi(x)' G(x,y) dx +sol = integral(mesh,mesh.ctr,u,G,tol); +ref = integral(mesh,mesh.ctr,u,G); +norm(full(sol)-ref)./norm(ref) + +%------------------------------------- + +% \int_{mesh(x)} \int_{mesh(y)} psi(x)' G(x,y) psi(y) dx dy +sol = integral(mesh,mesh,u,G,v,tol); +ref = integral(mesh,mesh,u,G,v); +norm(full(sol)-ref)./norm(ref) + +% \int_{mesh(x)} \int_{mesh(y)} grad(psi(x))' G(x,y) grad(psi(y)) dx +sol = integral(mesh,mesh,nxgrad(u),G,nxgrad(v),tol); +ref = integral(mesh,mesh,nxgrad(u),G,nxgrad(v)); +norm(full(sol)-ref)./norm(ref) + + +disp('Done, thanks for use.') + + diff --git a/nonRegressionTest/nrtFemConvergence.m b/nonRegressionTest/nrtFemConvergence.m new file mode 100644 index 0000000..ecfa76a --- /dev/null +++ b/nonRegressionTest/nrtFemConvergence.m @@ -0,0 +1,85 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. You can \ \| |/ / | +%| refer to each library part each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : François Alouges - CMAP, Ecole polytechnique | +%| Creation : 06.07.17 | +%| Last modif : 06.07.17 | +%| Synopsis : Test of the finite element method | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openFem') +addpath('../openHmx') +addpath('../openMsh') + +errL2P1 = []; errH1P1 = errL2P1; errL2P2 = []; errH1P2 = errL2P2; h = []; +Uex = @(x) cos(x(:,1)).*cos(x(:,2))/3; +f = @(x) cos(x(:,1)).*cos(x(:,2)); + + +for nbPts=10:3:80 + % Square mesh + Omega = mshSquare(nbPts^2,[2*pi 2*pi]); + Omega.gss = 7; + h = [h, 2*pi/nbPts]; + %plot(Omega); + + + %%% SOLVE LINEAR PROBLEM + disp('~~~~~~~~~~~~~ SOLVE LINEAR PROBLEM ~~~~~~~~~~~~~') + + + % Finite elements + u = fem('P1'); v = fem('P1'); + u2 = fem('P2'); v2 = fem('P2'); + + % Matrix and RHS + K = integral(Omega,grad(u),grad(v)) + integral(Omega,u,v); + K2 = integral(Omega,grad(u2),grad(v2)) + integral(Omega,u2,v2); + F = integral(Omega, v, f); + F2 = integral(Omega, v2, f); + + % Résolution + uh = K\F; + uh2 = K2\F2; + + % erreur en norme L2 et H1 + errL2P1 = [errL2P1, u.diff(Omega, uh, Uex, 'L2')]; + errH1P1 = [errH1P1, u.diff(Omega, uh, Uex, 'H1')]; + errL2P2 = [errL2P2, u2.diff(Omega, uh2, Uex, 'L2')]; + errH1P2 = [errH1P2, u2.diff(Omega, uh2, Uex, 'H1')]; +end + +% Plot the error graphs +figure(2) +subplot(1,2,1) +loglog(h,errL2P1,'b+-',h,errL2P2,'r+-',h,(h*10^-0.5).^2,'k--',h,(h*10^-0.5).^3,'k:') +legend('EF P1', 'EF P2','slope 2','slope 3') +title('error L2, CB Neumann') + +xlabel('h') +subplot(1,2,2) +loglog(h,errH1P1,'b+-',h,errH1P2,'r+-',h,h,'k',h,(h*10^-0.5).^2,'k--') +legend('EF P1', 'EF P2','slope 1','slope 2') +title('error H1, CB Neumann') +xlabel('h') + +disp('Done.') \ No newline at end of file diff --git a/nonRegressionTest/nrtSparseLU.m b/nonRegressionTest/nrtSparseLU.m new file mode 100644 index 0000000..bc464c6 --- /dev/null +++ b/nonRegressionTest/nrtSparseLU.m @@ -0,0 +1,105 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. You can \ \| |/ / | +%| refer to each library part each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Comparse sparse LU with H-Matrix sparse LU | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openFem') +addpath('../openHmx') +addpath('../openMsh') + +% Parameters +Nvtx = 1e4; +L = [1 0.1 0.1]; + +% Cube mesh +mesh = mshCube(Nvtx,L); +mesh.gss = 4; + +% Graphical representation +plot(mesh); +axis equal; +title('Mesh representation') +xlabel('X'); ylabel('Y'); zlabel('Z'); +alpha(0.1) +hold on + +% Finites elements +u = fem('P1'); +v = fem('P1'); + +% Random vector at dof +V = rand(size(v.dof(mesh),1),1); + +% Mass matrix +tic +M = integral(mesh,u,v); +toc +ref = M * V; +figure +spy(M) +drawnow + +% LU factorisation +tic +[L,U] = lu(M); +toc +norm(L*(U*V) - ref)/norm(ref) +figure +spy(L) + +% H-Matrix +tic +Mh = hmx(u.dof(mesh),v.dof(mesh),M,1e-12); +toc +norm(Mh*V - ref)/norm(ref) +figure +spy(Mh) + +% LhUh factorisation +tic +[Lh,Uh] = lu(Mh); +toc +norm(Lh*(Uh*V) - ref)/norm(ref) +figure +spy(Lh) +drawnow + +% Solver +tic +Mm1V = U \ (L \ V); +toc +tic +Mhm1V = Uh \ (Lh \ V); +toc +tic +ref = M \ V; +toc +norm(Mm1V - ref)/norm(ref) +norm(Mhm1V - ref)/norm(ref) + +whos + + diff --git a/openFem/fem.m b/openFem/fem.m new file mode 100644 index 0000000..677f2ff --- /dev/null +++ b/openFem/fem.m @@ -0,0 +1,107 @@ +classdef fem +%+========================================================================+ +%| | +%| OPENFEM, FINITE AND BOUNDARY ELEMENT | +%| openFem is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openFem, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Finite element class definition | +%+========================================================================+ + +properties + typ = []; % FINITE ELEMENT TYPE (P0, P1) + opr = []; % OPERATOR APPLED TO FINITE ELEMENT +end + +methods + % CONSTRUCTOR + function fe = fem(str) + fe.typ = str; + fe.opr = '[psi]'; + end + + % GRADIENT OF THE BASIS FUNCTION + function fe = grad(varargin) + fe = varargin{1}; + if (nargin == 1) + fe.opr = 'grad[psi]'; + else + fe.opr = ['grad[psi]',num2str(varargin{2})]; + end + end + + % NORMAL DOT BASIS FUNCTION + function fe = ndot(varargin) + fe = varargin{1}; + if (nargin == 1) + fe.opr = 'n*[psi]'; + else + fe.opr = ['n*[psi]',num2str(varargin{2})]; + end + end + + % NORMAL CROSS GRADIENT OF THE BASIS FUNCTION + function fe = nxgrad(varargin) + fe = varargin{1}; + if (nargin == 1) + fe.opr = 'nxgrad[psi]'; + else + fe.opr = ['nxgrad[psi]',num2str(varargin{2})]; + end + end + + % DEGREES OF FREEDOM + function [X,elt2dof] = dof(fe,mesh) + [X,elt2dof] = femDof(fe,mesh); + end + + % L2 AND H1 ERRORS + function err = diff(fe, mesh, sol, ref, type ) + err = femDiff(fe, mesh, sol, ref, type ); + end + + % DOF TO QUADRATURE MATRIX + function M = dqm(fe,mesh) + if strcmp(fe.typ(1),'P') + M = femLagrangePn(fe,mesh); + else + erro('fem.m : unavailable case') + end + end + + % NUMERICAL REGULARIZAION + function S = regularize(varargin) + S = femRegularize(varargin); + end + + % SUBDOMAIN TRANSFERT MATRIX + function M = sub(u,mesh1,mesh2) + dof1 = u.dof(mesh1); + dof2 = u.dof(mesh2); + [~,I1,I2] = intersect(dof1,dof2,'rows'); + M = sparse(I1,I2,1,size(dof1,1),size(dof2,1)); + end + + % DIRICHLET ELIMINATION MATRIX + function M = dir(u,mesh1,mesh2) + dof1 = u.dof(mesh1); + dof2 = u.dof(mesh2); + [~,nodir] = setdiff(dof1,dof2,'rows'); + M = sparse(nodir,1:length(nodir),1,size(dof1,1),length(nodir)); + end +end +end diff --git a/openFem/femDiff.m b/openFem/femDiff.m new file mode 100644 index 0000000..e0d8bb9 --- /dev/null +++ b/openFem/femDiff.m @@ -0,0 +1,60 @@ +function err = femDiff(fe, mesh, Uh, Uex, type ) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openFem, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : François Alouges - CMAP, Ecole polytechnique | +%| Creation : 06.07.17 | +%| Last modif : 06.07.17 | +%| Synopsis : L2 and H1 errors | +%+========================================================================+ + +% Mesh integration data +[X,Wx] = mesh.qud; + +% Finite element matrix +Mu = fe.dqm(mesh); + +% Function to be applied +Uexact = Uex(X); +if (size(Uexact,2) > 1) + error('mshIntegral.m : unavailable case') +end + +Uapp = Mu * Uh; +switch type + case 'L2' + err = sqrt(sum(Wx.*(Uexact-Uapp).^2)); + case 'H1' + eps = 1e-6; + gradef = grad(fe); + Gu = gradef.dqm(mesh); + DxUapp = Gu{1} * Uh; + DyUapp = Gu{2} * Uh; + DzUapp = Gu{3} * Uh; + n1 = size(X,1); + eps1 = eps*ones(n1,1)*[1,0,0]; + eps2 = eps*ones(n1,1)*[0,1,0]; + eps3 = eps*ones(n1,1)*[0,0,1]; + DxUexact = (Uex(X+eps1)-Uex(X-eps1))/(2*eps); + DyUexact = (Uex(X+eps2)-Uex(X-eps2))/(2*eps); + DzUexact = (Uex(X+eps3)-Uex(X-eps3))/(2*eps); + err = sqrt(sum(Wx.*((Uexact-Uapp).^2+(DxUexact-DxUapp).^2+(DyUexact-DyUapp).^2+(DzUexact-DzUapp).^2))); + otherwise + error('Unknown error type. Known types are ''L2'' or ''H1''.'); +end +end + diff --git a/openFem/femDof.m b/openFem/femDof.m new file mode 100644 index 0000000..61163c4 --- /dev/null +++ b/openFem/femDof.m @@ -0,0 +1,46 @@ +function [X,elt2dof] = femDof(fe,mesh) +%+========================================================================+ +%| | +%| OPENFEM, FINITE AND BOUNDARY ELEMENT | +%| openFem is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openFem, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| François Alouges - CMAP, Ecole Polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Define degrees of freedom | +%+========================================================================+ + +% Lagrange order 0, constant by element +if strcmp(fe.typ,'P0') + X = mesh.ctr; + elt2dof = (1:size(mesh.elt,1))'; + +% Lagrange order 1, piecewise linear by element +elseif strcmp(fe.typ,'P1') + X = mesh.vtx; + elt2dof = mesh.elt; + +% Lagrange order 2, piecewise quadratic by element +elseif strcmp(fe.typ,'P2') + [edg2vtx,elt2edg] = mesh.edg; + X = [mesh.vtx ; 0.5.*(mesh.vtx(edg2vtx(:,1),:)+mesh.vtx(edg2vtx(:,2),:))]; + elt2dof = [mesh.elt , elt2edg + size(mesh.vtx,1)]; + +% Others +else + error('femDof.m : unavailable case') +end +end diff --git a/openFem/femGreenKernel.m b/openFem/femGreenKernel.m new file mode 100644 index 0000000..092cbc8 --- /dev/null +++ b/openFem/femGreenKernel.m @@ -0,0 +1,91 @@ +function Gxy = femGreenKernel(X,Y,green,k) +%+========================================================================+ +%| | +%| OPENFEM, FINITE AND BOUNDARY ELEMENT | +%| openFem is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openFem, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Classical green kernel function | +%+========================================================================+ + +% Security +if (size(X,2) ~= 3) || (size(Y,2) ~= 3) + error('femGreenKernel.m : unavailable case') +end +if isempty(k) + k = 0; +end + +% Distances between particles +Rxy = sqrt( ... + (X(:,1) - Y(:,1)).^2 + ... + (X(:,2) - Y(:,2)).^2 + ... + (X(:,3) - Y(:,3)).^2 ); + +% For empty wave-number +if isempty(k) + k = 0; +end + +% Green kernel definition +if strcmp(green,'[1/r]') + Gxy = 1./Rxy; + +elseif strcmp(green,'[exp(ikr)/r]') + Gxy = exp(1i*k*Rxy)./Rxy; + +elseif strcmp(green(1:end-1),'gradx[1/r]') + j = str2double(green(end)); + Gxy = - (X(:,j)-Y(:,j)) ./ (Rxy.^3); + +elseif strcmp(green(1:end-1),'grady[1/r]') + j = str2double(green(end)); + Gxy = (X(:,j)-Y(:,j)) ./ (Rxy.^3); + +elseif strcmp(green(1:end-1),'gradx[exp(ikr)/r]') + j = str2double(green(end)); + Gxy = (1i*k - 1./Rxy) .* exp(1i*k.*Rxy) .* ... + (X(:,j)-Y(:,j)) ./ (Rxy.^2); + +elseif strcmp(green(1:end-1),'grady[exp(ikr)/r]') + j = str2double(green(end)); + Gxy = - (1i*k - 1./Rxy) .* exp(1i*k.*Rxy) .* ... + (X(:,j)-Y(:,j)) ./ (Rxy.^2); + +elseif strcmp(green(1:end-2),'[ij/r+rirj/r^3]') + i = str2double(green(end-1)); + j = str2double(green(end)); + Gxy = (i==j)./Rxy + (X(:,i)-Y(:,i)).*(X(:,j)-Y(:,j))./(Rxy.^3); + +elseif strcmp(green(1:end-3),'[rirjrk/r^5]') + i = str2double(green(end-2)); + j = str2double(green(end-1)); + k = str2double(green(end)); + Gxy = (X(:,i)-Y(:,i)).*(X(:,j)-Y(:,j)).*(X(:,k)-Y(:,k))./(Rxy.^5); + +else + error('Error in hmxGreenKernel.m : unknown green kernel') +end + +% Singularity +if strcmp(green,'[exp(ikr)/r]') + Gxy(Rxy<1e-6) = 0 + 1i*k; +else + Gxy(Rxy<1e-6) = 0; +end + +end diff --git a/openFem/femHmatrix.m b/openFem/femHmatrix.m new file mode 100644 index 0000000..45c77bf --- /dev/null +++ b/openFem/femHmatrix.m @@ -0,0 +1,170 @@ +function Mh = femHmatrix(Xdof,Ydof,Mx,X,green,Y,My,tol) +%+========================================================================+ +%| | +%| OPENFEM, FINITE AND BOUNDARY ELEMENT | +%| openFem is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openFem, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Finite element builder with H-matrix | +%+========================================================================+ + +% Initialisation +Mh = hmx(size(Xdof,1),size(Ydof,1),tol); + +% Rectangular box for Xdof +Xmin = min(Xdof,[],1); +Xmax = max(Xdof,[],1); +Xctr = 0.5*(Xmin+Xmax); +Xdgl = Xmax-Xmin; + +% Rectangular box for Ydof +Ymin = min(Ydof,[],1); +Ymax = max(Ydof,[],1); +Yctr = 0.5*(Ymin+Ymax); +Ydgl = Ymax-Ymin; + +% Compression for separated boxes +if sum( abs(Yctr-Xctr) > max(Xdgl+Ydgl) ) + Mh.typ = 1; + +% Full computation for small box (stopping criterion) +elseif sum(Mh.dim < 100) + Mh.typ = 2; + +% H-Matrix (recursion) +else + Mh.typ = 0; +end + +% H-Matrix (recursion) +if (Mh.typ == 0) + % Subdivision for Xdof + ind = hmxSubdivide(Xdof); + Mh.row = {find(ind),find(ind),find(~ind),find(~ind)}; + + % Subdivision for Ydof + ind = hmxSubdivide(Ydof); + Mh.col = {find(ind),find(~ind),find(ind),find(~ind)}; + + % Single class + if isa(Xdof,'single') + for i = 1:4 + Mh.row{i} = single(Mh.row{i}); + Mh.col{i} = single(Mh.col{i}); + end + end + + % H-Matrix (recursion) + for i = 1:4 + % Dof indices + Ir = Mh.row{i}; + Ic = Mh.col{i}; + + % Quadrature indices + if iscell(Mx) && iscell(My) + Vx = 0; + Vy = 0; + for j = 1:3 + Vx = Vx + Mx{j}(:,Ir) * (1+rand(length(Ir),1)); + Vy = Vy + My{j}(:,Ic) * (1+rand(length(Ic),1)); + end + else + Vx = Mx(:,Ir) * (1+rand(length(Ir),1)); + Vy = My(:,Ic) * (1+rand(length(Ic),1)); + end + Ix = find(Vx); + Iy = find(Vy); + + % Security for empty matrix + if (size(Ix,1) == 0) + Ix = 1; + end + if (size(Iy,1) == 0) + Iy = 1; + end + + % Matrix subdivision + if iscell(Mx) && iscell(My) + Mxchd = cell(1,3); + Mychd = cell(1,3); + for j = 1:3 + Mxchd{j} = Mx{j}(Ix,Ir); + Mychd{j} = My{j}(Iy,Ic); + end + else + Mxchd = Mx(Ix,Ir); + Mychd = My(Iy,Ic); + end + + % Recursion + Mh.chd{i} = femHmatrix(Xdof(Ir,:),Ydof(Ic,:),... + Mxchd,X(Ix,:),green,Y(Iy,:),Mychd,tol); + end + + % Fusion + Mh = hmxFusion(Mh); + + +% Compressed leaf +elseif (Mh.typ == 1) + % ACA with partial pivoting + [A,B,flag] = hmxACA(X,Y,green,tol); + + % Update + if flag + if iscell(Mx) && iscell(My) + A = [Mx{1}'*A , Mx{2}'*A , Mx{3}'*A]; + B = [B*My{1} ; B*My{2} ; B*My{3} ]; + [A,B] = hmxQRSVD(A,B,tol); + else + A = Mx' * A; + B = B * My; + end + Mh.dat{1} = A; + Mh.dat{2} = B; + else + Mh.typ = 2; + end +end + + +% Full leaf +if (Mh.typ == 2) + % Quadrature matrix + [I,J] = ndgrid(1:size(X,1),1:size(Y,1)); + Gxy = green(X(I(:),:),Y(J(:),:)); + Gxy = reshape(Gxy,size(X,1),size(Y,1)); + + % Matrix integration + if iscell(Mx) && iscell(My) + Mh.dat = 0; + for i = 1:3 + Mh.dat = Mh.dat + Mx{i}' * Gxy * My{i}; + end + else + Mh.dat = Mx' * Gxy * My; + end + + % Full matrix recompression + rkMax = ceil(sqrt(min(Mh.dim))-log(Mh.tol)); + [A,B,flag] = hmxRSVD(Mh.dat,Mh.tol,rkMax); + if flag + Mh.dat = {A,B}; + Mh.typ = 1; + end +end +end diff --git a/openFem/femHmatrixParallel.m b/openFem/femHmatrixParallel.m new file mode 100644 index 0000000..d63d036 --- /dev/null +++ b/openFem/femHmatrixParallel.m @@ -0,0 +1,214 @@ +function [Mh,leaf] = femHmatrixParallel(varargin) +%+========================================================================+ +%| | +%| OPENFEM, FINITE AND BOUNDARY ELEMENT | +%| openFem is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openFem, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Paralelization of H-matrix finite element builder | +%+========================================================================+ + +% Fixed input +Xdof = varargin{1}; +Ydof = varargin{2}; +Mx = varargin{3}; +X = varargin{4}; +green = varargin{5}; +Y = varargin{6}; +My = varargin{7}; +tol = varargin{8}; + +% Variable input +if (length(varargin) == 8) + leaf = []; + Nsub = 1; +else + leaf = varargin{9}; + Nsub = varargin{10}; +end + +% Initialisation +Mh = hmx(size(Xdof,1),size(Ydof,1),tol); +Ileaf = Composite(); + +% Cores availables for computation +Nlabs = max(1,length(Ileaf)); + +% Security check +if (floor(log2(Nlabs)) ~= log2(Nlabs)) + error('femHmatrixParallel.m : number of pool labs have to be multiple of 2') +end + +% H-Matrix (recursion) +if (Nlabs >= 2*Nsub) + % Subdivision for Xdof + ind = hmxSubdivide(Xdof); + Mh.row = {find(ind),find(ind),find(~ind),find(~ind)}; + + % Subdivision for Ydof + ind = hmxSubdivide(Ydof); + Mh.col = {find(ind),find(~ind),find(ind),find(~ind)}; + + % Single class + if isa(Xdof,'single') + for i = 1:4 + Mh.row{i} = single(Mh.row{i}); + Mh.col{i} = single(Mh.col{i}); + end + end + + % H-Matrix (recursion) + for i = 1:4 + % Dof indices + Ir = Mh.row{i}; + Ic = Mh.col{i}; + + % Quadrature indices + if iscell(Mx) && iscell(My) + Vx = 0; + Vy = 0; + for j = 1:3 + Vx = Vx + Mx{j}(:,Ir) * (1+rand(length(Ir),1)); + Vy = Vy + My{j}(:,Ic) * (1+rand(length(Ic),1)); + end + else + Vx = Mx(:,Ir) * (1+rand(length(Ir),1)); + Vy = My(:,Ic) * (1+rand(length(Ic),1)); + end + Ix = find(Vx); + Iy = find(Vy); + + % Matrix subdivision + if iscell(Mx) && iscell(My) + Mxchd = cell(1,3); + Mychd = cell(1,3); + for j = 1:3 + Mxchd{j} = Mx{j}(Ix,Ir); + Mychd{j} = My{j}(Iy,Ic); + end + else + Mxchd = Mx(Ix,Ir); + Mychd = My(Iy,Ic); + end + + % Recursion + [Mh.chd{i},leaf] = femHmatrixParallel(Xdof(Ir,:),Ydof(Ic,:),... + Mxchd,X(Ix,:),green,Y(Iy,:),Mychd,tol,leaf,2*Nsub); + end + + % Leaves types + Mh.typ = 0; + +% Computation data +else + Mh.typ = -1; + ind = size(leaf,1) + 1; + leaf{ind,1} = Xdof; + leaf{ind,2} = Ydof; + leaf{ind,3} = Mx; + leaf{ind,4} = X; + leaf{ind,5} = Y; + leaf{ind,6} = My; +end + +% Computation +if Nsub == 1 + % No paralelism + if Nlabs == 1 + Mh = femHmatrix(leaf{1}, leaf{2}, leaf{3}, leaf{4}, ... + green,leaf{5},leaf{6},tol); + + % Parallelism + elseif (size(leaf,1) == Nlabs^2) + % Distances beetween boxes + dst = zeros(Nlabs^2,1); + for i = 1:length(leaf) + Xctr = 0.5 * (min(leaf{i,1},[],1) + max(leaf{i,1},[],1)); + Yctr = 0.5 * (min(leaf{i,2},[],1) + max(leaf{i,2},[],1)); + dst(i) = sqrt(sum((Yctr-Xctr).^2, 2)); + end + + % Sorted interactions + [~,I] = sort(dst); + + % Loop on workers + for i = 1:Nlabs + % Clock + tps = hmxClock(); + + % Optimal repartition + spmd + ind = I((i-1)*Nlabs + labindex); + tmp = femHmatrix(leaf{ind,1}, leaf{ind,2}, ... + leaf{ind,3}, leaf{ind,4}, green, ... + leaf{ind,5}, leaf{ind,6}, tol); + end + + % H-Matrix distribution + for j = 1:Nlabs + Mh = hmxDistribution(Mh,tmp{j},ind{j},log2(Nlabs),1); + end + + % Informations + disp([' ~~> Step ',num2str(i)', ' - Elapsed time is ', ... + num2str(hmxClock()-tps),' seconds.']) + + % Clean composite + clear tmp; + end + + % Problem + else + error('femHmatrixParallel.m : unavailable case.'); + end +end +end + + +function [Mh,num] = hmxDistribution(Mh,Mp,ind,stp,num) +% H-Matrix (recursion) +if stp && (Mh.typ == 0) + % Recursion + for i = 1:4 + [Mh.chd{i},num] = hmxDistribution(Mh.chd{i},Mp,ind,stp-1,num); + end + + % Fusion + Mh = hmxFusion(Mh); + +% Fusioned leaf +elseif stp + num = num + 4^stp; + +% Leaf +else + if (num == ind) + if (Mh.typ == -1) + Mh = Mp; + else + error('femHmatrixParallel.m : unavailable case.'); + end + end + num = num + 1; +end +end + + +function tps = hmxClock() +tps = clock; +tps = tps(4)*3600 + tps(5)*60 + tps(6); +end diff --git a/openFem/femLagrangePn.m b/openFem/femLagrangePn.m new file mode 100644 index 0000000..d8b2083 --- /dev/null +++ b/openFem/femLagrangePn.m @@ -0,0 +1,437 @@ +function M = femLagrangePn(fe,mesh) +%+========================================================================+ +%| | +%| OPENFEM, FINITE AND BOUNDARY ELEMENT | +%| openFem is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openFem, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| François Alouges - CMAP, Ecole Polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Finite element matrices | +%+========================================================================+ + +%%% FINITE ELEMENT MATRIX AND GRADIENT +if strcmp(fe.opr,'[psi]') || strcmp(fe.opr,'grad[psi]') + % Gaussian quadrature + x = mshReference(mesh); + [Xqud,~,elt2qud] = mesh.qud; + + % Degrees of freedom + [Xdof,elt2dof] = fe.dof(mesh); + + % Dimensions + Nelt = size(mesh.elt,1); + Nqud = size(Xqud,1); + Ngss = size(elt2qud,2); + Ndof = size(Xdof,1); + Nbas = size(elt2dof,2); + + % Basis fct constant per elements + if strcmp(fe.typ,'P0') + % Edge mesh + if (size(mesh.elt,2) == 2) + F = ones(1,Ngss); + dxF = zeros(1,Ngss); + + % Triangular mesh + elseif (size(mesh.elt,2) == 3) + F = ones(1,Ngss); + dxF = zeros(1,Ngss); + dyF = zeros(1,Ngss); + + % Tetrahedron mesh + elseif (size(mesh.elt,2) == 4) + F = ones(1,Ngss); + dxF = zeros(1,Ngss); + dyF = zeros(1,Ngss); + dzF = zeros(1,Ngss); + + else + error('femLagrangePn.m : unavailable case') + end + + % Basis fct piecewise linear per element + elseif strcmp(fe.typ,'P1') + % Initialization + F = zeros(size(mesh.elt,2),Ngss); + dxF = zeros(size(mesh.elt,2),Ngss); + dyF = zeros(size(mesh.elt,2),Ngss); + dzF = zeros(size(mesh.elt,2),Ngss) ; + + % Edge mesh + if (size(mesh.elt,2) == 2) + F(1,:) = 1 - x(:,1); + F(2,:) = x(:,1); + + dxF(1,:) = - 1; + dxF(2,:) = 1; + + % Triangular mesh + elseif (size(mesh.elt,2) == 3) + F(1,:) = 1 - x(:,1) - x(:,2); + F(2,:) = x(:,1); + F(3,:) = x(:,2); + + dxF(1,:) = - 1; + dxF(2,:) = 1; + + dyF(1,:) = - 1; + dyF(3,:) = 1; + + % Tetrahedron mesh + elseif (size(mesh.elt,2) == 4) + F(1,:) = 1 - x(:,1) - x(:,2) - x(:,3); + F(2,:) = x(:,1); + F(3,:) = x(:,2); + F(4,:) = x(:,3); + + dxF(1,:) = - 1; + dxF(2,:) = 1; + + dyF(1,:) = - 1; + dyF(3,:) = 1; + + dzF(1,:) = - 1; + dzF(4,:) = 1; + + else + error('femLagrangePn.m : unavailable case') + end + + % Lagrange order 2, piecewise quadratic by element + elseif strcmp(fe.typ,'P2') + % Edge mesh + if (size(mesh.elt,2) == 2) + % Initialization + F = zeros(3,Ngss); + dxF = zeros(3,Ngss); + dyF = zeros(3,Ngss); + dzF = zeros(3,Ngss); + X = x(:,1); + + F(1,:) = (1 - X).*(1 - 2*X); + F(2,:) = X.*(2*X - 1); + F(3,:) = X.*(1 - X); + + dxF(1,:) = 4*X - 3; + dxF(2,:) = 4*X - 1; + dxF(3,:) = 2*X - 1; + + % Triangular mesh + elseif (size(mesh.elt,2) == 3) + % Initialization + F = zeros(6,Ngss); + dxF = zeros(6,Ngss); + dyF = zeros(6,Ngss); + dzF = zeros(6,Ngss); + X = x(:,1); + Y = x(:,2); + + F(1,:) = (1 - X - Y).*(1 - 2*X - 2*Y); + F(2,:) = X.*(2*X - 1); + F(3,:) = Y.*(2*Y - 1); + F(4,:) = 4*X.*(1 - X - Y); + F(5,:) = 4*X.*Y; + F(6,:) = 4*Y.*(1 - X - Y); + + dxF(1,:) = -3 + 4*(X + Y); + dxF(2,:) = 4*X - 1; + dxF(4,:) = 4*(1 - 2*X - Y); + dxF(5,:) = 4*Y; + dxF(6,:) = -4*Y; + + dyF(1,:) = -3 + 4*(X + Y); + dyF(3,:) = 4*Y - 1; + dyF(4,:) = -4*X; + dyF(5,:) = 4*X; + dyF(6,:) = 4*(1 - X - 2*Y); + + % Tetrahedron mesh + elseif (size(mesh.elt,2) == 4) + % Initialization + F = zeros(10,Ngss); + dxF = zeros(10,Ngss); + dyF = zeros(10,Ngss); + dzF = zeros(10,Ngss); + X = x(:,1); + Y = x(:,2); + Z = x(:,3); + + F(1,:) = (1 - X - Y - Z).*(1 - 2*X - 2*Y - 2*Z); + F(2,:) = X.*(2*X - 1); + F(3,:) = Y.*(2*Y - 1); + F(4,:) = Z.*(2*Z - 1); + F(5,:) = 4*X.*(1 - X - Y - Z); + F(6,:) = 4*X.*Y; + F(7,:) = 4*Y.*(1 - X - Y - Z); + F(8,:) = 4*Z.*(1 - X - Y - Z); + F(9,:) = 4*X.*Z; + F(10,:) = 4*Y.*Z; + + dxF(1,:) = -3 + 4*(X + Y + Z); + dxF(2,:) = 4*X - 1; + dxF(5,:) = 4*(1 - 2*X - Y - Z); + dxF(6,:) = 4*Y; + dxF(7,:) = -4*Y; + dxF(8,:) = -4*Z; + dxF(9,:) = 4*Z; + + dzF(1,:) = -3 + 4*(X + Y + Z); + dzF(4,:) = 4*Z - 1; + dzF(5,:) = -4*X; + dzF(7,:) = -4*Y; + dzF(8,:) = 4*(1 - X - Y - 2*Z); + dzF(9,:) = 4*X; + dzF(10,:) = 4*Y; + + dyF(1,:) = -3 + 4*(X + Y + Z); + dyF(3,:) = 4*Y - 1; + dyF(5,:) = -4*X; + dyF(6,:) = 4*X; + dyF(7,:) = 4*(1 - X - 2*Y - Z); + dyF(8,:) = -4*Z; + dyF(10,:) = 4*Z; + + dzF(1,:) = -3 + 4*(X + Y + Z); + dzF(4,:) = 4*Z - 1; + dzF(5,:) = -4*X; + dzF(7,:) = -4*Y; + dzF(8,:) = 4*(1 - X - Y - 2*Z); + dzF(9,:) = 4*X; + dzF(10,:) = 4*Y; + + else + error('femLagrangePn.m : unavailable case') + end + + else + error('femLagrangePn.m: unavailable case'); + end + + % Numbering dof to quadrature + idx = zeros(Nbas*Nqud,1); + jdx = zeros(Nbas*Nqud,1); + for i = 1:Nbas + for j = 1:Ngss + ind = j+(i-1)*Ngss : Nbas*Ngss : Nbas*Nqud; + idx(ind) = elt2qud(:,j); + jdx(ind) = elt2dof(:,i); + end + end + + % Finite element matrix + if strcmp(fe.opr,'[psi]') + bas = reshape(F',[1,Ngss*Nbas]); + bas = kron(ones(1,Nelt),bas); + M = sparse(idx,jdx,bas,Nqud,Ndof); + + % Gradient of Finite element matrix + elseif strcmp(fe.opr,'grad[psi]') + % Edge mesh + if (size(mesh.elt,2) == 2) + notYet + + % Triangular mesh + elseif (size(mesh.elt,2) == 3) + % Vector basis + E1 = mesh.vtx(mesh.elt(:,2),:) - mesh.vtx(mesh.elt(:,1),:); + E2 = mesh.vtx(mesh.elt(:,3),:) - mesh.vtx(mesh.elt(:,1),:); + + % Gramm matrix coefficients + a = E1(:,1).^2 + E1(:,2).^2 + E1(:,3).^2; + b = E1(:,1).*E2(:,1) + E1(:,2).*E2(:,2) + E1(:,3).*E2(:,3); + c = b; + d = E2(:,1).^2 + E2(:,2).^2 + E2(:,3).^2; + + % Determinant + detG = a.*d - b.*c; + + % Inverse by co-factor + Dx1 = d ./ detG; + Dx2 = -b ./ detG; + Dy1 = -c ./ detG; + Dy2 = a ./ detG; + + % Gradient projection to integration points + dbas = cell(1,3); + for n = 1:3 + dbas{n} = zeros(Nbas,Nqud); + for d = 1:Nbas + DCVx = Dx1.*E1(:,n) + Dx2.*E2(:,n); + DCVy = Dy1.*E1(:,n) + Dy2.*E2(:,n); + dbas{n}(d,:) = kron(DCVx',dxF(d,:)) + kron(DCVy',dyF(d,:)); + end + end + + % Tetrahedron mesh + elseif (size(mesh.elt,2) == 4) + % Vector basis + E1 = mesh.vtx(mesh.elt(:,2),:) - mesh.vtx(mesh.elt(:,1),:); + E2 = mesh.vtx(mesh.elt(:,3),:) - mesh.vtx(mesh.elt(:,1),:); + E3 = mesh.vtx(mesh.elt(:,4),:) - mesh.vtx(mesh.elt(:,1),:); + + % Gramm matrix + a = E1(:,1).^2 + E1(:,2).^2 + E1(:,3).^2; + b = E1(:,1).*E2(:,1) + E1(:,2).*E2(:,2) + E1(:,3).*E2(:,3); + c = E1(:,1).*E3(:,1) + E1(:,2).*E3(:,2) + E1(:,3).*E3(:,3); + d = b; + e = E2(:,1).^2 + E2(:,2).^2 + E2(:,3).^2; + f = E2(:,1).*E3(:,1) + E2(:,2).*E3(:,2) + E2(:,3).*E3(:,3); + g = c; + h = f; + i = E3(:,1).^2 + E3(:,2).^2 + E3(:,3).^2; + + % Determinant (Sarrus rules) + detG = a.*e.*i + b.*f.*g + c.*d.*h - c.*e.*g - f.*h.*a - i.*b.*d; + + % Inverse by co-factor + Dx1 = (e.*i - f.*h) ./ detG; + Dx2 = (c.*h - b.*i) ./ detG; + Dx3 = (b.*f - c.*e) ./ detG; + Dy1 = (f.*g - d.*i) ./ detG; + Dy2 = (a.*i - c.*g) ./ detG; + Dy3 = (c.*d - a.*f) ./ detG; + Dz1 = (d.*h - e.*g) ./ detG; + Dz2 = (b.*g - a.*h) ./ detG; + Dz3 = (a.*e - b.*d) ./ detG; + + % Gradient projection to integration points + dbas = cell(1,3); + for n = 1:3 + dbas{n} = zeros(Nbas,Nqud); + for d = 1:Nbas + DCVx = Dx1.*E1(:,n) + Dx2.*E2(:,n) + Dx3.*E3(:,n); + DCVy = Dy1.*E1(:,n) + Dy2.*E2(:,n) + Dy3.*E3(:,n); + DCVz = Dz1.*E1(:,n) + Dz2.*E2(:,n) + Dz3.*E3(:,n); + dbas{n}(d,:) = kron(DCVx',dxF(d,:)) ... + + kron(DCVy',dyF(d,:)) ... + + kron(DCVz',dzF(d,:)); + end + end + end + + % Dof to quadrature matrix + M = cell(1,3); + for n = 1:3 + % Basis functions values + val = zeros(Nbas*Nqud,1); + for i = 1:Nbas + for j = 1:Ngss + indl = j+(i-1)*Ngss : Nbas*Ngss : Nbas*Nqud; + indr = j:Ngss:Nqud; + val(indl) = dbas{n}(i,indr); + end + end + + % Sparse format + M{n} = sparse(idx,jdx,val,Nqud,Ndof); + end + end + + +%%% NORMALS * DQM +elseif strcmp(fe.opr,'n*[psi]') + % Finite element + fe.opr = '[psi]'; + dqm = fe.dqm(mesh); + + % Normals + N = mesh.nrmQud; + + % Dot product + m = size(N,1); + M{1} = spdiags(N(:,1),0,m,m) * dqm; + M{2} = spdiags(N(:,2),0,m,m) * dqm; + M{3} = spdiags(N(:,3),0,m,m) * dqm; + + +%%%% NORMAL x DQM +elseif strcmp(fe.opr,'nxgrad[psi]') + % Finite elements + fe.opr = 'grad[psi]'; + dqm = fe.dqm(mesh); + + % Normals + nrm = mesh.nrmQud; + m = size(nrm,1); + N{1} = spdiags(nrm(:,1),0,m,m); + N{2} = spdiags(nrm(:,2),0,m,m); + N{3} = spdiags(nrm(:,3),0,m,m); + + % Cross product + M = cell(1,3); + for i = 1:3 + ip1 = mod(i,3) + 1; + ip2 = mod(ip1,3) + 1; + M{i} = N{ip1} * dqm{ip2} - N{ip2} * dqm{ip1}; + end + + +%%% GRADIENT (j) +elseif strcmp(fe.opr(1:end-1),'grad[psi]') + % Component + j = str2double(fe.opr(end)); + + % Finite elements + fe.opr = 'grad[psi]'; + dqm = fe.dqm(mesh); + + % Gradient (j) + M = dqm{j}; + + +%%% NORMALS * DQM (j) +elseif strcmp(fe.opr(1:end-1),'n*[psi]') + % Component + j = str2double(fe.opr(end)); + + % Finite element + fe.opr = '[psi]'; + dqm = fe.dqm(mesh); + + % Normal (component j) + N = mesh.nrmQud; + + % Dot product (j) + m = size(N,1); + M = spdiags(N(:,j),0,m,m) * dqm; + + +%%%% NORMAL x DQM (j) +elseif strcmp(fe.opr(1:end-1),'nxgrad[psi]') + % Component + j = str2double(fe.opr(end)); + + % Finite element + fe.opr = 'grad[psi]'; + dqm = fe.dqm(mesh); + + % Normals + N = mesh.nrmQud; + m = size(N,1); + + % Cross component + jp1 = mod(j,3) + 1; + jp2 = mod(jp1,3) + 1; + + % Cross product + M = spdiags(N(:,jp1),0,m,m) * dqm{jp2} - ... + spdiags(N(:,jp2),0,m,m) * dqm{jp1}; + +else + error('femLagrangePn.m : unavailable case') +end +end diff --git a/openFem/femRegularize.m b/openFem/femRegularize.m new file mode 100644 index 0000000..26c9268 --- /dev/null +++ b/openFem/femRegularize.m @@ -0,0 +1,283 @@ +function Ms = femRegularize(varargin) +%+========================================================================+ +%| | +%| OPENFEM, FINITE AND BOUNDARY ELEMENT | +%| openFem is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openFem, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| François Alouges - CMAP, Ecole Polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Finite element regularization matrix for laplace kernel | +%+========================================================================+ + +%%% INPUT ANALYSIS +if (nargin == 4) + X = varargin{1}; + Ymsh = varargin{2}; + green = varargin{3}; + v = varargin{4}; +else + Xmsh = varargin{1}; + Ymsh = varargin{2}; + u = varargin{3}; + green = varargin{4}; + v = varargin{5}; +end + + +%%% INITIALIZATION +% Mesh data from Y +vtx = Ymsh.vtx; +elt = Ymsh.elt; +ctr = Ymsh.ctr; +nrm = Ymsh.nrm; +tau = cell2mat(Ymsh.tgt); +nu = cell2mat(Ymsh.nrmEdg); +Nelt = size(elt,1); + +% Quadrature data from Y +[Y,Wy,elt2qud] = Ymsh.qud; +Yun = ones(1,size(elt2qud,2)); + +% Degrees of freedom from Y +[~,elt2dof] = v.dof(Ymsh); +Nbas = size(elt2dof,2); + +% Quadrature data from X +if (nargin == 5) + [X,Wx] = Xmsh.qud; +end +Nx = size(X,1); + +% Rangesearch with max(|edge|)_Y +[Ielt,Relt] = knnsearch(X,ctr,'K',50); +Mx = cell(Nelt,1); + + +%%% RIGHT INTEGRATION WITH REGULARIZATION +for el = 1:Nelt + % Triangular data for Y + Sel = vtx(elt(el,:),:); + Nel = nrm(el,:); + Tel = reshape(tau(el,:),3,3)'; + NUel = reshape(nu(el,:),3,3)'; + + % Local size + edga = Sel(2,:) - Sel(1,:); + edgb = Sel(3,:) - Sel(1,:); + edgc = Sel(3,:) - Sel(2,:); + rMin = max([norm(edga),norm(edgb),norm(edgc)]); + + % Quadratures points in interaction + Iy = elt2qud(el,:); + Ix = sort(Ielt(el,Relt(el,:) 0 + B = Mh.dat \ B; + elseif (Mh.chd{2}.typ == 3) + B = hmxSolveLower(Mh,B); + elseif (Mh.chd{3}.typ == 3) + B = hmxSolveUpper(Mh,B); + else + [Lh,Uh] = lu(Mh); + B = hmxSolveLower(Lh,B); + B = hmxSolveUpper(Uh,B); + end + end + + % ITERATIVE SOLVER + function B = gmres(Mh,B,restart,tol,maxit) + B = gmres(@(V) Mh*V,B,restart,tol,maxit); + end + + % STRUCTURE VISUALISATION + function spy(Mh) + hmxSpy(Mh); + end + + % DIMENSIONS + function dim = size(varargin) + if length(varargin) == 1 + dim = varargin{1}.dim; + else + dim = varargin{1}.dim(varargin{2}); + end + end + + % NORM(S) + + % MPOWER +end +end diff --git a/openHmx/hmxACA.m b/openHmx/hmxACA.m new file mode 100644 index 0000000..702930d --- /dev/null +++ b/openHmx/hmxACA.m @@ -0,0 +1,149 @@ +function [A,B,flag] = hmxACA(X,Y,green,tol) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Adaptative Cross Approximation, partial & total pivoting | +%+========================================================================+ + +% Partial or total pivoting +if isnumeric(green) + mtx = 1; +else + mtx = 0; +end + +% Dimensions +Nx = size(X,1); +Ny = size(Y,1); + +% First row +if mtx + B = green(1,:).'; +else + B = green(X(1,:),Y); +end + +% Maximum for pivoting +[delta,j] = max(B); + +% First column +if abs(delta) <= 10*eps(B(1)) + A = zeros(Nx,1,class(B)); +elseif mtx + A = green(:,1) ./ delta; +else + A = green(X,Y(j,:)) ./ delta; +end + +% Sorted interactions +X0 = mean(X,1); +Y0 = mean(Y,1); +[~,ix] = sort( (X-ones(Nx,1)*X0) * (Y0-X0)' ); +[~,iy] = sort( (Y-ones(Ny,1)*Y0) * (X0-Y0)' ); + +% Length compatibility +if Nx > Ny + iy = iy(mod(0:Nx-1,Ny)'+1); +else + ix = ix(mod(0:Ny-1,Nx)'+1); +end + +% Add random interactions +ix = [ix ; ceil(Nx*rand(max(Nx,Ny),1))]; +iy = [iy ; ceil(Ny*rand(max(Nx,Ny),1))]; + +% Reference +if mtx + ref = green(sub2ind(size(green),ix,iy)); +else + ref = green(X(ix,:),Y(iy,:)); +end +nrf = norm(ref,'inf'); + +% Numerical solution +sol = A(ix) .* B(iy); + +% Construction +n = 1; +while (norm(ref-sol,'inf')/nrf > tol) + % Initialisation + ind = (1:Nx)'; + i = 0; + delta = 0; + + % Find non zeros pivot + while abs(delta) <= 10*eps(B(1)) + % Extract void pivot + if i + ind = ind([1:i-1,i+1:end]); + if isempty(ind) + A = []; + B = []; + flag = 0; + return + end + end + + % Row index + [~,i] = max(A(ind,n)); + + % Compute new row + if mtx + row = green(ind(i),:).' - B*A(ind(i),1:n).'; + else + row = green(X(ind(i),:),Y) - B*A(ind(i),1:n).'; + end + + % Column index + [delta,j] = max(row); + end + + % Update row + B(:,n+1) = row; + + % Compute new column + if mtx + A(:,n+1) = (green(:,j) - A*B(j,1:n).') ./ delta; + else + A(:,n+1) = (green(X,Y(j,:)) - A*B(j,1:n).') ./ delta; + end + + % Incrementation + n = n + 1; + + % Accuracy of the compression + sol = sol + A(ix,n) .* B(iy,n); + + % Compression failed + if (numel(A)+numel(B) > Nx*Ny) + A = []; + B = []; + flag = 0; + return + end +end + +% B transposition lead to A * B +B = B.'; +flag = 1; +end diff --git a/openHmx/hmxBuilder.m b/openHmx/hmxBuilder.m new file mode 100644 index 0000000..8b3f872 --- /dev/null +++ b/openHmx/hmxBuilder.m @@ -0,0 +1,140 @@ +function Mh = hmxBuilder(X,Y,green,tol) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Particles builder with direct and low-rank separation | +%+========================================================================+ + +% Initialisation +Mh = hmx(size(X,1),size(Y,1),tol); + +% Rectangular box for X +Xmin = min(X,[],1); +Xmax = max(X,[],1); +Xctr = 0.5*(Xmin+Xmax); +Xdgl = Xmax-Xmin; + +% Rectangular box for Y +Ymin = min(Y,[],1); +Ymax = max(Y,[],1); +Yctr = 0.5*(Ymin+Ymax); +Ydgl = Ymax-Ymin; + +% Compression for separated boxes +if sum( abs(Yctr-Xctr) > max(Xdgl+Ydgl) ) + Mh.typ = 1; + +% Full computation for small box (stopping criterion) +elseif sum(Mh.dim < 100) + Mh.typ = 2; + +% H-Matrix +else + Mh.typ = 0; +end + +% H-Matrix (recursion) +if (Mh.typ == 0) + % Subdivision for X + ind = hmxSubdivide(X); + Mh.row = {find(ind),find(ind),find(~ind),find(~ind)}; + + % Subdivision for Y + ind = hmxSubdivide(Y); + Mh.col = {find(ind),find(~ind),find(ind),find(~ind)}; + + % Single class + if isa(X,'single') + for i = 1:4 + Mh.row{i} = single(Mh.row{i}); + Mh.col{i} = single(Mh.col{i}); + end + end + + % H-Matrix (recursion) + for i = 1:4 + if isa(green,'function_handle') + Mh.chd{i} = hmxBuilder(X(Mh.row{i},:),Y(Mh.col{i},:),green,tol); + elseif isnumeric(green) + Mh.chd{i} = hmxBuilder(X(Mh.row{i},:),Y(Mh.col{i},:), ... + green(Mh.row{i},Mh.col{i}),tol); + else + error('hmxBuilder.m : unavailable case') + end + end + + % Fusion + Mh = hmxFusion(Mh); + +% Compressed leaf +elseif (Mh.typ == 1) + % ACA with partial pivoting + if isa(green,'function_handle') + [A,B,flag] = hmxACA(X,Y,green,tol); + + % ACA with total pivoting + elseif isnumeric(green) && ~issparse(green) + [A,B,flag] = hmxACA(X,Y,green,tol); + + % No compressor + else + flag = 0; + end + + % Update + if flag + Mh.dat{1} = A; + Mh.dat{2} = B; + else + Mh.typ = 2; + end +end + +% Full or sparse leaf +if (Mh.typ == 2) + % Matrix + if isa(green,'function_handle') + [I,J] = ndgrid(1:size(X,1),1:size(Y,1)); + Mh.dat = green(X(I,:),Y(J,:)); + Mh.dat = reshape(Mh.dat,size(X,1),size(Y,1)); + elseif isnumeric(green) + Mh.dat = green; + else + error('hmxBuilder.m : unavailable case') + end + + % Sparse matrix + if issparse(Mh.dat) + Mh.typ = 3; + + % Full matrix recompression + else + rkMax = ceil(sqrt(min(Mh.dim))-log(Mh.tol)); + [A,B,flag] = hmxRSVD(Mh.dat,Mh.tol,rkMax); + if flag + Mh.dat = {A,B}; + Mh.typ = 1; + end + end +end +end diff --git a/openHmx/hmxChol.m b/openHmx/hmxChol.m new file mode 100644 index 0000000..049de82 --- /dev/null +++ b/openHmx/hmxChol.m @@ -0,0 +1,65 @@ +function Mh = hmxChol(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Cholesky factorization of H-Matrix | +%+========================================================================+ + +% H-Matrix (recursion) +if (Mh.typ == 0) + % U11 -> M11 + Mh.chd{1} = hmxChol(Mh.chd{1}); + + % U12 -> U11' \ M12 + Mh.chd{2} = hmxSolveLower(Mh.chd{1}',Mh.chd{2}); + + % U21 -> 0 + Mh.chd{3}.dat = sparse(Mh.chd{3}.dim(1),Mh.chd{3}.dim(2)); + Mh.chd{3}.typ = 3; + + % M22 -> M22 - U12'*U12 + Mh.chd{4} = Mh.chd{4} - Mh.chd{2}' * Mh.chd{2}; + + % U22 -> M22 + Mh.chd{4} = hmxChol(Mh.chd{4}); + + % Fusion + Mh = hmxFusion(Mh); + +% Compressed leaf +elseif (Mh.typ == 1) + error('hmxChol : unavailable case') + +% Full leaf +elseif (Mh.typ == 2) + Mh.dat = chol(Mh.dat); + +% Sparse leaf +elseif (Mh.typ == 3) + Mh.dat = chol(Mh.dat); + +% Unknown type +else + error('hmxChol.m : unavailable case') +end +end diff --git a/openHmx/hmxCtranspose.m b/openHmx/hmxCtranspose.m new file mode 100644 index 0000000..ccb15c9 --- /dev/null +++ b/openHmx/hmxCtranspose.m @@ -0,0 +1,63 @@ +function Mh = hmxCtranspose(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Conjugate transposition of H-Matrix | +%+========================================================================+ + +% Dimensions +Mh.dim = [Mh.dim(2) Mh.dim(1)]; + +% H-Matrix (recursion) +if (Mh.typ == 0) + % Data + tmp = Mh.chd{2}; + Mh.chd{1} = hmxCtranspose(Mh.chd{1}); + Mh.chd{2} = hmxCtranspose(Mh.chd{3}); + Mh.chd{3} = hmxCtranspose(tmp); + Mh.chd{4} = hmxCtranspose(Mh.chd{4}); + + % Indices + I = [1 3 2 4]; + tmp = Mh.row; + Mh.row = Mh.col(I); + Mh.col = tmp(I); + +% Compressed leaf +elseif (Mh.typ == 1) + Mh.dat = {Mh.dat{2}' , Mh.dat{1}'}; + +% Full leaf +elseif (Mh.typ == 2) + Mh.dat = Mh.dat'; + +% Sparse leaf +elseif (Mh.typ == 3) + Mh.dat = Mh.dat'; + +% Unknown type +else + error('hmxCtranspose.m : unavailable case') +end + +end diff --git a/openHmx/hmxDouble.m b/openHmx/hmxDouble.m new file mode 100644 index 0000000..c647596 --- /dev/null +++ b/openHmx/hmxDouble.m @@ -0,0 +1,54 @@ +function Mh = hmxDouble(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Convert H-Matrix to double precision | +%+========================================================================+ + +% H-Matrix (recursion) +if (Mh.typ == 0) + for i = 1:4 + Mh.chd{i} = hmxDouble(Mh.chd{i}); + Mh.row{i} = double(Mh.row{i}); + Mh.col{i} = double(Mh.col{i}); + end + +% Compressed leaf +elseif (Mh.typ == 1) + Mh.dat{1} = double(Mh.dat{1}); + Mh.dat{2} = double(Mh.dat{2}); + +% Full leaf +elseif (Mh.typ == 2) + Mh.dat = double(Mh.dat); + +% Sparse leaf +elseif (Mh.typ == 3) + Mh.dat = Mh.dat; + +% Unknown type +else + error('hmxDouble.m : unavailable case') +end + +end diff --git a/openHmx/hmxFull.m b/openHmx/hmxFull.m new file mode 100644 index 0000000..79a86c0 --- /dev/null +++ b/openHmx/hmxFull.m @@ -0,0 +1,52 @@ +function M = hmxFull(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Convert H-Matrix to full matrix | +%+========================================================================+ + +% H-Matrix (recursion) +if (Mh.typ == 0) + M = zeros(Mh.dim(1),Mh.dim(2),class(Mh.row{1})); + for i = 1:4 + M(Mh.row{i},Mh.col{i}) = hmxFull(Mh.chd{i}); + end + +% Compressed leaf +elseif (Mh.typ == 1) + M = Mh.dat{1} * Mh.dat{2}; + +% Full leaf +elseif (Mh.typ == 2) + M = Mh.dat; + +% Sparse leaf +elseif (Mh.typ == 3) + M = full(Mh.dat); + +% Unknown type +else + error('hmxFull.m : unavailable case') +end + +end diff --git a/openHmx/hmxFusion.m b/openHmx/hmxFusion.m new file mode 100644 index 0000000..b885af9 --- /dev/null +++ b/openHmx/hmxFusion.m @@ -0,0 +1,97 @@ +function Mh = hmxFusion(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Fusion and recompress for full, sparse and low-ran k | +%+========================================================================+ + +% H-Matrix +if (Mh.typ == 0) + % Leaves type + typ = zeros(1,4); + for i = 1:4 + typ(i) = Mh.chd{i}.typ; + end + + % Low-rank fusion + if (sum(typ==1) == 4) + % Rank for each leaf + rk = zeros(1,4); + for i = 1:4 + rk(i) = size(Mh.chd{i}.dat{1},2); + end + + % Low rank matrix + A = zeros(Mh.dim(1),sum(rk),class(Mh.chd{1}.dat{1})); + B = zeros(sum(rk),Mh.dim(2),class(Mh.chd{1}.dat{2})); + j = 0; + for i = 1:4 + A(Mh.row{i},j+(1:rk(i))) = Mh.chd{i}.dat{1}; + B(j+(1:rk(i)),Mh.col{i}) = Mh.chd{i}.dat{2}; + j = j + rk(i); + end + [A,B] = hmxQRSVD(A,B,Mh.tol); + + % Update + Mh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Mh.dat = {A,B}; + Mh.typ = 1; + end + + % Full fusion + if (sum(typ==2) == 4) + M = full(Mh); + Mh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Mh.dat = M; + Mh.typ = 2; + end + + % Sparse fusion + if (sum(typ==3) == 4) + % Emptyness for each leaf + emp = 0; + for i = 1:4 + emp = emp + isempty(find(Mh.chd{i}.dat,1)); + end + + % Update empty + if (emp == 4) + Mh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Mh.dat = sparse(Mh.dim(1),Mh.dim(2)); + Mh.typ = 3; + end + + % Update sparse + if (emp == 0) + M = sparse(Mh); + Mh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Mh.dat = M; + Mh.typ = 3; + end + end + +% Unvalid case +else + error('hmxBuilder.m : unavailable case') +end +end diff --git a/openHmx/hmxInv.m b/openHmx/hmxInv.m new file mode 100644 index 0000000..abaf163 --- /dev/null +++ b/openHmx/hmxInv.m @@ -0,0 +1,73 @@ +function Mh = hmxInv(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Inversion of H-Matrix based on Schur complement | +%+========================================================================+ + +% H-Matrix (bloc recursion) +if (Mh.typ == 0) + % Am1 -> M11 + Mh.chd{1} = hmxInv(Mh.chd{1}); + + % - Am1 * B -> X12 + X12 = - Mh.chd{1} * Mh.chd{2}; + + % C * Am1 -> X21 + X21 = Mh.chd{3} * Mh.chd{1}; + + % D - C * Am1 * B = S -> M22 (schur complement) + Mh.chd{4} = Mh.chd{4} + Mh.chd{3} * X12; + + % S^-1 -> M22 + Mh.chd{4} = hmxInv(Mh.chd{4}); + + % - Am1 * B * S -> M12 + Mh.chd{2} = X12 * Mh.chd{4}; + + % Am1 + Am1 * B * S * C * Am1 -> M11 + Mh.chd{1} = Mh.chd{1} - Mh.chd{2} * X21; + + % - S * C * Am1 -> M21 + Mh.chd{3} = - Mh.chd{4} * X21; + + % Fusion + Mh = hmxFusion(Mh); + +% Compressed leaf +elseif (Mh.typ == 1) + error('hmxInv : unavailable case') + +% Full leaf +elseif (Mh.typ == 2) + Mh.dat = inv(Mh.dat); + +% Sparse leaf +elseif (Mh.typ == 3) + Mh.dat = inv(Mh.dat); + +% Unknown type +else + error('hmxInv.m : unavailable case') +end +end diff --git a/openHmx/hmxLU.m b/openHmx/hmxLU.m new file mode 100644 index 0000000..999c97c --- /dev/null +++ b/openHmx/hmxLU.m @@ -0,0 +1,99 @@ +function [Lh,Uh] = hmxLU(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : LU factorization of H-Matrix | +%+========================================================================+ + +% H-Matrix (recursion) +if (Mh.typ == 0) + % Lower initialisation + Lh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Lh.row = Mh.row; + Lh.col = Mh.col; + Lh.typ = 0; + + % Nullify upper corner + Lh.chd{2} = hmx(Mh.chd{2}.dim(1),Mh.chd{2}.dim(2),Mh.tol); + Lh.chd{2}.dat = sparse(Lh.chd{2}.dim(1),Lh.chd{2}.dim(2)); + Lh.chd{2}.typ = 3; + + % Upper initialisation + Uh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Uh.row = Mh.row; + Uh.col = Mh.col; + Uh.typ = 0; + + % Nullify lower corner + Uh.chd{3} = hmx(Mh.chd{3}.dim(1),Mh.chd{3}.dim(2),Mh.tol); + Uh.chd{3}.dat = sparse(Uh.chd{3}.dim(1),Uh.chd{3}.dim(2)); + Uh.chd{3}.typ = 3; + + % [L11,U11] -> M11 + [Lh.chd{1},Uh.chd{1}] = hmxLU(Mh.chd{1}); + + % U12 -> L11 \ M12 + Uh.chd{2} = hmxSolveLower(Lh.chd{1},Mh.chd{2}); + + % L21 -> M21 / U11 + Lh.chd{3} = hmxSolveUpper(Mh.chd{3},Uh.chd{1}); + + % M22 -> M22 - L21*U12 + Mh.chd{4} = Mh.chd{4} - Lh.chd{3} * Uh.chd{2}; + + % [L22,U22] -> M22 + [Lh.chd{4},Uh.chd{4}] = hmxLU(Mh.chd{4}); + + % Fusion + Lh = hmxFusion(Lh); + Uh = hmxFusion(Uh); + +% Compressed leaf +elseif (Mh.typ == 1) + error('hmxLU : unavailable case') + +% Full leaf +elseif (Mh.typ == 2) + [L,U] = lu(Mh.dat); + Lh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Lh.dat = L; + Lh.typ = 2; + Uh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Uh.dat = U; + Uh.typ = 2; + +% Sparse leaf +elseif (Mh.typ == 3) + [L,U] = lu(Mh.dat); + Lh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Lh.dat = L; + Lh.typ = 3; + Uh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Uh.dat = U; + Uh.typ = 3; + +% Unknown type +else + error('hmxLU.m : unavailable case') +end +end diff --git a/openHmx/hmxLdl.m b/openHmx/hmxLdl.m new file mode 100644 index 0000000..e0fde9d --- /dev/null +++ b/openHmx/hmxLdl.m @@ -0,0 +1,86 @@ +function [Mh,Dh] = hmxLdl(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : LDLt factorization of H-Matrix | +%+========================================================================+ + +% H-Matrix (recursion) +if (Mh.typ == 0) + % Digaonal initialisation + Dh = hmx(Mh.dim(1),Mh.dim(2),Mh.tol); + Dh.row = Mh.row; + Dh.col = Mh.col; + Dh.typ = 0; + + % Nullify upper corner + Dh.chd{2} = hmx(Mh.chd{2}.dim(1),Mh.chd{2}.dim(2),Mh.tol); + Dh.chd{2}.dat = sparse(Dh.chd{2}.dim(1),Dh.chd{2}.dim(2)); + Dh.chd{2}.typ = 3; + + % Nullify lower corner + Dh.chd{3} = hmx(Mh.chd{3}.dim(1),Mh.chd{3}.dim(2),Mh.tol); + Dh.chd{3}.dat = sparse(Dh.chd{3}.dim(1),Dh.chd{3}.dim(2)); + Dh.chd{3}.typ = 3; + + % [L11,D11] -> M11 + [Mh.chd{1},Dh.chd{1}] = hmxLdl(Mh.chd{1}); + + % L12 -> 0 + Mh.chd{2}.dat = sparse(Mh.chd{2}.dim(1),Mh.chd{2}.dim(2)); + Mh.chd{2}.typ = 3; + + % L21 -> M21 / U11 + Mh.chd{3} = hmxSolveUpper(Mh.chd{3},Dh.chd{1}*Mh.chd{1}'); + + % M22 -> M22 - L21*U12 + Mh.chd{4} = Mh.chd{4} - Mh.chd{3} * Dh.chd{1} * Mh.chd{3}' ; + + % [L22,U22] -> M22 + [Mh.chd{4},Dh.chd{4}] = hmxLdl(Mh.chd{4}); + + % Fusion + Mh = hmxFusion(Mh); + +% Compressed leaf +elseif (Mh.typ == 1) + error('hmxLdl : unavailable case') + +% Full leaf +elseif (Mh.typ == 2) + Dh = Mh; + [Mh.dat,Dh.dat] = ldl(Mh.dat); + +% Sparse leaf +elseif (Mh.typ == 3) + Dh = Mh; + [L,D,P] = ldl(Mh.dat); + L = P * L; + Mh.dat = L; + Dh.dat = D; + +% Unknown type +else + error('hmxLdl.m : unavailable case') +end +end diff --git a/openHmx/hmxMtimes.m b/openHmx/hmxMtimes.m new file mode 100644 index 0000000..cbd618e --- /dev/null +++ b/openHmx/hmxMtimes.m @@ -0,0 +1,197 @@ +function Mh = hmxMtimes(Ml,Mr) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Matrix product with H-Matrix | +%+========================================================================+ + +%%% H-Matrix * H-Matrix --> H-Matrix +if isa(Ml,'hmx') && isa(Mr,'hmx') + % Check dimensions + if (Ml.dim(2) ~= Mr.dim(1)) + error('hmxMtimes.m : matrix dimensions must agree.') + end + + % Initialisation + Mh = hmx(Ml.dim(1),Mr.dim(2),Ml.tol); + + % (H-Matrix * H-Matrix) --> H-Matrix (recursion) + if (Ml.typ==0) && (Mr.typ==0) + % Bloc product indices + I = [1 2; 1 2; 3 4; 3 4]; + J = [1 3; 2 4; 1 3; 2 4]; + + % Bloc product + for i = 1:4 + Mh.chd{i} = hmxMtimes(Ml.chd{I(i,1)},Mr.chd{J(i,1)}) + ... + hmxMtimes(Ml.chd{I(i,2)},Mr.chd{J(i,2)}); + Mh.row{i} = Ml.row{I(i,1)}; + Mh.col{i} = Mr.col{J(i,2)}; + end + Mh.typ = 0; + + % Fusion + Mh = hmxFusion(Mh); + + else + % Empty * --- ---> --- + if issparse(Ml.dat) && isempty(find(Ml.dat,1)) + Mh.dat = sparse(Mh.dim(1),Mh.dim(2)); + Mh.typ = 3; + + % --- * Empty ---> --- + elseif issparse(Mr.dat) && isempty(find(Mr.dat,1)) + Mh.dat = sparse(Mh.dim(1),Mh.dim(2)); + Mh.typ = 3; + + % H-Matrix * Compr --> Compr + elseif (Ml.typ==0) && (Mr.typ==1) + Mh.dat = {hmxMtimes(Ml,Mr.dat{1}) , Mr.dat{2}}; + Mh.typ = 1; + + % H-Matrix * --- --> --- + elseif (Ml.typ==0) + Mh.dat = hmxMtimes(Ml,Mr.dat); + if ~issparse(Mh.dat) + Mh.typ = 2; + else + Mh.typ = 3; + end + + % Compr * --- --> --- + elseif (Ml.typ==1) + % Compr * H-Matrix --> Compr + if (Mr.typ==0) + Mh.dat = {Ml.dat{1} , hmxMtimes(Ml.dat{2},Mr)}; + Mh.typ = 1; + + % Compr * Compr --> Compr + elseif (Mr.typ==1) + Mh.dat = {Ml.dat{1} , (Ml.dat{2} * Mr.dat{1}) * Mr.dat{2}}; + Mh.typ = 1; + + % Compr * Full --> Compr + elseif (Mr.typ==2) + Mh.dat = {Ml.dat{1} , Ml.dat{2} * Mr.dat}; + Mh.typ = 1; + + % Compr * Sparse --> Compr + elseif (Mr.typ==3) + Mh.dat = {Ml.dat{1} , Ml.dat{2} * Mr.dat}; + Mh.typ = 1; + + else + error('hmxMtimes : unvailable case') + end + + % Full * Compr --> compr + elseif (Ml.typ==2) && (Mr.typ==1) + Mh.dat = {Ml.dat*Mr.dat{1} , Mr.dat{2}}; + Mh.typ = 1; + + % Full * --- --> --- + elseif (Ml.typ==2) + Mh.dat = hmxMtimes(Ml.dat,Mr); + Mh.typ = 2; + + % Sparse * Compr --> compr + elseif (Ml.typ==3) && (Mr.typ==1) + Mh.dat = {Ml.dat*Mr.dat{1} , Mr.dat{2}}; + Mh.typ = 1; + + % Sparse * --- --> --- + elseif (Ml.typ==3) + Mh.dat = hmxMtimes(Ml.dat,Mr); + if ~issparse(Mh.dat) + Mh.typ = 2; + else + Mh.typ = 3; + end + + else + error('hmxMtimes : unvailable case') + end + end + + +%%% H-Matrix * Matrix --> Matrix +elseif isa(Ml,'hmx') + % Check dimensions + if (Ml.dim(2) ~= size(Mr,1)) + error('hmxMtimes.m : matrix dimensions must agree.') + end + + % H-Matrix (recursion) + if (Ml.typ == 0) + % Recursion + tmp = cell(1,4); + spr = 0; + for i = 1:4 + tmp{i} = hmxMtimes(Ml.chd{i},Mr(Ml.col{i},:)); + spr = spr + issparse(tmp{i}); + end + + % Initialization + if (spr==4) + Mh = sparse(Ml.dim(1),size(Mr,2)); + else + Mh = zeros(Ml.dim(1),size(Mr,2),class(Mr)); + end + + % Update + for i = 1:4 + Mh(Ml.row{i},:) = Mh(Ml.row{i},:) + tmp{i}; + end + + % Compressed leaf + elseif (Ml.typ == 1) + Mh = Ml.dat{1} * (Ml.dat{2} * Mr); + + % Full leaf + elseif (Ml.typ == 2) + Mh = Ml.dat * full(Mr); + + % Sparse leaf + elseif (Ml.typ == 3) + if issparse(Mr) + Mh = Ml.dat * Mr; + else + Mh = full(Ml.dat) * Mr; + end + + % Unknown type + else + error('hmxMtimes.m : unavailable case') + end + + +%%% Matrix * H-Matrix --> Matrix +elseif isa(Mr,'hmx') + Mh = hmxMtimes(Mr.',Ml.').'; + + +%%% Unavailable +else + error('hmxMtimes.m : unavailable case') +end +end diff --git a/openHmx/hmxPlus.m b/openHmx/hmxPlus.m new file mode 100644 index 0000000..eedb319 --- /dev/null +++ b/openHmx/hmxPlus.m @@ -0,0 +1,224 @@ +function Ml = hmxPlus(Ml,Mr) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Matrix summation with H-Matrix | +%+========================================================================+ + +%%% H-Matrix + H-Matrix -> H-Matrix +if isa(Ml,'hmx') && isa(Mr,'hmx') + % Check dimensions + if sum(Ml.dim ~= Mr.dim) + error('hmxPlus.m : matrix dimensions must agree.') + end + + % H-Matrix + H-Matrix --> H-Matrix (recursion) + if (Ml.typ == 0) && (Mr.typ == 0) + % Construction + for i = 1:4 + Ml.chd{i} = hmxPlus(Ml.chd{i},Mr.chd{i}); + end + + % Fusion + Ml = hmxFusion(Ml); + + else + % Empty + --- ---> --- + if issparse(Ml.dat) && isempty(find(Ml.dat,1)) + Ml = Mr; + + % --- + Empty ---> --- + elseif issparse(Mr.dat) && isempty(find(Mr.dat,1)) + + % H-Matrix + Compr -> H-Matrix + elseif (Ml.typ == 0) && (Mr.typ == 1) + Ml = hmxPlusAB(Ml,Mr.dat{1},Mr.dat{2}); + + % H-Matrix + --- -> --- + elseif (Ml.typ == 0) + Ml = hmxPlus(Ml,Mr.dat); + + % Compr + --- -> --- + elseif (Ml.typ == 1) + Ml = hmxPlusAB(Mr,Ml.dat{1},Ml.dat{2}); + + % Full + --- -> Full + elseif (Ml.typ == 2) + Ml = hmxPlus(Mr,Ml.dat); + + % Sparse + --- -> Sparse + elseif (Ml.typ == 3) + Ml = hmxPlus(Mr,Ml.dat); + + else + error('hmxPlus : unvailable case') + end + end + + +%%% H-Matrix + Matrix -> H-Matrix +elseif isa(Ml,'hmx') + % Check dimensions + if sum(Ml.dim ~= size(Mr)) + error('hmxPlus.m : matrix dimensions must agree.') + end + + % H-Matrix (recursion) + if (Ml.typ == 0) + % Construction + for i = 1:4 + Ml.chd{i} = hmxPlus(Ml.chd{i},Mr(Ml.row{i},Ml.col{i})); + end + + % Fusion + Ml = hmxFusion(Ml); + + % Compressed leaf + elseif (Ml.typ == 1) + % Save compressed data + A = Ml.dat{1}; + B = Ml.dat{2}; + + % Exchange with matrix + Ml.dat = Mr; + if ~issparse(Mr) + Ml.typ = 2; %%%%%%% TYPE CHANGE %%%%%%% + else + Ml.typ = 3; %%%%%%% TYPE CHANGE %%%%%%% + end + + % Update + Ml = hmxPlusAB(Ml,A,B); + + % Full leaf + elseif (Ml.typ == 2) + Ml.dat = Ml.dat + full(Mr); + + % Sparse leaf + elseif (Ml.typ == 3) + if issparse(Mr) + Ml.dat = Ml.dat + Mr; + else + Ml.dat = full(Ml.dat) + Mr; + Ml.typ = 2; %%%%%%% TYPE CHANGE %%%%%%% + end + + % Unknown type + else + error('hmxPlus.m : unavailable case') + end + + +%%% Matrix + H-Matrix -> Matrix +elseif isa(Mr,'hmx') + Ml = hmxPlus(Mr,Ml); + +%%% Unavailable +else + error('hmxPlus.m : unavailable case') +end +end + + +function Mh = hmxPlusAB(Mh,A,B) +% H-Matrix (recursion) +if (Mh.typ == 0) + % Construction + for i = 1:4 + Mh.chd{i} = hmxPlusAB(Mh.chd{i},A(Mh.row{i},:),B(:,Mh.col{i})); + end + + % Fusion + Mh = hmxFusion(Mh); + +% Compressed leaf +elseif (Mh.typ == 1) + A = [Mh.dat{1},A]; + B = [Mh.dat{2};B]; + [A,B] = hmxQRSVD(A,B,Mh.tol); + Mh.dat = {A,B}; + +% Full leaf +elseif (Mh.typ == 2) + % Recompression + rkMax = ceil(sqrt(min(Mh.dim))-log(Mh.tol)); + [Ah,Bh,flag] = hmxRSVD(Mh.dat,Mh.tol,rkMax); + + % Update + if flag + A = [A,Ah]; + B = [B;Bh]; + [A,B] = hmxQRSVD(A,B,Mh.tol); + Mh.dat = {A,B}; + Mh.typ = 1; %%%%%%% TYPE CHANGE %%%%%%% + + else + Mh.dat = Mh.dat + A*B; + end + +% Sparse leaf +elseif (Mh.typ == 3) + % Indices + [I,J,V] = find(Mh.dat); + r = length(I); + + % Empty + Compr -> Compr + if (r == 0) + Mh.dat = {A,B}; + Mh.typ = 1; %%%%%%% TYPE CHANGE %%%%%%% + + % Sparse + Compr -> Compr + elseif (r > 0) && (r <= 1.1*size(A,2)) + % Low-rank representation + Ah = zeros(Mh.dim(1),r,class(A)); + Bh = zeros(r,Mh.dim(2),class(B)); + K = (1:r)'; + + % Compression + Ah(sub2ind(size(Ah),I,K)) = ones(size(I),class(A)); + Bh(sub2ind(size(Bh),K,J)) = V; + + % Addition + A = [Ah,A]; + B = [Bh;B]; + + % Recompression + [A,B] = hmxQRSVD(A,B,Mh.tol); + + % Update + Mh.dat = {A,B}; + Mh.typ = 1; %%%%%%% TYPE CHANGE %%%%%%% + + % Sparse + Compr -> Full + else + Mh.dat = full(Mh.dat); + Mh.typ = 2; %%%%%%% TYPE CHANGE %%%%%%% + Mh = hmxPlusAB(Mh,A,B); + end + + +% Unknown type +else + error('hmxPlus.m : unavailable case') +end +end diff --git a/openHmx/hmxQRSVD.m b/openHmx/hmxQRSVD.m new file mode 100644 index 0000000..4ac942c --- /dev/null +++ b/openHmx/hmxQRSVD.m @@ -0,0 +1,48 @@ +function [A,B] = hmxQRSVD(A,B,tol) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : QR factorization and SVD compression for low-rank matrices| +%+========================================================================+ + +% For non-empty matrix +if ~isempty(A) + % QR Factorisation A = QA * RA; + [QA,RA] = qr(A,0); + + % QR Factorisation Bt = QB * RB + [QB,RB] = qr(B.',0); + + % SVD : U*S*V = RA * RB.' + [U,S,V] = svd(RA * RB.','econ'); + + % Indices singular values > tol/10 + ind = find(abs(diag(S)./S(1)) > tol/10); + + % Recompression A = QA * U * S + A = QA * (U(:,ind) * S(ind,ind)); + + % Recompression B = V' * QB^t + B = V(:,ind)' * QB.'; +end +end diff --git a/openHmx/hmxRSVD.m b/openHmx/hmxRSVD.m new file mode 100644 index 0000000..23b897a --- /dev/null +++ b/openHmx/hmxRSVD.m @@ -0,0 +1,69 @@ +function [A,B,flag] = hmxRSVD(M,tol,rk) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Antoine Liutkus - Inria | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : RSVD from Halko et al. 'finding structure with randomness | +%+========================================================================+ + +% Dimensions +[m,n] = size(M); +p = min(2*rk,n); + +% Randomized +X = randn(n,p,class(M)); +Y = M*X; +W1 = orth(Y); +B = W1'*M; + +% Truncated SVD +[W2,S,V] = svd(B,'econ'); +U = W1*W2; + +% SVD final matrix +rk = min(rk,size(U,2)); +U = U(:,1:rk); +S = S(1:rk,1:rk); +V = V(:,1:rk); + +% No values +if numel(S) == 0 + A = zeros(m,0); + B = zeros(0,n); + flag = 1; + return +end + +% Final low-rank with fixed accuracy +I = find(abs(diag(S))/S(1) >= tol/10); +if (length(I) == rk) + A = []; + B = []; + flag = 0; +else + A = U(:,I); + B = S(I,I) * V(:,I)'; + flag = 1; +end + +end diff --git a/openHmx/hmxSherMorr.m b/openHmx/hmxSherMorr.m new file mode 100644 index 0000000..9b890b7 --- /dev/null +++ b/openHmx/hmxSherMorr.m @@ -0,0 +1,74 @@ +function [Mh,A,B] = hmxSherMorr(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Convert H-Matrix to Shermann Morrison form Sh + A*B | +%+========================================================================+ + +% H-Matrix (recursion) +if (Mh.typ == 0) + % Initialization + A = zeros(Mh.dim(1),0,class(Mh.row{1})); + B = zeros(0,Mh.dim(2),class(Mh.row{1})); + l = 0; + + % Recursion + for i = 1:4 + % Children computation + [Mh.chd{i},Ai,Bi] = hmxSherMorr(Mh.chd{i}); + ri = size(Ai,2); + + % Parent incrementation + A(Mh.row{i},l+1:l+ri) = Ai; + B(l+1:l+ri,Mh.col{i}) = Bi; + + % Rank incrementation + l = l+ri; + end + + % Recompression + [A,B] = hmxQRSVD(A,B,Mh.tol); + +% Compressed leaf +elseif (Mh.typ == 1) + A = Mh.dat{1}; + B = Mh.dat{2}; + Mh.dat{1} = zeros(Mh.dim(1),0,class(A)); + Mh.dat{2} = zeros(0,Mh.dim(2),class(A)); + +% Full leaf +elseif (Mh.typ == 2) + A = zeros(Mh.dim(1),0,class(Mh.dat)); + B = zeros(0,Mh.dim(2),class(Mh.dat)); + +% Sparse leaf +elseif (Mh.typ == 3) + A = zeros(Mh.dim(1),0); + B = zeros(0,Mh.dim(2)); + +% Unknown type +else + error('hmxSherMorr.m : unavailable case') +end + +end diff --git a/openHmx/hmxSingle.m b/openHmx/hmxSingle.m new file mode 100644 index 0000000..5f7fe80 --- /dev/null +++ b/openHmx/hmxSingle.m @@ -0,0 +1,54 @@ +function Mh = hmxSingle(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Convert H-Matrix to single precision | +%+========================================================================+ + +% H-Matrix (recursion) +if (Mh.typ == 0) + for i = 1:4 + Mh.chd{i} = hmxSingle(Mh.chd{i}); + Mh.row{i} = single(Mh.row{i}); + Mh.col{i} = single(Mh.col{i}); + end + +% Compressed leaf +elseif (Mh.typ == 1) + Mh.dat{1} = single(Mh.dat{1}); + Mh.dat{2} = single(Mh.dat{2}); + +% Full leaf +elseif (Mh.typ == 2) + Mh.dat = single(Mh.dat); + +% Sparse leaf +elseif (Mh.typ == 3) + Mh.dat = Mh.dat; + +% Unknown type +else + error('hmxSingle.m : unavailable case') +end + +end diff --git a/openHmx/hmxSolveLower.m b/openHmx/hmxSolveLower.m new file mode 100644 index 0000000..0c4fac0 --- /dev/null +++ b/openHmx/hmxSolveLower.m @@ -0,0 +1,139 @@ +function Bh = hmxSolveLower(Lh,Bh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Solve lower H-Matrix system | +%+========================================================================+ + +%%% Security +if isstruct(Lh) && (Lh.typ == 0) + if (Lh.chd{2}.typ ~= 3) + error('hmxSolveLower.m : left matrix is not a lower structure.') + elseif ~isempty(find(Lh.chd{2}.dat,1)) + error('hmxSolveLower.m : left matrix is not a lower structure.') + end +end + + +%%% H-Matrix \ H-Matrix -> H-Matrix +if isa(Lh,'hmx') && isa(Bh,'hmx') + % Check dimensions + if (Lh.dim(1) ~= Bh.dim(1)) + error('hmxSolveLower.m : matrix dimensions must agree.') + end + + % H-Matrix \ H-Matrix -> H-Matrix (recursion) + if (Lh.typ == 0) && (Bh.typ == 0) + % X11 -> L11 \ B11 + Bh.chd{1} = hmxSolveLower(Lh.chd{1},Bh.chd{1}); + + % X12 -> L11 \ B12 + Bh.chd{2} = hmxSolveLower(Lh.chd{1},Bh.chd{2}); + + % X21 -> L22 \ (B21 - L21*X11) + Bh.chd{3} = Bh.chd{3} - Lh.chd{3} * Bh.chd{1}; + Bh.chd{3} = hmxSolveLower(Lh.chd{4},Bh.chd{3}); + + % X22 -> L22 \ (B22 - L21 * X12) + Bh.chd{4} = Bh.chd{4} - Lh.chd{3} * Bh.chd{2}; + Bh.chd{4} = hmxSolveLower(Lh.chd{4},Bh.chd{4}); + + % Full \ H-Matrix -> Full + elseif (Lh.typ == 2) && (Bh.typ == 0) + B = Lh.dat \ full(Bh); + Bh = hmx(size(B,1),size(B,2),Bh.tol); + Bh.dat = B; + Bh.typ = 2; + + % Sparse \ H-Matrix -> Sparse + elseif (Lh.typ == 3) && (Bh.typ == 0) + B = Lh.dat \ sparse(Bh); + Bh = hmx(size(B,1),size(B,2),Bh.tol); + Bh.dat = B; + Bh.typ = 3; + + % --- \ Compr -> Compr + elseif (Bh.typ == 1) + Bh.dat = { hmxSolveLower(Lh,Bh.dat{1}) , Bh.dat{2} }; + + % --- \ Full -> Full + elseif (Bh.typ == 2) + Bh.dat = hmxSolveLower(Lh,Bh.dat); + + % --- \ Sparse -> Sparse + elseif (Bh.typ == 3) + Bh.dat = hmxSolveLower(Lh,Bh.dat); + + else + error('hmxSolveLower : unavailable case') + end + + +%%% H-Matrix \ Matrix -> Matrix +elseif isa(Lh,'hmx') + % Check dimensions + if (Lh.dim(1) ~= size(Bh,1)) + error('hmxhmxSolveLower.m : matrix dimensions must agree.') + end + + % H-Matrix (recursion) + if (Lh.typ == 0) + % X1 -> L11 \ B1 + X1 = hmxSolveLower(Lh.chd{1},Bh(Lh.row{1},:)); + + % X2 -> L22 \ (B2 - L21*X1) + X2 = Bh(Lh.row{3},:) - Lh.chd{3}*X1; + X2 = hmxSolveLower(Lh.chd{4},X2); + + % Bh = [X1 X2] + if issparse(X1) + Bh = sparse(Lh.dim(1),size(Bh,2)); + else + Bh = zeros(Lh.dim(1),size(Bh,2),class(X1)); + end + Bh(Lh.col{1},:) = X1; + Bh(Lh.col{2},:) = X2; + + % Compressed leaf + elseif (Lh.typ == 1) + error('hmxSolveLower : unavailable case') + + % Full leaf + elseif (Lh.typ == 2) + Bh = Lh.dat \ Bh; + + % Sparse leaf + elseif (Lh.typ == 3) + Bh = Lh.dat \ Bh; + + % Unknown type + else + error('hmxSolveLower : unavailable case') + end + + +%%% Unavailable +else + error('hmxSolveLower.m : unavailable case') +end +end diff --git a/openHmx/hmxSolveUpper.m b/openHmx/hmxSolveUpper.m new file mode 100644 index 0000000..117b073 --- /dev/null +++ b/openHmx/hmxSolveUpper.m @@ -0,0 +1,185 @@ +function Bh = hmxSolveUpper(Bh,Uh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Solve upper H-Matrix system | +%+========================================================================+ + +%%% Security +if isstruct(Uh) && (Uh.typ == 0) + if (Uh.chd{3}.typ ~= 3) + error('hmxSolveUpper.m : left matrix is not an upper structure.') + elseif ~isempty(find(Uh.chd{3}.dat,1)) + error('hmxSolveUpper.m : left matrix is not an upper structure.') + end +end + + +%%% H-Matrix / H-Matrix -> H-Matrix +if isa(Bh,'hmx') && isa(Uh,'hmx') + % Check dimensions + if (Bh.dim(2) ~= Uh.dim(2)) + error('hmxSolveUpper.m : matrix dimensions must agree.') + end + + % H-Matrix / H-Matrix -> H-Matrix (recursion) + if (Bh.typ == 0) && (Uh.typ == 0) + % X11 -> B11 / U11 + Bh.chd{1} = hmxSolveUpper(Bh.chd{1},Uh.chd{1}); + + % X21 -> B21 / U11 + Bh.chd{3} = hmxSolveUpper(Bh.chd{3},Uh.chd{1}); + + % X12 -> (B12 - X11*U12) / U22 + Bh.chd{2} = Bh.chd{2} - Bh.chd{1} * Uh.chd{2}; + Bh.chd{2} = hmxSolveUpper(Bh.chd{2},Uh.chd{4}); + + % X22 -> (B22 - X21 * U12) / U22 + Bh.chd{4} = Bh.chd{4} - Bh.chd{3} * Uh.chd{2}; + Bh.chd{4} = hmxSolveUpper(Bh.chd{4},Uh.chd{4}); + + % H-Matrix / Full -> Full + elseif (Bh.typ == 0) && (Uh.typ == 2) + B = full(Bh) / Uh.dat; + Bh = hmx(size(B,1),size(B,2),Bh.tol); + Bh.dat = B; + Bh.typ = 2; + + % H-Matrix / Sparse -> Sparse + elseif (Bh.typ == 0) && (Uh.typ == 3) + B = sparse(Bh) / Uh.dat; + Bh = hmx(size(B,1),size(B,2),Bh.tol); + Bh.dat = B; + Bh.typ = 3; + + % Compr / --- -> Compr + elseif (Bh.typ == 1) + Bh.dat = {Bh.dat{1} , hmxSolveUpper(Bh.dat{2},Uh)}; + + % Full / --- -> Full + elseif (Bh.typ == 2) + Bh.dat = hmxSolveUpper(Bh.dat,Uh); + + % Sparse / --- -> Sparse + elseif (Bh.typ == 3) + Bh.dat = hmxSolveUpper(Bh.dat,Uh); + + else + error('hmxSolveUpper : unavailable case') + end + + +%%% Matrix / H-Matrix -> Matrix +elseif isa(Uh,'hmx') + % Check dimensions + if (size(Bh,2) ~= Uh.dim(2)) + error('hmxSolveUpper.m : matrix dimensions must agree.') + end + + % H-Matrix (recursion) + if (Uh.typ == 0) + % X1 -> B1 / U11 + X1 = hmxSolveUpper(Bh(:,Uh.col{1}),Uh.chd{1}); + + % X2 -> U22 / (B2 - X1*U12) + X2 = Bh(:,Uh.col{2}) - X1*Uh.chd{2}; + X2 = hmxSolveUpper(X2,Uh.chd{4}); + + % Final vector + if issparse(X1) + Bh = sparse(size(Bh,1),Uh.dim(2)); + else + Bh = zeros(size(Bh,1),Uh.dim(2),class(X1)); + end + Bh(:,Uh.row{1}) = X1; + Bh(:,Uh.row{3}) = X2; + + % Compressed leaf + elseif (Uh.typ == 1) + error('hmxSolveUpper : unavailable case') + + % Full leaf + elseif (Uh.typ == 2) + Bh = Bh / Uh.dat; + + % Sparse leaf + elseif (Uh.typ == 3) + Bh = Bh / Uh.dat; + + % Unknown type + else + error('hmxSolveUpper : unavailable case') + end + + + +%%% H-Matrix \ Matrix -> Matrix +elseif isa(Bh,'hmx') + % Check dimensions + if (Bh.dim(1) ~= size(Uh,1)) + error('hmxSolveUpper.m : matrix dimensions must agree.') + end + + % H-Matrix (recursion) + if (Bh.typ == 0) + % X2 -> B22 \ U2 + X2 = hmxSolveUpper(Bh.chd{4},Uh(Bh.row{3},:)); + + % X1 -> B11 \ (U1 - B12*X2) + X1 = Uh(Bh.row{1},:) - Bh.chd{2}*X2; + X1 = hmxSolveUpper(Bh.chd{1},X1); + + % Uh = [X1 X2] + if issparse(X1) + Uh = sparse(Bh.dim(1),size(Uh,2)); + else + Uh = zeros(Bh.dim(1),size(Uh,2),class(X1)); + end + Uh(Bh.col{1},:) = X1; + Uh(Bh.col{2},:) = X2; + Bh = Uh; + + % Compressed leaf + elseif (Bh.typ == 1) + error('hmxSolveUpper : unavailable case') + + % Full leaf + elseif (Bh.typ == 2) + Bh = Bh.dat \ Uh; + + % Sparse leaf + elseif (Bh.typ == 3) + Bh = Bh.dat \ Uh; + + % Unknown type + else + error('hmxSolveUpper : unavailable case') + end + + + +%%% Unavailable +else + error('hmxSolveUpper.m : unavailable case') +end +end diff --git a/openHmx/hmxSparse.m b/openHmx/hmxSparse.m new file mode 100644 index 0000000..365a44f --- /dev/null +++ b/openHmx/hmxSparse.m @@ -0,0 +1,52 @@ +function M = hmxSparse(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Convert H-Matrix to sparse matrix | +%+========================================================================+ + +% H-Matrix (recursion) +if (Mh.typ == 0) + M = sparse(Mh.dim(1),Mh.dim(2)); + for i = 1:4 + M(Mh.row{i},Mh.col{i}) = hmxSparse(Mh.chd{i}); + end + +% Compressed leaf +elseif (Mh.typ == 1) + M = sparse(Mh.dat{1} * Mh.dat{2}); + +% Full leaf +elseif (Mh.typ == 2) + M = sparse(Mh.dat); + +% Sparse leaf +elseif (Mh.typ == 3) + M = Mh.dat; + +% Unknown type +else + error('hmxSparse.m : unavailable case') +end + +end diff --git a/openHmx/hmxSpy.m b/openHmx/hmxSpy.m new file mode 100644 index 0000000..ed173c6 --- /dev/null +++ b/openHmx/hmxSpy.m @@ -0,0 +1,82 @@ +function M = hmxSpy(varargin) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Spy H-Matrix architecture | +%+========================================================================+ + +% Input data +Mh = varargin{1}; + +% H-Matrix (recursion) +if (Mh.typ == 0) + A = hmxSpy(Mh.chd{1},[]); + B = hmxSpy(Mh.chd{2},[]); + C = hmxSpy(Mh.chd{3},[]); + D = hmxSpy(Mh.chd{4},[]); + M = [A,B;C,D]; + +% Compressed leaf +elseif (Mh.typ == 1) + M = sparse(Mh.dim(1),Mh.dim(2)); + rk = size(Mh.dat{1},2); + M(:,1) = 1; + M(:,rk) = 1; + M(1,:) = 1; + M(rk,:) = 1; + +% Full leaf +elseif (Mh.typ == 2) + M = sparse(Mh.dim(1),Mh.dim(2)); + M(:,1) = 2; + M(:,end) = 2; + M(1,:) = 2; + M(end,:) = 2; + +% Sparse leaf +elseif (Mh.typ == 3) + M = 3*(abs(Mh.dat)>0); + if isempty(find(M,1)) + M(:,1) = 4; + M(:,end) = 4; + M(1,:) = 4; + M(end,:) = 4; + end + +% Unknown type +else + error('hmxSpy.m : unavailable case') +end + + +% Graphical representation +if (length(varargin) == 1) + spy(M==1,'b') + hold on + spy(M==2,'r') + spy(M==3,'m') + spy(M==4,'g') + hold off + title('openHmx : H-Matrix structure'); +end +end diff --git a/openHmx/hmxSubdivide.m b/openHmx/hmxSubdivide.m new file mode 100644 index 0000000..6a22645 --- /dev/null +++ b/openHmx/hmxSubdivide.m @@ -0,0 +1,44 @@ +function ind = hmxSubdivide(X) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Subdivide particles with median repartition | +%+========================================================================+ + +% Box definition for particles +Xmin = min(X,[],1); +Xmax = max(X,[],1); +Xdgl = Xmax-Xmin; + +% Largest dimension +[~,i] = max(Xdgl); + +% Median repartition on largest dimension +ind = (X(:,i)<=median(X(:,i))); + +% Recursion for worst cases +if (sum(ind)<0.25*size(X,1)) || (sum(ind)>0.75*size(X,1)) + I = setdiff(1:size(X,2),i); + ind = hmxSubdivide(X(:,I)); +end +end \ No newline at end of file diff --git a/openHmx/hmxTimes.m b/openHmx/hmxTimes.m new file mode 100644 index 0000000..2fd93e1 --- /dev/null +++ b/openHmx/hmxTimes.m @@ -0,0 +1,70 @@ +function Mh = hmxTimes(Ml,Mr) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Scalar product with H-Matrix | +%+========================================================================+ + +%%% H-Matrix .* H-Matrix +if isa(Ml,'hmx') && isa(Mr,'hmx') + Mh = []; + warning('hmxTimes.m : H-Matrix terms multiplication not yet implemented') + + +%%% H-Matrix .* scal || scal .* H-Matrix -> H-Matrix +else + % Input analysis + if isa(Ml,'hmx') + Mh = Ml; + x = Mr; + elseif isa(Mr,'hmx') + Mh = Mr; + x = Ml; + else + error('hmxTimes.m : unavailable case') + end + + % H-Matrix (recursion) + if (Mh.typ == 0) + for i = 1:4 + Mh.chd{i} = hmxTimes(x,Mh.chd{i}); + end + + % Compressed leaf + elseif (Mh.typ == 1) + Mh.dat{1} = x .* Mh.dat{1}; + + % Full leaf + elseif (Mh.typ == 2) + Mh.dat = x .* Mh.dat; + + % Sparse leaf + elseif (Mh.typ == 3) + Mh.dat = x .* Mh.dat; + + % Unknown type + else + error('hmxTimes.m : unavailable case') + end +end +end diff --git a/openHmx/hmxTranspose.m b/openHmx/hmxTranspose.m new file mode 100644 index 0000000..c41da40 --- /dev/null +++ b/openHmx/hmxTranspose.m @@ -0,0 +1,63 @@ +function Mh = hmxTranspose(Mh) +%+========================================================================+ +%| | +%| OPENHMX, H-MATRIX COMPRESSION AND ALGEBRA | +%| openHmx is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openHmx, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| [2] : 13th International Conference on Mathematical | | | +%| and Numerical Aspects of Wave Propagation, University of | | | +%| Minnesota, may 2017. "OpenHmX, an open-source H-Matrix | | | +%| toolbox in Matlab". | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Transposition of H-Matrix | +%+========================================================================+ + +% Dimensions +Mh.dim = [Mh.dim(2) Mh.dim(1)]; + +% H-Matrix (recursion) +if (Mh.typ == 0) + % Data + tmp = Mh.chd{2}; + Mh.chd{1} = hmxTranspose(Mh.chd{1}); + Mh.chd{2} = hmxTranspose(Mh.chd{3}); + Mh.chd{3} = hmxTranspose(tmp); + Mh.chd{4} = hmxTranspose(Mh.chd{4}); + + % Indices + I = [1 3 2 4]; + tmp = Mh.row; + Mh.row = Mh.col(I); + Mh.col = tmp(I); + +% Compressed leaf +elseif (Mh.typ == 1) + Mh.dat = {Mh.dat{2}.' , Mh.dat{1}.'}; + +% Full leaf +elseif (Mh.typ == 2) + Mh.dat = Mh.dat.'; + +% Sparse leaf +elseif (Mh.typ == 3) + Mh.dat = Mh.dat.'; + +% Unknown type +else + error('hmxTranspose.m : unavailable case') +end + +end diff --git a/openMsh/msh.m b/openMsh/msh.m new file mode 100644 index 0000000..2e3eea1 --- /dev/null +++ b/openMsh/msh.m @@ -0,0 +1,154 @@ +classdef msh +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Mesh class definition | +%+========================================================================+ + +properties + vtx = []; % VERTEX COORDINATES (3 dimensions) + elt = []; % ELEMENTS LIST (particles, edges, triangles or tetrahedron) + gss = 1; % NUMBER OF INTEGRATION POINTS +end + +methods + % CONSTRUCTOR + function mesh = msh(varargin) + % Read file + if (length(varargin) == 1) + mesh = msh; + ext = varargin{1}(end-2:end); + if strcmp(ext,'ply') + [mesh.vtx,mesh.elt] = mshReadPly(varargin{1}); + elseif strcmp(ext,'vtk') + [mesh.vtx,mesh.elt] = mshReadVtk(varargin{1}); + else + error('msh.m : unavailable case') + end + + % Use input data + elseif (length(varargin) == 2) + mesh.vtx = varargin{1}; + mesh.elt = varargin{2}; + end + + % Clean mesh + mesh = mshClean(mesh); + end + + % FREE BOUNDARY + function bnd2vtx = bnd(mesh) + bnd2vtx = mshBoundary(mesh); + end + + % CENTER + function X = ctr(mesh) + X = mshCenter(mesh); + end + + % EDGES + function [edg2vtx,elt2edg] = edg(mesh) + [edg2vtx,elt2edg] = mshEdge(mesh); + end + + % EDGES LENGTH + function lgt = edgLgt(mesh) + edg2vtx = edg(mesh); + lgt = mesh.vtx(edg2vtx(:,2),:) - mesh.vtx(edg2vtx(:,1),:); + lgt = sqrt(sum(lgt.^2,2)); + lgt = [min(lgt) max(lgt)]; + end + + % FACES + function [fce2vtx,elt2fce] = fce(mesh) + [fce2vtx,elt2fce] = mshFace(mesh); + end + + % NUMERICAL INTEGRATION + function I = integral(varargin) + I = mshIntegral(varargin); + end + + % MESH REPRESENTATION + function plot(varargin) + mshPlot(varargin); + end + + % GAUSSIAN QUADRATURE + function [X,W,elt2qud] = qud(mesh) + [X,W,elt2qud] = mshQuadrature(mesh); + end + + % SUBMESHING + function mesh = sub(mesh,Ielt) + mesh.elt = mesh.elt(Ielt,:); + mesh = mshClean(mesh); + end + + % SURFACES + function S = ndv(mesh) + S = mshNdvolume(mesh); + end + + + %%%%%%%%%%%%%%%%%%%%%%%% TRIANGULAR MESH ONLY %%%%%%%%%%%%%%%%%%%%%%%%% + % TANGENTS + function T = tgt(mesh) + if (size(mesh.elt,2) == 3) + T = cell(1,3); + for i = 1:3 + ip1 = mod(i,3)+1; + ip2 = mod(ip1,3)+1; + A = mesh.vtx(mesh.elt(:,ip1),:); + B = mesh.vtx(mesh.elt(:,ip2),:); + T{i} = (B-A)./(sqrt(sum((B-A).^2,2))*[1 1 1]); + end + else + error('msh.m : unavailable case') + end + end + + % NORMALS + function N = nrm(mesh) + T = mesh.tgt; + N = cross(T{1},T{2}); + N = N ./ (sqrt(sum(N.^2,2)) * [1 1 1]); + end + + % EDGES NORMALS + function Nu = nrmEdg(mesh) + Nu = cell(1,3); + for i = 1:3 + Nu{i} = cross(mesh.tgt{i},mesh.nrm); + end + end + + % GAUSSIAN NORMALES + function N = nrmQud(mesh) + x = mshReference(mesh); + N = zeros(size(x,1)*size(mesh.elt,1),size(mesh.vtx,2)); + for j = 1:size(x,1) + idx = (j:size(x,1):size(x,1) * size(mesh.elt,1))'; + N(idx,:) = mesh.nrm; + end + end + +end +end diff --git a/openMsh/mshBoundary.m b/openMsh/mshBoundary.m new file mode 100644 index 0000000..2584591 --- /dev/null +++ b/openMsh/mshBoundary.m @@ -0,0 +1,48 @@ +function bnd2vtx = mshBoundary(mesh) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Extract element from boundary | +%+========================================================================+ + +% Particles mesh +if (size(mesh.elt,2) == 1) + error('mshBoundary.m : unavailable case') + +% Edge mesh +elseif (size(mesh.elt,2) == 2) + edg2vtx = mesh.edg; + mlt = accumarray(edg2vtx(:),1,[size(mesh.vtx,1),1]); + bnd2vtx = find(mlt==1); + +% Triangular mesh +elseif (size(mesh.elt,2) == 3) + dt = triangulation(mesh.elt,mesh.vtx); + bnd2vtx = freeBoundary(dt); + +% Tetrahedron mesh +elseif (size(mesh.elt,2) == 4) + dt = triangulation(mesh.elt,mesh.vtx); + bnd2vtx = freeBoundary(dt); + +else + error('mshBoundary.m : unavailable case') +end +end diff --git a/openMsh/mshCenter.m b/openMsh/mshCenter.m new file mode 100644 index 0000000..262659c --- /dev/null +++ b/openMsh/mshCenter.m @@ -0,0 +1,34 @@ +function X = mshCenter(mesh) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Compute circumcenter for any dimension | +%+========================================================================+ + +% Initialize +[m,n] = size(mesh.elt); +X = zeros(m,size(mesh.vtx,2)); + +% Construction by element dimension +for i = 1:n + X = X + (1/n) .* mesh.vtx(mesh.elt(:,i),:); +end + +end diff --git a/openMsh/mshClean.m b/openMsh/mshClean.m new file mode 100644 index 0000000..1412bd0 --- /dev/null +++ b/openMsh/mshClean.m @@ -0,0 +1,37 @@ +function mesh = mshClean(mesh) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Clean vertex and renumber element from initial mesh | +%+========================================================================+ + +% Get vertex from initial numerotation +Ivtx = zeros(size(mesh.vtx,1),1); +Ivtx(mesh.elt(:)) = 1; +mesh.vtx = mesh.vtx(logical(Ivtx),:); + +% Reorder elements +Ivtx(Ivtx==1) = 1:sum(Ivtx,1); +if size(mesh.elt,1) == 1 + mesh.elt = Ivtx(mesh.elt)'; +else + mesh.elt = Ivtx(mesh.elt); +end +end diff --git a/openMsh/mshCube.m b/openMsh/mshCube.m new file mode 100644 index 0000000..f686c68 --- /dev/null +++ b/openMsh/mshCube.m @@ -0,0 +1,38 @@ +function mesh = mshCube(N,L) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Build uniform mesh for a cube | +%+========================================================================+ + +% Optimal number of point for each dimension +n = L/min(L); +n = round( n * (N/prod(n))^(1/3) ); + +% Delaunay mesh +x = -0.5*L(1) : L(1)/n(1) : 0.5*L(1); +y = -0.5*L(2) : L(2)/n(2) : 0.5*L(2); +z = -0.5*L(3) : L(3)/n(3) : 0.5*L(3); +[x,y,z] = meshgrid(x,y,z); +DT = delaunayTriangulation([x(:) y(:) z(:)]); + +% Build mesh +mesh = msh(DT.Points,DT.ConnectivityList); +end diff --git a/openMsh/mshDisk.m b/openMsh/mshDisk.m new file mode 100644 index 0000000..f8ee59c --- /dev/null +++ b/openMsh/mshDisk.m @@ -0,0 +1,56 @@ +function mesh = mshDisk(N,rad) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Build uniform mesh for a disk | +%+========================================================================+ + +% Radial discretisation +dr = sqrt(pi*rad^2/N); +dr = rad/ceil(rad/dr); +r = dr:dr:rad; + +% Angular uniform discretization +rho = cell(length(r),1); theta = rho; +for ir = 1:length(r) + dtheta = dr/r(ir); + dtheta = 2*pi/ceil(2*pi/dtheta); + theta{ir} = (0:dtheta:2*pi-dtheta)'; + rho{ir} = r(ir)*ones(length(theta{ir}),1); +end + +% Carthesian coordinates +[x,y] = pol2cart(cell2mat(theta),cell2mat(rho)); +X = [0 0 ; x y]; + +% Unicity test +tmp = unique(X,'rows','stable'); +if max(abs(X-tmp)) > 1e-12 + error('mshDisk : non unicity of vertices') +end + +% Delaunay triangulation +DT = delaunayTriangulation(x,y); + +% Final mesh +elt = DT.ConnectivityList; +vtx = [DT.Points,zeros(size(DT.Points,1),1)]; +mesh = msh(vtx,elt); +end diff --git a/openMsh/mshEdge.m b/openMsh/mshEdge.m new file mode 100644 index 0000000..7d01e9f --- /dev/null +++ b/openMsh/mshEdge.m @@ -0,0 +1,66 @@ +function [edg2vtx,elt2edg] = mshEdge(mesh) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Compute edges tables | +%+========================================================================+ + +% Particles mesh +if (size(mesh.elt,2) == 1) + error('mshEdge.m : unavailable case') + +% Edge mesh +elseif (size(mesh.elt,2) == 2) + edg2vtx = mesh.elt; + elt2edg = (1:size(mesh.elt,1))'; + +% Triangular mesh +elseif (size(mesh.elt,2) == 3) + % All edges + edg2vtx = [ mesh.elt(:,[1 2]) ; mesh.elt(:,[2 3]) ; mesh.elt(:,[3 1]) ]; + + % Edges unicity + tmp = sort(edg2vtx,2); + [~,I,elt2edg] = unique(tmp,'rows'); + + % Final Edges + edg2vtx = edg2vtx(I,:); + elt2edg = reshape(elt2edg,size(mesh.elt,1),size(mesh.elt,2)); + +% Tetrahedron mesh +elseif (size(mesh.elt,2) == 4) + % All edges + edg2vtx = [ mesh.elt(:,[1 2]) ; mesh.elt(:,[2 3]) ; mesh.elt(:,[3 1]) ; + mesh.elt(:,[1 4]) ; mesh.elt(:,[2 4]) ; mesh.elt(:,[3 4]) ]; + + % Edges sunicity + tmp = sort(edg2vtx,2); + [~,I,elt2edg] = unique(tmp,'rows'); + + % Final Edges + edg2vtx = edg2vtx(I,:); + elt2edg = reshape(elt2edg,size(mesh.elt,1),6); + +% Unknown type +else + error('mshEdge.m : unavailable case') +end + +end diff --git a/openMsh/mshFace.m b/openMsh/mshFace.m new file mode 100644 index 0000000..2ba4272 --- /dev/null +++ b/openMsh/mshFace.m @@ -0,0 +1,57 @@ +function [fce2vtx,elt2fce] = mshFace(mesh) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Compute face table | +%+========================================================================+ + +% Particles mesh +if (size(mesh.elt,2) == 1) + error('mshFace.m : unavailable case') + +% Edge mesh +elseif (size(mesh.elt,2) == 2) + error('mshFace.m : unavailable case') + +% Triangular mesh +elseif (size(mesh.elt,2) == 3) + fce2vtx = mesh.elt; + elt2fce = (1:size(mesh.elt,1))'; + +% Tetrahedron mesh +elseif (size(mesh.elt,2) == 4) + % All faces + fce2vtx = [ mesh.elt(:,[1,2,3]) ; mesh.elt(:,[2,3,4]) ; ... + mesh.elt(:,[3,4,1]) ; mesh.elt(:,[4,1,2]) ]; + + % Faces unicity + tmp = sort(fce2vtx,2); + [~,I,elt2fce] = unique(tmp,'rows'); + + % Final faces + fce2vtx = fce2vtx(I,:); + elt2fce = reshape(elt2fce,size(mesh.elt,1),size(mesh.elt,2)); + +% Unknown type +else + error('mshEdge.m : unavailable case') +end + +end diff --git a/openMsh/mshIntegral.m b/openMsh/mshIntegral.m new file mode 100644 index 0000000..e3c9448 --- /dev/null +++ b/openMsh/mshIntegral.m @@ -0,0 +1,347 @@ +function I = mshIntegral(data) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Numerical integation | +%+========================================================================+ + + +%%% NUMERICAL INTEGRATION --> \int_{mesh(x)} f(x) dx +if (length(data) == 2) + % Mesh integration data + Xmsh = data{1}; + [X,Wx] = Xmsh.qud; + + % Function to be applied + F = data{2}; + Fx = F(X); + if (size(Fx,2) > 1) + error('mshIntegral.m : unavailable case') + end + + % Integration + I = Wx' * Fx; + + +%%% FINITE ELEMENT INTEGRATION --> \int_{mesh(x)} f(x) psi(x) dx +elseif (length(data) == 3) && isa(data{2},'function_handle') && isa(data{3},'fem') + % Mesh integration data + Xmsh = data{1}; + [X,Wx] = Xmsh.qud; + Wx = spdiags(Wx,0,length(Wx),length(Wx)); + + % Function to be applied + F = data{2}; + Fx = F(X); + if (size(Fx,2) > 1) + error('mshIntegral.m : unavailable case') + end + + % Finite element matrix + v = data{3}; + Mv = v.dqm(Xmsh); + + % Integration + I = Fx.' * Wx * Mv; + + +%%% FINITE ELEMENT INTEGRATION --> \int_{mesh(x)} psi(x)' f(x) dx +elseif (length(data) == 3) && isa(data{2},'fem') && isa(data{3},'function_handle') + % Mesh integration data + Xmsh = data{1}; + [X,Wx] = Xmsh.qud; + Wx = spdiags(Wx,0,length(Wx),length(Wx)); + + % Finite element matrix + u = data{2}; + Mu = u.dqm(Xmsh); + + % Function to be applied + F = data{3}; + Fx = F(X); + if (size(Fx,2) > 1) + error('mshIntegral.m : unavailable case') + end + + % Integration + I = Mu' * Wx * Fx; + + +%%% FINITE ELEMENT OPERATOR --> \int_{mesh(x)} psi'(x) psi(x) dx +elseif (length(data) == 3) && isa(data{2},'fem') && isa(data{3},'fem') + % Mesh integration data + Xmsh = data{1}; + [~,Wx] = Xmsh.qud; + Wx = spdiags(Wx,0,length(Wx),length(Wx)); + + % Finite element matrix + u = data{2}; + Mu = u.dqm(Xmsh); + + % Finite element matrix + v = data{3}; + Mv = v.dqm(Xmsh); + + % Integration + if iscell(Mu) && iscell(Mv) + I = sparse(1,1); + for i = 1:3 + I = I + Mu{i}' * Wx * Mv{i}; + end + else + I = Mu' * Wx * Mv; + end + + +%%% FINITE ELEMENT OPERATOR --> \int_{mesh(x)} psi(x)' f(x) psi(x) dx +elseif (length(data) == 4) && isa(data{1},'msh') && isa(data{2},'fem') + % Mesh integration data + Xmsh = data{1}; + [X,Wx] = Xmsh.qud; + Nx = size(X,1); + Wx = spdiags(Wx,0,Nx,Nx); + + % Finite element matrix + u = data{2}; + Mu = u.dqm(Xmsh); + + % Function to be applied + F = data{3}; + Fx = F(X); + if (size(Fx,2) > 1) + error('mshIntegral.m : unavailable case') + else + Fx = spdiags(Fx,0,Nx,Nx); + end + + % Finite element matrix + v = data{4}; + Mv = v.dqm(Xmsh); + + % Integration + if iscell(Mu) && iscell(Mv) + I = sparse(1,1); + for i = 1:3 + I = I + Mu{i}' * Wx * Fx * Mv{i}; + end + else + I = Mu' * Wx * Fx * Mv; + end + + +%%% BOUNDARY ELEMENT INTEGRATION --> \int_{mesh(y)} f(x,y) psi(y) dy +elseif (length(data) == 4) && isnumeric(data{1}) && isa(data{2},'msh') + % Evaluation points + X = data{1}; + Nx = size(X,1); + + % Mesh integration data + Ymsh = data{2}; + [Y,Wy] = Ymsh.qud; + Ny = size(Y,1); + Wy = spdiags(Wy,0,Ny,Ny); + + % Function to be applied + F = data{3}; + Fxy = zeros(Nx,Ny); + for j = 1:Ny + Fxy(:,j) = F(X,Y(j,:)); + end + + % Finite element matrix + v = data{4}; + Mv = v.dqm(Ymsh); + + % Integration + I = Fxy * Wy * Mv; + + +%%% BOUNDARY ELEMENT INTEGRATION --> \int_{mesh(x)} psi(x)' f(x,y) dx +elseif (length(data) == 4) && isa(data{1},'msh') && isnumeric(data{2}) + % Mesh integration data + Xmsh = data{1}; + [X,Wx] = Xmsh.qud; + Nx = size(X,1); + Wx = spdiags(Wx,0,Nx,Nx); + + % Evaluation points + Y = data{2}; + Ny = size(Y,1); + + % Finite element matrix + u = data{3}; + Mu = u.dqm(Xmsh); + + % Function to be applied + F = data{4}; + Fxy = zeros(Nx,Ny); + for j = 1:Ny + Fxy(:,j) = F(X,Y(j,:)); + end + + % Integration + I = Mu' * Wx * Fxy; + + +%%% BOUNDARY ELEMENT OPERATOR --> \int_{mesh(x)} \int_{mesh(y)} psi(x)' f(x,y) psi(y) dxdy +elseif (length(data) == 5) && isa(data{1},'msh') && isa(data{2},'msh') + % Mesh integration data + Xmsh = data{1}; + [X,Wx] = Xmsh.qud; + Nx = size(X,1); + Wx = spdiags(Wx,0,Nx,Nx); + + % Mesh integration data + Ymsh = data{2}; + [Y,Wy] = Ymsh.qud; + Ny = size(Y,1); + Wy = spdiags(Wy,0,Ny,Ny); + + % Finite element matrix + u = data{3}; + Mu = u.dqm(Xmsh); + + % Function applied to quadrature + F = data{4}; + Fxy = zeros(Nx,Ny); + for j = 1:Ny + Fxy(:,j) = F(X,Y(j,:)); + end + + % Finite element matrix + v = data{5}; + Mv = v.dqm(Ymsh); + + % Integration + if iscell(Mu) && iscell(Mv) + I = 0; + for i = 1:3 + I = I + Mu{i}' * Wx * Fxy * Wy * Mv{i}; + end + else + I = Mu' * Wx * Fxy * Wy * Mv; + end + + +%%% H-MATRIX BOUNDARY ELEMENT INTEGRATION --> \int_{mesh(y)} f(x,y) psi(y) dy +elseif (length(data) == 5) && isnumeric(data{1}) && isa(data{2},'msh') + % Evaluation points + X = data{1}; + Nx = size(X,1); + + % Collocation identity matrix + Mx = speye(Nx,Nx); + + % Mesh integration data + Ymsh = data{2}; + [Y,Wy] = Ymsh.qud; + Wy = spdiags(Wy,0,length(Wy),length(Wy)); + + % Green kernel + green = data{3}; + + % Integrated finite element matrix + v = data{4}; + Mv = v.dqm(Ymsh); + Mv = Wy * Mv; + + % Accuracy + tol = data{5}; + + % H-Matrix integration + I = hmx(X,v.dof(Ymsh),Mx,X,green,Y,Mv,tol); + + +%%% H-MATRIX BOUNDARY ELEMENT INTEGRATION --> \int_{mesh(x)} psi(x)' f(x,y) dx +elseif (length(data) == 5) && isa(data{1},'msh') && isnumeric(data{2}) + % Mesh integration data + Xmsh = data{1}; + [X,Wx] = Xmsh.qud; + Wx = spdiags(Wx,0,length(Wx),length(Wx)); + + % Evaluation points + Y = data{2}; + Ny = size(Y,1); + + % Collocation identity matrix + My = speye(Ny,Ny); + + % Integrated finite element matrix + u = data{3}; + Mu = u.dqm(Xmsh); + Mu = Wx * Mu; + + % Green kernel + green = data{4}; + + % Accuracy + tol = data{5}; + + % H-Matrix integration + I = hmx(u.dof(Xmsh),Y,Mu,X,green,Y,My,tol); + + +%%% H-MATRIX BOUNDARY ELEMENT OPERATOR --> \int_{mesh(x)} \int_{mesh(y)} psi(x)' f(x,y) psi(y) dxdy +elseif (length(data) == 6) + % Mesh integration data + Xmsh = data{1}; + [X,Wx] = Xmsh.qud; + Wx = spdiags(Wx,0,length(Wx),length(Wx)); + + % Mesh integration data + Ymsh = data{2}; + [Y,Wy] = Ymsh.qud; + Wy = spdiags(Wy,0,length(Wy),length(Wy)); + + % Finite element matrix + u = data{3}; + Mu = u.dqm(Xmsh); + + % Green kernel + green = data{4}; + + % Finite element + v = data{5}; + Mv = v.dqm(Ymsh); + + % Integration + if iscell(Mu) && iscell(Mv) + for i = 1:3 + Mu{i} = Wx * Mu{i}; + Mv{i} = Wy * Mv{i}; + end + else + Mu = Wx * Mu; + Mv = Wy * Mv; + end + + % Accuracy + tol = data{6}; + + % H-Matrix integration + I = hmx(u.dof(Xmsh),v.dof(Ymsh),Mu,X,green,Y,Mv,tol); + + +% UNKNOWN +else + error('mshIntegral.m : unavailable case') +end + +end \ No newline at end of file diff --git a/openMsh/mshNdvolume.m b/openMsh/mshNdvolume.m new file mode 100644 index 0000000..b215cdf --- /dev/null +++ b/openMsh/mshNdvolume.m @@ -0,0 +1,65 @@ +function S = mshNdvolume(mesh) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Compute element volume of dimension n | +%+========================================================================+ + +% Particles mesh +if (size(mesh.elt,2) == 1) + error('mshSurface.m : unavailable case') + +% Edge mesh +elseif (size(mesh.elt,2) == 2) + % Basis vector + E1 = mesh.vtx(mesh.elt(:,2),:) - mesh.vtx(mesh.elt(:,1),:); + + % Surface + S = sqrt(sum(E1.^2,2)); + +% Triangular mesh +elseif (size(mesh.elt,2) == 3) + % Basis vector + E1 = mesh.vtx(mesh.elt(:,2),:) - mesh.vtx(mesh.elt(:,1),:); + E2 = mesh.vtx(mesh.elt(:,3),:) - mesh.vtx(mesh.elt(:,1),:); + E3 = cross(E1,E2) ; + + % Surface + S = 0.5*sqrt(sum(E3.^2,2)); + +% Tetrahedron mesh +elseif (size(mesh.elt,2) == 4) + % Basis vector + E1 = mesh.vtx(mesh.elt(:,2),:) - mesh.vtx(mesh.elt(:,1),:); + E2 = mesh.vtx(mesh.elt(:,3),:) - mesh.vtx(mesh.elt(:,1),:); + E3 = mesh.vtx(mesh.elt(:,4),:) - mesh.vtx(mesh.elt(:,1),:); + + % Surface + S = 1/6 .* abs( ... + E1(:,1) .* (E2(:,2).*E3(:,3) - E2(:,3).*E3(:,2)) ... + - E2(:,1) .* (E1(:,2).*E3(:,3) - E1(:,3).*E3(:,2)) ... + + E3(:,1) .* (E1(:,2).*E2(:,3) - E1(:,3).*E2(:,2)) ); + +% Unknown type +else + error('mshSurface.m : unavailable case') +end + +end diff --git a/openMsh/mshPlot.m b/openMsh/mshPlot.m new file mode 100644 index 0000000..30fa225 --- /dev/null +++ b/openMsh/mshPlot.m @@ -0,0 +1,80 @@ +function mshPlot(data) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Plot mesh with or without data | +%+========================================================================+ + +% Mesh +mesh = data{1}; + +% Particles mesh +if (size(mesh.elt,2) == 1) + x = mesh.vtx(mesh.elt,1); + y = mesh.vtx(mesh.elt,2); + z = mesh.vtx(mesh.elt,3); + if (length(data)==1) + plot3(x,y,z,'.k'); + else + plot3(x,y,z,data{2}); + end + +% Edge mesh +elseif (size(mesh.elt,2) == 2) + x = [mesh.vtx(mesh.elt(:,1),1) mesh.vtx(mesh.elt(:,2),1)]'; + y = [mesh.vtx(mesh.elt(:,1),2) mesh.vtx(mesh.elt(:,2),2)]'; + z = [mesh.vtx(mesh.elt(:,1),3) mesh.vtx(mesh.elt(:,2),3)]'; + if (length(data)==1) + plot3(x,y,z,'.-k'); + else + plot3(x,y,z,data{2}) + end + +% Triangular mesh +elseif (size(mesh.elt,2) == 3) + if (length(data) == 1) + V = zeros(size(mesh.elt,1),1); + elseif (numel(data{2}) == 1) + V = data{2} * ones(size(mesh.elt,1),1); + else + V = data{2}; + end + h = trisurf(mesh.elt,mesh.vtx(:,1),mesh.vtx(:,2),mesh.vtx(:,3),V); + if (length(data) == 1) + set(h,'EdgeColor','k'); + set(h,'FaceColor','w'); + hold on + plot3(mesh.vtx(:,1),mesh.vtx(:,2),mesh.vtx(:,3),'.k') + hold off + else + set(h,'EdgeColor','none'); + end + +% Tetrahedron mesh +elseif (size(mesh.elt,2) == 4) + fce2vtx = mesh.fce; + data{1} = msh(mesh.vtx,fce2vtx); + mshPlot(data); + +% Unknown type +else + error('mshPlot.m : unavailable case') +end +end diff --git a/openMsh/mshQuadrature.m b/openMsh/mshQuadrature.m new file mode 100644 index 0000000..4839cf9 --- /dev/null +++ b/openMsh/mshQuadrature.m @@ -0,0 +1,69 @@ +function [X,W,elt2qud] = mshQuadrature(mesh) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| François Alouges - CMAP, Ecole Polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Apply reference quadrature to any mesh | +%+========================================================================+ + +% Reference quadrature +[x,w] = mshReference(mesh); + +% Initialization +X = zeros(size(x,1)*size(mesh.elt,1),size(mesh.vtx,2)); +elt2qud = zeros(size(mesh.elt,1),size(x,1)); + +% For each quadrature point +for j = 1:size(x,1) + % Indice + idx = (j:size(x,1):size(x,1)*size(mesh.elt,1))'; + elt2qud(:,j) = idx; + + % Particles mesh + if (size(mesh.elt,2) == 1) + error('mshQuadrature.m : unavailable case') + + % Edge mesh + elseif (size(mesh.elt,2) == 2) + X(idx,:) = (1-x(j,1)) * mesh.vtx(mesh.elt(:,1),:) ... + + x(j,1) * mesh.vtx(mesh.elt(:,2),:) ; + + % Triangular mesh + elseif (size(mesh.elt,2) == 3) + X(idx,:) = (1-x(j,1)-x(j,2)) * mesh.vtx(mesh.elt(:,1),:) ... + + x(j,1) * mesh.vtx(mesh.elt(:,2),:) ... + + x(j,2) * mesh.vtx(mesh.elt(:,3),:); + + % Tetrahedron mesh + elseif (size(mesh.elt,2) == 4) + X(idx,:) = (1-x(j,1)-x(j,2)-x(j,3)) * mesh.vtx(mesh.elt(:,1),:) ... + + x(j,1) * mesh.vtx(mesh.elt(:,2),:) ... + + x(j,2) * mesh.vtx(mesh.elt(:,3),:) ... + + x(j,3) * mesh.vtx(mesh.elt(:,4),:); + + % Unknown type + else + error('mshQuadrature.m : unavailable case') + end +end + +% Quadrature weight +W = kron(mesh.ndv,w); +end \ No newline at end of file diff --git a/openMsh/mshReadPly.m b/openMsh/mshReadPly.m new file mode 100644 index 0000000..c90ff37 --- /dev/null +++ b/openMsh/mshReadPly.m @@ -0,0 +1,480 @@ +function [vertex,face] = mshReadPly(filename) +% read_ply - read data from PLY file. +% +% [vertex,face] = read_ply(filename); +% +% 'vertex' is a 'nb.vert x 3' array specifying the position of the vertices. +% 'face' is a 'nb.face x 3' array specifying the connectivity of the mesh. +% +% IMPORTANT: works only for triangular meshes. +% +% Copyright (c) 2003 Gabriel Peyr + +[d,c] = plyread(filename); + +vi = d.face.vertex_indices; +nf = length(vi); +face = zeros(nf,3); +for i=1:nf + face(i,:) = vi{i}+1; +end + +vertex = [d.vertex.x, d.vertex.y, d.vertex.z]; +end + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +function [Elements,varargout] = plyread(Path,Str) +%PLYREAD Read a PLY 3D data file. +% [DATA,COMMENTS] = PLYREAD(FILENAME) reads a version 1.0 PLY file +% FILENAME and returns a structure DATA. The fields in this structure +% are defined by the PLY header; each element type is a field and each +% element property is a subfield. If the file contains any comments, +% they are returned in a cell string array COMMENTS. +% +% [TRI,PTS] = PLYREAD(FILENAME,'tri') or +% [TRI,PTS,DATA,COMMENTS] = PLYREAD(FILENAME,'tri') converts vertex +% and face data into triangular connectivity and vertex arrays. The +% mesh can then be displayed using the TRISURF command. +% +% Note: This function is slow for large mesh files (+50K faces), +% especially when reading data with list type properties. +% +% Example: +% [Tri,Pts] = PLYREAD('cow.ply','tri'); +% trisurf(Tri,Pts(:,1),Pts(:,2),Pts(:,3)); +% colormap(gray); axis equal; +% +% See also: PLYWRITE + +% Pascal Getreuer 2004 + +[fid,Msg] = fopen(Path,'rt'); % open file in read text mode + +if fid == -1, error(Msg); end + +Buf = fscanf(fid,'%s',1); +if ~strcmp(Buf,'ply') + fclose(fid); + error('Not a PLY file.'); +end + + +%%% read header %%% + +Position = ftell(fid); +Format = ''; +NumComments = 0; +Comments = {}; % for storing any file comments +NumElements = 0; +NumProperties = 0; +Elements = []; % structure for holding the element data +ElementCount = []; % number of each type of element in file +PropertyTypes = []; % corresponding structure recording property types +ElementNames = {}; % list of element names in the order they are stored in the file +PropertyNames = []; % structure of lists of property names + +while 1 + Buf = fgetl(fid); % read one line from file + BufRem = Buf; + Token = {}; + Count = 0; + + while ~isempty(BufRem) % split line into tokens + [tmp,BufRem] = strtok(BufRem); + + if ~isempty(tmp) + Count = Count + 1; % count tokens + Token{Count} = tmp; + end + end + + if Count % parse line + switch lower(Token{1}) + case 'format' % read data format + if Count >= 2 + Format = lower(Token{2}); + + if Count == 3 & ~strcmp(Token{3},'1.0') + fclose(fid); + error('Only PLY format version 1.0 supported.'); + end + end + case 'comment' % read file comment + NumComments = NumComments + 1; + Comments{NumComments} = ''; + for i = 2:Count + Comments{NumComments} = [Comments{NumComments},Token{i},' ']; + end + case 'element' % element name + if Count >= 3 + if isfield(Elements,Token{2}) + fclose(fid); + error(['Duplicate element name, ''',Token{2},'''.']); + end + + NumElements = NumElements + 1; + NumProperties = 0; + Elements = setfield(Elements,Token{2},[]); + PropertyTypes = setfield(PropertyTypes,Token{2},[]); + ElementNames{NumElements} = Token{2}; + PropertyNames = setfield(PropertyNames,Token{2},{}); + CurElement = Token{2}; + ElementCount(NumElements) = str2double(Token{3}); + + if isnan(ElementCount(NumElements)) + fclose(fid); + error(['Bad element definition: ',Buf]); + end + else + error(['Bad element definition: ',Buf]); + end + case 'property' % element property + if ~isempty(CurElement) & Count >= 3 + NumProperties = NumProperties + 1; + eval(['tmp=isfield(Elements.',CurElement,',Token{Count});'],... + 'fclose(fid);error([''Error reading property: '',Buf])'); + + if tmp + error(['Duplicate property name, ''',CurElement,'.',Token{2},'''.']); + end + + % add property subfield to Elements + eval(['Elements.',CurElement,'.',Token{Count},'=[];'], ... + 'fclose(fid);error([''Error reading property: '',Buf])'); + % add property subfield to PropertyTypes and save type + eval(['PropertyTypes.',CurElement,'.',Token{Count},'={Token{2:Count-1}};'], ... + 'fclose(fid);error([''Error reading property: '',Buf])'); + % record property name order + eval(['PropertyNames.',CurElement,'{NumProperties}=Token{Count};'], ... + 'fclose(fid);error([''Error reading property: '',Buf])'); + else + fclose(fid); + + if isempty(CurElement) + error(['Property definition without element definition: ',Buf]); + else + error(['Bad property definition: ',Buf]); + end + end + case 'end_header' % end of header, break from while loop + break; + end + end +end + +%%% set reading for specified data format %%% + +if isempty(Format) + warning('Data format unspecified, assuming ASCII.'); + Format = 'ascii'; +end + +switch Format + case 'ascii' + Format = 0; + case 'binary_little_endian' + Format = 1; + case 'binary_big_endian' + Format = 2; + otherwise + fclose(fid); + error(['Data format ''',Format,''' not supported.']); +end + +if ~Format + Buf = fscanf(fid,'%f'); % read the rest of the file as ASCII data + BufOff = 1; +else + % reopen the file in read binary mode + fclose(fid); + + if Format == 1 + fid = fopen(Path,'r','ieee-le.l64'); % little endian + else + fid = fopen(Path,'r','ieee-be.l64'); % big endian + end + + % find the end of the header again (using ftell on the old handle doesn't give the correct position) + BufSize = 8192; + Buf = [blanks(10),char(fread(fid,BufSize,'uchar')')]; + i = []; + tmp = -11; + + while isempty(i) + i = findstr(Buf,['end_header',13,10]); % look for end_header + CR/LF + i = [i,findstr(Buf,['end_header',10])]; % look for end_header + LF + + if isempty(i) + tmp = tmp + BufSize; + Buf = [Buf(BufSize+1:BufSize+10),char(fread(fid,BufSize,'uchar')')]; + end + end + + % seek to just after the line feed + fseek(fid,i + tmp + 11 + (Buf(i + 10) == 13),-1); +end + + +%%% read element data %%% + +% PLY and MATLAB data types (for fread) +PlyTypeNames = {'char','uchar','short','ushort','int','uint','float','double', ... + 'char8','uchar8','short16','ushort16','int32','uint32','float32','double64'}; +MatlabTypeNames = {'schar','uchar','int16','uint16','int32','uint32','single','double'}; +SizeOf = [1,1,2,2,4,4,4,8]; % size in bytes of each type + +for i = 1:NumElements + % get current element property information + eval(['CurPropertyNames=PropertyNames.',ElementNames{i},';']); + eval(['CurPropertyTypes=PropertyTypes.',ElementNames{i},';']); + NumProperties = size(CurPropertyNames,2); + + % fprintf('Reading %s...\n',ElementNames{i}); + + if ~Format %%% read ASCII data %%% + for j = 1:NumProperties + Token = getfield(CurPropertyTypes,CurPropertyNames{j}); + + if strcmpi(Token{1},'list') + Type(j) = 1; + else + Type(j) = 0; + end + end + + % parse buffer + if ~any(Type) + % no list types + Data = reshape(Buf(BufOff:BufOff+ElementCount(i)*NumProperties-1),NumProperties,ElementCount(i))'; + BufOff = BufOff + ElementCount(i)*NumProperties; + else + ListData = cell(NumProperties,1); + + for k = 1:NumProperties + ListData{k} = cell(ElementCount(i),1); + end + + % list type + for j = 1:ElementCount(i) + for k = 1:NumProperties + if ~Type(k) + Data(j,k) = Buf(BufOff); + BufOff = BufOff + 1; + else + tmp = Buf(BufOff); + ListData{k}{j} = Buf(BufOff+(1:tmp))'; + BufOff = BufOff + tmp + 1; + end + end + end + end + else %%% read binary data %%% + % translate PLY data type names to MATLAB data type names + ListFlag = 0; % = 1 if there is a list type + SameFlag = 1; % = 1 if all types are the same + + for j = 1:NumProperties + Token = getfield(CurPropertyTypes,CurPropertyNames{j}); + + if ~strcmp(Token{1},'list') % non-list type + tmp = rem(strmatch(Token{1},PlyTypeNames,'exact')-1,8)+1; + + if ~isempty(tmp) + TypeSize(j) = SizeOf(tmp); + Type{j} = MatlabTypeNames{tmp}; + TypeSize2(j) = 0; + Type2{j} = ''; + + SameFlag = SameFlag & strcmp(Type{1},Type{j}); + else + fclose(fid); + error(['Unknown property data type, ''',Token{1},''', in ', ... + ElementNames{i},'.',CurPropertyNames{j},'.']); + end + else % list type + if length(Token) == 3 + ListFlag = 1; + SameFlag = 0; + tmp = rem(strmatch(Token{2},PlyTypeNames,'exact')-1,8)+1; + tmp2 = rem(strmatch(Token{3},PlyTypeNames,'exact')-1,8)+1; + + if ~isempty(tmp) & ~isempty(tmp2) + TypeSize(j) = SizeOf(tmp); + Type{j} = MatlabTypeNames{tmp}; + TypeSize2(j) = SizeOf(tmp2); + Type2{j} = MatlabTypeNames{tmp2}; + else + fclose(fid); + error(['Unknown property data type, ''list ',Token{2},' ',Token{3},''', in ', ... + ElementNames{i},'.',CurPropertyNames{j},'.']); + end + else + fclose(fid); + error(['Invalid list syntax in ',ElementNames{i},'.',CurPropertyNames{j},'.']); + end + end + end + + % read file + if ~ListFlag + if SameFlag + % no list types, all the same type (fast) + Data = fread(fid,[NumProperties,ElementCount(i)],Type{1})'; + else + % no list types, mixed type + Data = zeros(ElementCount(i),NumProperties); + + for j = 1:ElementCount(i) + for k = 1:NumProperties + Data(j,k) = fread(fid,1,Type{k}); + end + end + end + else + ListData = cell(NumProperties,1); + + for k = 1:NumProperties + ListData{k} = cell(ElementCount(i),1); + end + + if NumProperties == 1 + BufSize = 512; + SkipNum = 4; + j = 0; + + % list type, one property (fast if lists are usually the same length) + while j < ElementCount(i) + Position = ftell(fid); + % read in BufSize count values, assuming all counts = SkipNum + [Buf,BufSize] = fread(fid,BufSize,Type{1},SkipNum*TypeSize2(1)); + Miss = find(Buf ~= SkipNum); % find first count that is not SkipNum + fseek(fid,Position + TypeSize(1),-1); % seek back to after first count + + if isempty(Miss) % all counts are SkipNum + Buf = fread(fid,[SkipNum,BufSize],[int2str(SkipNum),'*',Type2{1}],TypeSize(1))'; + fseek(fid,-TypeSize(1),0); % undo last skip + + for k = 1:BufSize + ListData{1}{j+k} = Buf(k,:); + end + + j = j + BufSize; + BufSize = floor(1.5*BufSize); + else + if Miss(1) > 1 % some counts are SkipNum + Buf2 = fread(fid,[SkipNum,Miss(1)-1],[int2str(SkipNum),'*',Type2{1}],TypeSize(1))'; + + for k = 1:Miss(1)-1 + ListData{1}{j+k} = Buf2(k,:); + end + + j = j + k; + end + + % read in the list with the missed count + SkipNum = Buf(Miss(1)); + j = j + 1; + ListData{1}{j} = fread(fid,[1,SkipNum],Type2{1}); + BufSize = ceil(0.6*BufSize); + end + end + else + % list type(s), multiple properties (slow) + Data = zeros(ElementCount(i),NumProperties); + + for j = 1:ElementCount(i) + for k = 1:NumProperties + if isempty(Type2{k}) + Data(j,k) = fread(fid,1,Type{k}); + else + tmp = fread(fid,1,Type{k}); + ListData{k}{j} = fread(fid,[1,tmp],Type2{k}); + end + end + end + end + end + end + + % put data into Elements structure + for k = 1:NumProperties + if (~Format & ~Type(k)) | (Format & isempty(Type2{k})) + eval(['Elements.',ElementNames{i},'.',CurPropertyNames{k},'=Data(:,k);']); + else + eval(['Elements.',ElementNames{i},'.',CurPropertyNames{k},'=ListData{k};']); + end + end +end + +clear Data ListData; +fclose(fid); + +if (nargin > 1 & strcmpi(Str,'Tri')) | nargout > 2 + % find vertex element field + Name = {'vertex','Vertex','point','Point','pts','Pts'}; + Names = []; + + for i = 1:length(Name) + if any(strcmp(ElementNames,Name{i})) + Names = getfield(PropertyNames,Name{i}); + Name = Name{i}; + break; + end + end + + if any(strcmp(Names,'x')) & any(strcmp(Names,'y')) & any(strcmp(Names,'z')) + eval(['varargout{1}=[Elements.',Name,'.x,Elements.',Name,'.y,Elements.',Name,'.z];']); + else + varargout{1} = zeros(1,3); + end + + varargout{2} = Elements; + varargout{3} = Comments; + Elements = []; + + % find face element field + Name = {'face','Face','poly','Poly','tri','Tri'}; + Names = []; + + for i = 1:length(Name) + if any(strcmp(ElementNames,Name{i})) + Names = getfield(PropertyNames,Name{i}); + Name = Name{i}; + break; + end + end + + if ~isempty(Names) + % find vertex indices property subfield + PropertyName = {'vertex_indices','vertex_indexes','vertex_index','indices','indexes'}; + + for i = 1:length(PropertyName) + if any(strcmp(Names,PropertyName{i})) + PropertyName = PropertyName{i}; + break; + end + end + + if ~iscell(PropertyName) + % convert face index lists to triangular connectivity + eval(['FaceIndices=varargout{2}.',Name,'.',PropertyName,';']); + N = length(FaceIndices); + Elements = zeros(N*2,3); + Extra = 0; + + for k = 1:N + Elements(k,:) = FaceIndices{k}(1:3); + + for j = 4:length(FaceIndices{k}) + Extra = Extra + 1; + Elements(N + Extra,:) = [Elements(k,[1,j-1]),FaceIndices{k}(j)]; + end + end + Elements = Elements(1:N+Extra,:) + 1; + end + end +else + varargout{1} = Comments; +end +end \ No newline at end of file diff --git a/openMsh/mshReadVtk.m b/openMsh/mshReadVtk.m new file mode 100644 index 0000000..a2de66a --- /dev/null +++ b/openMsh/mshReadVtk.m @@ -0,0 +1,92 @@ +function [vertex,face] = mshReadVtk(filename, verbose) +% read_vtk - read data from VTK file. +% +% [vertex,face] = read_vtk(filename, verbose); +% +% 'vertex' is a 'nb.vert x 3' array specifying the position of the vertices. +% 'face' is a 'nb.face x 3' array specifying the connectivity of the mesh. +% +% Copyright (c) Mario Richtsfeld + +if nargin<2 + verbose = 1; +end + +fid = fopen(filename,'r'); +if( fid==-1 ) + error('Can''t open the file.'); + return; +end + +str = fgets(fid); % -1 if eof +if ~strcmp(str(3:5), 'vtk') + error('The file is not a valid VTK one.'); +end + +%%% read header %%% +str = fgets(fid); +str = fgets(fid); +str = fgets(fid); +str = fgets(fid); +nvert = sscanf(str,'%*s %d %*s', 1); + +% read vertices +[A,cnt] = fscanf(fid,'%f %f %f', 3*nvert); +if cnt~=3*nvert + warning('Problem in reading vertices.'); +end +A = reshape(A, 3, cnt/3); +vertex = A; + +% read polygons +str = fgets(fid); +str = fgets(fid); + +info = sscanf(str,'%c %*s %*s', 1); + +% if((info ~= 'P') && (info ~= 'V')) +% str = fgets(fid); +% info = sscanf(str,'%c %*s %*s', 1); +% end + +if(info == 'C') + + nface = sscanf(str,'%*s %d %*s', 1); + + [A,cnt] = fscanf(fid,'%d %d %d %d\n', 4*nface); + if cnt~=4*nface + warning('Problem in reading faces.'); + end + + A = reshape(A, 4, cnt/4); + face = A(2:4,:)+1; +end + +% if(info ~= 'P') +% face = 0; +% end + +% read vertex ids +% if(info == 'V') +% +% nv = sscanf(str,'%*s %d %*s', 1); +% +% [A,cnt] = fscanf(fid,'%d %d \n', 2*nv); +% if cnt~=2*nv +% warning('Problem in reading faces.'); +% end +% +% A = reshape(A, 2, cnt/2); +% face = repmat(A(2,:)+1, 3, 1); +% end + +%if((info ~= 'P') && (info ~= 'V')) +% face = 0; +%end + +vertex = vertex'; +face = face'; + +fclose(fid); + +return \ No newline at end of file diff --git a/openMsh/mshReference.m b/openMsh/mshReference.m new file mode 100644 index 0000000..b7cf28e --- /dev/null +++ b/openMsh/mshReference.m @@ -0,0 +1,142 @@ +function [x,w] = mshReference(mesh) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| François Alouges - CMAP, Ecole Polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Numerical quadrature for reference element | +%+========================================================================+ + +% Particles mesh +if (size(mesh.elt,2) == 1) + error('mshReference.m : unavailable case') + +% Edge mesh +elseif (size(mesh.elt,2) == 2) + if (mesh.gss == 1) + x = 0.5; + w = 1; + + else + error('mshReference.m : unavailable case') + end + +% Triangular mesh +elseif (size(mesh.elt,2) == 3) + if (mesh.gss == 1) + x = [1/3 1/3]; + w = 1; + + elseif (mesh.gss == 3) + x = [1/6 1/6 + 2/3 1/6 + 1/6 2/3]; + w = [1/3 1/3 1/3]'; + + elseif (mesh.gss == 7) + a = (155-sqrt(15))/1200; + b = (155+sqrt(15))/1200; + x = [1/3 1/3 + (6-sqrt(15))/21 (6-sqrt(15))/21 + (6-sqrt(15))/21 (9+2*sqrt(15))/21 + (9+2*sqrt(15))/21 (6-sqrt(15))/21 + (6+sqrt(15))/21 (6+sqrt(15))/21 + (6+sqrt(15))/21 (9-2*sqrt(15))/21 + (9-2*sqrt(15))/21 (6+sqrt(15))/21]; + w = [9/40 a a a b b b]'; + + elseif mesh.gss == 12 + A = 0.063089014491502; + B = 0.249286745170910; + C = 0.310352451033785; + D = 0.053145049844816; + P1 = 0.025422453185103; + P2 = 0.058393137863189; + P3 = 0.041425537809187; + x(1:mesh.gss,1) = [A 1-2*A A B 1-2*B B C D 1-C-D 1-C-D C D]; + x(1:mesh.gss,2) = [A A 1-2*A B B 1-2*B D C C D 1-C-D 1-C-D]; + w = [P1 P1 P1 P2 P2 P2 P3 P3 P3 P3 P3 P3]'*2; + + else + error('mshReference.m : unavailable case') + end + +% Tetrahedron mesh +elseif (size(mesh.elt,2) == 4) + if (mesh.gss == 1) + x = [1/4 1/4 1/4]; + w = 1; + + elseif (mesh.gss == 4) + a = (5-sqrt(5))/20; + b = (5+3*sqrt(5))/20; + x = [a a a; + a a b; + a b a; + b a a]; + w = [1/4 1/4 1/4 1/4]'; + + elseif (mesh.gss == 5) + a = 1/4; + b = 1/6; + c = 1/2; + x = [a a a; + b b b; + b b c; + b c b; + c b b]; + w = [-4/5 9/20 9/20 9/20 9/20]'; + + elseif (mesh.gss == 15) + a = 1/4; + b1 = (7+sqrt(15))/34; + b2 = (7-sqrt(15))/34; + c1 = (13-3*sqrt(15))/34; + c2 = (13+3*sqrt(15))/34; + d = (5-sqrt(15))/20; + e = (5+sqrt(15))/20; + x = [a a a; + b1 b1 b1; + b1 b1 c1; + b1 c1 b1; + c1 b1 b1; + b2 b2 b2; + b2 b2 c2; + b2 c2 b2; + c2 b2 b2; + d d e; + d e d; + e d d; + d e e; + e d e; + e e d]; + w1 = 6*(2665-14*sqrt(15))/226800; + w2 = 6*(2665+14*sqrt(15))/226800; + w = [48/405 w1 w1 w1 w1 w2 w2 w2 w2 30/567 30/567 30/567 30/567 30/567 30/567]'; + + else + error('mshReference.m : unavailable case') + end + +% Unknown type +else + error('mshReference.m : unavailable case') +end + +end diff --git a/openMsh/mshSemiAnalyticInt.m b/openMsh/mshSemiAnalyticInt.m new file mode 100644 index 0000000..ff7b38e --- /dev/null +++ b/openMsh/mshSemiAnalyticInt.m @@ -0,0 +1,109 @@ +function [Rm1,rRm1,gradRm1] = mshSemiAnalyticInt(X0,S,n,tau,nu,tol) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| François Alouges - CMAP, Ecole Polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Semi-analytic integration on triangle for set of particles| +%+========================================================================+ + +% Vector particles X0 -> Vertices of the triangle +NX0 = size(X0,1); +unNX0 = ones(NX0,1); +un3 = ones(1,3); +xX0S = unNX0*(S(:,1)') - X0(:,1)*un3; +yX0S = unNX0*(S(:,2)') - X0(:,2)*un3; +zX0S = unNX0*(S(:,3)') - X0(:,3)*un3; + +% Vector norm +nrmX0S = sqrt(xX0S.^2 + yX0S.^2 + zX0S.^2); + +% Height of particles to triangle +h = [xX0S(:,1),yX0S(:,1),zX0S(:,1)]*n'; + +% Soli angle (cf wikipedia) +ca = zeros(NX0,3); +for i = 1:3 + ip1 = mod(i,3) + 1; + ca(:,i) = 1./(nrmX0S(:,i).*nrmX0S(:,ip1)) .* ( ... + xX0S(:,i).*xX0S(:,ip1) + yX0S(:,i).*yX0S(:,ip1) + zX0S(:,i).*zX0S(:,ip1) ) ; +end +sa = sqrt(1-ca.^2); +omega = -pi; +for i = 1:3 + ip1 = mod(i,3) + 1; + ip2 = mod(ip1,3) + 1; + omega = omega + acos( (ca(:,i)-ca(:,ip1).*ca(:,ip2)) ./ (sa(:,ip1).*sa(:,ip2)) ); +end +omega = omega.*sign(h); +omega(abs(h)<=1e-8) = 0; + +% Output initialization +Rm1 = -h.*omega; +rRm1 = zeros(NX0,3); +gradRm1 = -omega*n; + +% Edge integration +for ia = 1:3 + % Edge numerotation + iap1 = mod(ia,3)+1; + iap2 = mod(iap1,3)+1; + + % Projections + ps = xX0S(:,iap1)*tau(ia,1) + yX0S(:,iap1)*tau(ia,2) + zX0S(:,iap1)*tau(ia,3); + psp1 = xX0S(:,iap2)*tau(ia,1) + yX0S(:,iap2)*tau(ia,2) + zX0S(:,iap2)*tau(ia,3); + ps2 = ps .* (nrmX0S(:,iap2)-nrmX0S(:,iap1)); + + % Length and height of the edge + ar = abs(psp1(1)-ps(1)); + xnu = [(xX0S(:,iap1) - ps.*tau(ia,1)), ... + (yX0S(:,iap1) - ps.*tau(ia,2)), ... + (zX0S(:,iap1) - ps.*tau(ia,3))] ; + ah = sqrt(sum(xnu.^2,2)); + + % Integration of 1/r on the edge - general case h>tol + intaRm1 = asinh(psp1./ah) - asinh(ps./ah); + + % Integration of 1/r on the edge - singular case + im = (nrmX0S(:,iap1)-abs(ps) < tol); + intaRm1(im) = 0; + il = logical((ps>tol) .* (psp1>tol) .* im); % particles on the left of the edge + intaRm1(il) = log(nrmX0S(il,iap2)./nrmX0S(il,iap1)); + ir = logical((ps<-tol) .* (psp1<-tol) .* im); % paticles of the right of the edge + intaRm1(ir) = -log(nrmX0S(ir,iap2)./nrmX0S(ir,iap1)); + + % Integration r on the edge + intaR = 0.5.*(ar.*nrmX0S(:,iap2) + intaRm1.*ah.^2 + ps2); + + % Integration of 1/r + Rm1 = Rm1 + intaRm1 .* (... + xX0S(:,iap1)*nu(ia,1) + ... + yX0S(:,iap1)*nu(ia,2) + ... + zX0S(:,iap1)*nu(ia,3) ); + + % Integration of r/r + rRm1 = rRm1 + intaR*nu(ia,:); + + % Integration of grad(1/|r|) + gradRm1 = gradRm1 + intaRm1*nu(ia,:); +end + +% Normal composant of grad(r) +rRm1 = rRm1 + (h.*Rm1)*n; +end diff --git a/openMsh/mshSphere.m b/openMsh/mshSphere.m new file mode 100644 index 0000000..58dcfab --- /dev/null +++ b/openMsh/mshSphere.m @@ -0,0 +1,40 @@ +function mesh = mshSphere(N,rad) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Build uniform mesh for a sphere | +%+========================================================================+ + +% Fibonnacci rules +or = (1+sqrt(5))/2; +theta = (mod((2*pi/or) .* (0:N-1),2*pi))'; +phi = asin( -1 + 2/(N-1) * (0:N-1))'; + +% Carthesian coordinates +[x,y,z] = sph2cart(theta,phi,rad); +X = [0 0 0 ; x y z]; + +% Delaunay triangulation +DT = delaunayTriangulation(X); +[elt,vtx] = freeBoundary(DT); + +% Mesh +mesh = msh(vtx,elt); +end diff --git a/openMsh/mshSquare.m b/openMsh/mshSquare.m new file mode 100644 index 0000000..30e4da8 --- /dev/null +++ b/openMsh/mshSquare.m @@ -0,0 +1,42 @@ +function mesh = mshSquare(N,L) +%+========================================================================+ +%| | +%| OPENMSH, MESH MANAGEMENT AND NUMERICAL QUADRATURE | +%| openMsh is part of GYPSYLAB toolbox - v0.20 | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. For openMsh, \ \| |/ / | +%| we suggest as reference : \ | | / | +%| [1] : www.cmap.polytechnique.fr/~aussal/gypsilab \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| François Alouges - CMAP, Ecole polytechnique | +%| Creation : 06.07.17 | +%| Last modif : 06.07.17 | +%| Synopsis : Build uniform mesh for a unit square | +%+========================================================================+ + +% Optimal number of point for each dimension +n = L/min(L); +n = round( n * (N/prod(n))^(1/2) ); + +% Delaunay mesh +x = -0.5*L(1) : L(1)/n(1) : 0.5*L(1); +y = -0.5*L(2) : L(2)/n(2) : 0.5*L(2); + +% Triangulation +[x,y] = meshgrid(x,y); +z = zeros(size(x)); +DT = delaunayTriangulation([x(:) y(:)]); +Points = [DT.Points z(:)]; + +% Build mesh +mesh = msh(Points,DT.ConnectivityList); +end \ No newline at end of file diff --git a/problems/cavityModeNeumann.m b/problems/cavityModeNeumann.m new file mode 100644 index 0000000..d229fe9 --- /dev/null +++ b/problems/cavityModeNeumann.m @@ -0,0 +1,191 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. You can \ \| |/ / | +%| refer to each library part each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Exterior eigen mode for a cubic cavity, neumann condition | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openFem') +addpath('../openHmx') +addpath('../openMsh') + +% Mise en route du calcul paralelle +% matlabpool; +% parpool(8) + +% Parameters +X0 = [0 0 -1]; +f = 300; +typ = 'P1'; +tol = 1e-3; + +% Spherical mesh +bnd = msh('meshes/unitCubeCavity_1e3.ply'); +bnd.gss = 3; + +% Radiating mesh +dom = msh('meshes/Oxz_1e4.ply'); + +% Wave number with high frequency security +k = f*2*pi/340; + +% Incident wave +PW = @(X) exp(1i*k*X*X0'); + +% Incident wave representation +figure +plot(bnd,real(PW(bnd.vtx))) +alpha(0.7) +hold on +plot(dom,real(PW(dom.vtx))) +axis equal; +title('Incident wave') +xlabel('X'); ylabel('Y'); zlabel('Z'); +shading interp +hold off + + +%%% SOLVE LINEAR PROBLEM +disp('~~~~~~~~~~~~~ SOLVE LINEAR PROBLEM ~~~~~~~~~~~~~') + +% Finite elements +u = fem(typ); +v = fem(typ); + +% Green kernel function --> G(x,y) = exp(ik|x-y|)/|x-y| +Gxy = @(X,Y) femGreenKernel(X,Y,'[exp(ikr)/r]',k); + +% Finite element boundary operator --> +% k^2 * \int_Sx \int_Sy n.psi(x) G(x,y) n.psi(y) dx dy +% - \int_Sx \int_Sy nxgrad(psi(x)) G(x,y) nxgrad(psi(y)) dx dy +tic +LHS = 1/(4*pi) .* (k^2 * single(integral(bnd,bnd,ndot(u),Gxy,ndot(v),tol)) ... + - single(integral(bnd,bnd,nxgrad(u),Gxy,nxgrad(v),tol))); +toc + +% Regularization +tic +LHS = LHS + 1/(4*pi) .* (k^2 * femRegularize(bnd,bnd,ndot(u),'[1/r]',ndot(v)) ... + - femRegularize(bnd,bnd,nxgrad(u),'[1/r]',nxgrad(v))); +toc + +% Structure +figure +spy(LHS) + +% LU factorization +tic +[Lh,Uh] = lu(LHS); +toc +figure +spy(Lh) +figure +spy(Uh) + +% Finite element incident wave trace --> \int_Sx psi(x) dnx(pw(x)) dx +gradxPW1 = @(X) 1i*k*X0(1) .* PW(X); +gradxPW2 = @(X) 1i*k*X0(2) .* PW(X); +gradxPW3 = @(X) 1i*k*X0(3) .* PW(X); +RHS = - (integral(bnd,ndot(u,1),gradxPW1) + ... + integral(bnd,ndot(u,2),gradxPW2) + ... + integral(bnd,ndot(u,3),gradxPW3) ); + +% Solve linear system [H] mu = - dnP0 +tic +mu = Uh \ (Lh \ RHS); % LHS \ RHS; +toc + + +%%% BOUNDARY RADIATION +disp('~~~~~~~~~~~~~ RADIATION ON THE BOUNDARY ~~~~~~~~~~~~~') + +% Finite element mass matrix --> \int_Sx psi(x)' psi(x) dx +Id = integral(bnd,u,v); + +% Green kernel function --> G(x,y) = exp(ik|x-y|)/|x-y| +Gxy1 = @(X,Y) femGreenKernel(X,Y,'grady[exp(ikr)/r]1',k); +Gxy2 = @(X,Y) femGreenKernel(X,Y,'grady[exp(ikr)/r]2',k); +Gxy3 = @(X,Y) femGreenKernel(X,Y,'grady[exp(ikr)/r]3',k); + +% Finite element boundary operator --> \int_Sx \int_Sy psi(x)' grady(G(x,y)) ny.psi(y) dx dy +tic +Dbnd = 1/(4*pi) .* (integral(bnd,bnd,u,Gxy1,ndot(v,1),tol) + ... + integral(bnd,bnd,u,Gxy2,ndot(v,2),tol) + ... + integral(bnd,bnd,u,Gxy3,ndot(v,3),tol) ) ; +toc + +% Regularization +tic +Dbnd = Dbnd + 1/(4*pi) .* (femRegularize(bnd,bnd,u,'grady[1/r]1',ndot(v,1)) + ... + femRegularize(bnd,bnd,u,'grady[1/r]2',ndot(v,2)) + ... + femRegularize(bnd,bnd,u,'grady[1/r]3',ndot(v,3)) ) ; +toc + +% Boundary solution +Psca = 0.5*mu + Id \ double(Dbnd * mu) ; +Pinc = PW(u.dof(bnd)); +Pbnd = Pinc + Psca; + +% Graphical representation +figure +plot(bnd,abs(Pbnd)) +alpha(0.7) +axis equal; +title('Total field solution') +shading interp +colorbar + + +%%% DOMAIN RADIATION +disp('~~~~~~~~~~~~~ RADIATION ON THE DOMAIN ~~~~~~~~~~~~~') + +% Finite element boundary operator --> \int_Sx \int_Sy psi(x)' grady(G(x,y)) ny.psi(y) dx dy +tic +Ddom = 1/(4*pi) .* (integral(dom.vtx,bnd,Gxy1,ndot(v,1),tol) + ... + integral(dom.vtx,bnd,Gxy2,ndot(v,2),tol) + ... + integral(dom.vtx,bnd,Gxy3,ndot(v,3),tol) ) ; +toc + +% Regularization +tic +Ddom = Ddom + 1/(4*pi) .* (femRegularize(dom.vtx,bnd,'grady[1/r]1',ndot(v,1)) + ... + femRegularize(dom.vtx,bnd,'grady[1/r]2',ndot(v,2)) + ... + femRegularize(dom.vtx,bnd,'grady[1/r]3',ndot(v,3)) ) ; +toc + +% Boundary solution +Psca = double(Ddom * mu) ; +Pinc = PW(dom.vtx); +Pdom = Pinc + Psca; + +% Graphical representation +figure +plot(dom,abs(Pdom)) +axis equal; +title('Total field solution') +shading interp +colorbar + + +disp('Done.') diff --git a/problems/cubeEigenValues.m b/problems/cubeEigenValues.m new file mode 100644 index 0000000..18fd94e --- /dev/null +++ b/problems/cubeEigenValues.m @@ -0,0 +1,129 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. You can \ \| |/ / | +%| refer to each library part each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Eigen values and vectors, cube with dirichlet condition | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openFem') +addpath('../openMsh') + +% Parameters +Nvtx = 1e3; +Neig = 10; +L = [1 0.5 0.5]; + +% Cube mesh +mesh = mshCube(Nvtx,L); +% load tetmesh +% mesh = msh(X,tet); +mesh.gss = 4; + +% Boundary mesh +bnd2vtx = mesh.bnd; +meshb = msh(mesh.vtx,bnd2vtx); + +% Half boundary +ctr = mesh.ctr; +Iplus = find(ctr(:,1)>0); +meshh = mesh.sub(Iplus); + +% Graphical representation +plot(mesh); +hold on +plot(meshh,'r') +hold off +axis equal; +title('Mesh representation') +xlabel('X'); ylabel('Y'); zlabel('Z'); +alpha(0.1) +hold on + +% Finites elements +u = fem('P1'); +v = fem('P1'); + +% Mass matrix +tic +M = integral(mesh,u,v); +toc +abs(sum(sum(M)) - prod(L))/prod(L) + +% Rigidity matrix +tic +K = integral(mesh,grad(u),grad(v)); +toc +sum(sum(K)) + +% Dirichlet elimination matrix +P = u.dir(mesh,meshb); + +% Eigen value problem matrices +A = P' * K * P; +B = P' * M * P; + +% Find eigen values +tic +[V,EV] = eigs(A,B,2*Neig,'SM'); +toc + +% Sort by ascending order +[EV,ind] = sort(sqrt(real(diag(EV)))); +V = V(:,ind); + +% Eigen vector for all surface and normalisation +V = P*V; +V = V./(max(max(abs(V)))); + +% Graphical representation +figure +for n = 1:9 + subplot(3,3,n) + plot(mesh,V(:,n)) + title(['k = ',num2str(EV(n))]) + shading interp + alpha(0.1) + axis equal off +end + +% Analytical solutions of eigenvalues for an arbitrary cube +ref = zeros(Neig^3,1); +l = 1; +for i = 1:Neig + for j = 1:Neig + for k = 1:Neig + ref(l) = pi*sqrt( (i/L(1))^2 + (j/L(2))^2 + (k/L(3))^2 ); + l = l+1; + end + end +end +ref = sort(ref); +ref = ref(1:Neig); + +% Error +sol = EV(1:Neig); +[ref sol abs(sol-ref)./ref] + + +disp('Done, thanks for use.') diff --git a/problems/diskEigenValues.m b/problems/diskEigenValues.m new file mode 100644 index 0000000..97aeb46 --- /dev/null +++ b/problems/diskEigenValues.m @@ -0,0 +1,122 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. You can \ \| |/ / | +%| refer to each library part each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Eigen values and vectors, disk with dirichlet condition | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openFem') +addpath('../openMsh') + +% Parameters +Nvtx = 1e3; +Neig = 10; + +% Disk mesh +mesh = mshDisk(Nvtx,1); +mesh.gss = 3; + +% Boundary mesh +bnd2vtx = mesh.bnd; +meshb = msh(mesh.vtx,bnd2vtx); + +% Graphical representation +plot(mesh); +hold on +plot(meshb,'-ob') +hold off +axis equal; +title('Mesh representation') +xlabel('X'); ylabel('Y'); zlabel('Z'); +alpha(0.99) +hold on + +% Finites elements +u = fem('P1'); +v = fem('P1'); + +% Mass matrix +tic +M = integral(mesh,u,v); +toc +abs(sum(sum(M)) - pi)/pi + +% Rigidity matrix +tic +K = integral(mesh,grad(u),grad(v)); +toc +sum(sum(K)) + +% Dirichlet elimination matrix +P = u.dir(mesh,meshb); + +% Eigen value problem matrices +A = P' * K * P; +B = P' * M * P; + +% Find eigen values +tic +[V,EV] = eigs(A,B,2*Neig,'SM'); +toc + +% Sort by ascending order +[EV,ind] = sort(sqrt(real(diag(EV)))); +[~,uni] = unique(floor(1e2*EV)); +V = V(:,ind); + +% Eigen vector for all surface and normalisation +V = P*V; +V = V./(max(max(abs(V)))); + +% Graphical representation +figure +for n = 1:9 + subplot(3,3,n) + tmp = msh([mesh.vtx(:,1:2) V(:,n)],mesh.elt); + plot(tmp,V(:,n)) + title(['k = ',num2str(EV(n))]) + shading interp + axis equal off +end + +% Analytical solutions of eigenvalues for an unitary disk +ref = zeros(Neig^2,1); +k= 1; +for i = 0:Neig + for j = 0:Neig + ref(k) = fzero(@(X) besselj(i,X),j); + k = k+1; + end +end +ref = ref(ref>1e-6); +ref = 1e-6*unique(ceil(ref*1e6)); +ref = ref(1:Neig); + +% Error +sol = EV(uni(1:length(ref))); +[ref sol abs(sol(1:length(ref))-ref)./ref] + + +disp('Done, thanks for use.') + diff --git a/problems/meshes/Oxz_1e4.ply b/problems/meshes/Oxz_1e4.ply new file mode 100644 index 0000000..df3dc45 --- /dev/null +++ b/problems/meshes/Oxz_1e4.ply @@ -0,0 +1,29612 @@ +ply +format ascii 1.0 +comment MyBEM generated PLY File +element vertex 10000 +property float x +property float y +property float z +element face 19602 +property list uchar int vertex_indices +end_header +0.000000 -3.000000 -3.000000 +0.000000 -3.000000 -2.939394 +0.000000 -3.000000 -2.878788 +0.000000 -3.000000 -2.818182 +0.000000 -3.000000 -2.757576 +0.000000 -3.000000 -2.696970 +0.000000 -3.000000 -2.636364 +0.000000 -3.000000 -2.575758 +0.000000 -3.000000 -2.515152 +0.000000 -3.000000 -2.454545 +0.000000 -3.000000 -2.393939 +0.000000 -3.000000 -2.333333 +0.000000 -3.000000 -2.272727 +0.000000 -3.000000 -2.212121 +0.000000 -3.000000 -2.151515 +0.000000 -3.000000 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851 964 837 +3 616 838 937 diff --git a/problems/sphereScattering.m b/problems/sphereScattering.m new file mode 100644 index 0000000..9048b77 --- /dev/null +++ b/problems/sphereScattering.m @@ -0,0 +1,66 @@ +function u = sphereScattering(name,bndCond,rho,k,X) +% Copyright (c) 20015-2017, Matthieu Aussal, all rights reserved. +% Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and +% ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). +% Computation of analytic field for helmoltz spherical scatering + +% Sign convention +if k <= 0 + sgnk = @(v) v; +else + sgnk = @(v) conj(v); +end +k = abs(k); + +% Spherical data +[~,theta,r] = cart2sph(X(:,1),X(:,2),X(:,3)); +theta = pi/2 - theta; r = r'; +u = zeros(1,length(theta)); + +% Boundary condition +if strcmp(bndCond,'dir') + jsph = @(n,z) sqrt(pi./(2.*z)) .* besselj(n+0.5,z); + hsph = @(n,z) sqrt(pi./(2.*z)) .* besselh(n+0.5,2,z); + alpha = @(n,z) - jsph(n,z)./hsph(n,z); +elseif strcmp(bndCond,'neu') + jsph = @(n,z) sqrt(pi./(2.*z)) .* besselj(n+0.5,z); + hsph = @(n,z) sqrt(pi./(2.*z)) .* besselh(n+0.5,2,z); + djsph = @(n,z) (n*jsph(n-1,z) - (n+1)*jsph(n+1,z))/(2*n+1) ; + dhsph = @(n,z) -(1i./z.^2 - djsph(n,z)*hsph(n,z))/jsph(n,z); + alpha = @(n,z) - djsph(n,z)./dhsph(n,z); +end + +% Infinite spherical radiation +if strcmp(name,'inf') + n = 0; + Pn = legendre(n,cos(theta)); + add = alpha(n,k*rho) .* Pn(1,:); + while norm(add,'inf') > 1e-10 + u = u + add; + n = n + 1; + Pn = legendre(n,cos(theta)); + add = (-1)^n * (2*n+1) * alpha(n,k*rho) .* Pn(1,:); + end + u = (1i/k) .* u.'; + +% Finite spherical radiation +elseif strcmp(name,'bnd') || strcmp(name,'dom') + n = 0; + while abs(alpha(n,k*max(r))) > 1e-10 + Pn = legendre(n,cos(theta)); + u = u + (1i)^n * (2*n+1) .* ... + (alpha(n,k*rho).*hsph(n,k*r)) .* Pn(1,:); % + n = n+1; + end + u = u.'; + if strcmp(name,'dom') + u(r \int_Sx psi(x)' psi(x) dx +Id = integral(bnd,u,v); + +% Green kernel function --> G(x,y) = exp(ik|x-y|)/|x-y| +Gxy1 = @(X,Y) femGreenKernel(X,Y,'grady[exp(ikr)/r]1',k); +Gxy2 = @(X,Y) femGreenKernel(X,Y,'grady[exp(ikr)/r]2',k); +Gxy3 = @(X,Y) femGreenKernel(X,Y,'grady[exp(ikr)/r]3',k); + +% Finite element boundary operator --> \int_Sx \int_Sy psi(x)' grady(G(x,y)) ny.psi(y) dx dy +tic +Dbnd = 1/(4*pi) .* (integral(bnd,bnd,u,Gxy1,ndot(v,1),tol) + ... + integral(bnd,bnd,u,Gxy2,ndot(v,2),tol) + ... + integral(bnd,bnd,u,Gxy3,ndot(v,3),tol) ) ; +toc + +% Regularization +tic +Dbnd = Dbnd + 1/(4*pi) .* (femRegularize(bnd,bnd,u,'grady[1/r]1',ndot(v,1)) + ... + femRegularize(bnd,bnd,u,'grady[1/r]2',ndot(v,2)) + ... + femRegularize(bnd,bnd,u,'grady[1/r]3',ndot(v,3)) ) ; +toc + +% Operator [Id/2 + D] +LHS = 0.5*Id + Dbnd; + +% Structure +figure +spy(LHS) + +% LU factorization +tic +[Lh,Uh] = lu(LHS); +toc +figure +spy(Lh) +figure +spy(Uh) + +% Finite element incident wave trace --> \int_Sx psi(x) pw(x) dx +RHS = - integral(bnd,u,PW); + +% Solve linear system [Id/2 + D] * mu = - P0 +tic +mu = Uh \ (Lh \ RHS); % LHS \ RHS; +toc + + +%%% INFINITE SOLUTION +disp('~~~~~~~~~~~~~ INFINITE RADIATION ~~~~~~~~~~~~~') + +% Plane waves direction +Ninf = 1e3; +theta = 2*pi/1e3 .* (1:1e3)'; +nu = [sin(theta),zeros(size(theta)),cos(theta)]; + +% Green kernel function +xdoty = @(X,Y) X(:,1).*Y(:,1) + X(:,2).*Y(:,2) + X(:,3).*Y(:,3); +Ginf1 = @(X,Y) 1/(4*pi) .* (-1i*k*X(:,1)) .* exp(-1i*k*xdoty(X,Y)); +Ginf2 = @(X,Y) 1/(4*pi) .* (-1i*k*X(:,2)) .* exp(-1i*k*xdoty(X,Y)); +Ginf3 = @(X,Y) 1/(4*pi) .* (-1i*k*X(:,3)) .* exp(-1i*k*xdoty(X,Y)); + +% Finite element infinite operator --> \int_Sy dny(exp(ik*nu.y)) * psi(y) dx +Dinf = integral(nu,bnd,Ginf1,ndot(v,1),1e-6) + ... + integral(nu,bnd,Ginf2,ndot(v,2),1e-6) + ... + integral(nu,bnd,Ginf3,ndot(v,3),1e-6) ; +figure +spy(Dinf) + +% Finite element radiation +sol = Dinf * mu; + +% Analytical solution +ref = sphereScattering('inf','dir',1,k,nu); +norm(ref-sol,2)/norm(ref,2) +norm(ref-sol,'inf')/norm(ref,'inf') + +% Graphical representation +figure +plot(theta,log(abs(sol)),'b',theta,log(abs(ref)),'--r') + + +%%% DOMAIN SOLUTION +disp('~~~~~~~~~~~~~ RADIATION ~~~~~~~~~~~~~') + +% Finite element boundary operator --> \int_Sx \int_Sy psi(x)' grady(G(x,y)) ny.psi(y) dx dy +tic +Ddom = 1/(4*pi) .* (integral(dom.vtx,bnd,Gxy1,ndot(v,1),tol) + ... + integral(dom.vtx,bnd,Gxy2,ndot(v,2),tol) + ... + integral(dom.vtx,bnd,Gxy3,ndot(v,3),tol) ) ; +toc + +% Regularization +tic +Ddom = Ddom + 1/(4*pi) .* (femRegularize(dom.vtx,bnd,'grady[1/r]1',ndot(v,1)) + ... + femRegularize(dom.vtx,bnd,'grady[1/r]2',ndot(v,2)) + ... + femRegularize(dom.vtx,bnd,'grady[1/r]3',ndot(v,3)) ) ; +toc + +% Structure +figure +spy(Ddom) + +% Boundary solution +Psca = 0.5*mu + Id \ (Dbnd * mu) ; +Pinc = PW(u.dof(bnd)); +Pbnd = Pinc + Psca; + +% Domain solution +Psca = Ddom * mu; +Pinc = PW(dom.vtx); +Pdom = Pinc + Psca; + +% Annulation sphere interieure +r = sqrt(sum(dom.vtx.^2,2)); +Pdom(r<=1.01) = Pinc(r<=1.01); + +% Graphical representation +figure +plot(bnd,abs(Pbnd)) +hold on +plot(dom,abs(Pdom)) +axis equal; +title('Total field solution') +shading interp +colorbar +hold off + + +%%% ANAYTICAL SOLUTIONS FOR COMPARISONS +% Analytical solution +Pbnd = sphereScattering('dom','dir',1,k,1.001*bnd.vtx) + PW(bnd.vtx); +Pdom = sphereScattering('dom','dir',1,k,dom.vtx) + PW(dom.vtx); + +% Solution representation +figure +plot(bnd,abs(Pbnd)) +hold on +plot(dom,abs(Pdom)) +axis equal; +title('Analytical solution') +shading interp +colorbar +hold off + +disp('Done.') diff --git a/problems/sphereScatteringDt.m b/problems/sphereScatteringDt.m new file mode 100644 index 0000000..a9b26ab --- /dev/null +++ b/problems/sphereScatteringDt.m @@ -0,0 +1,238 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. You can \ \| |/ / | +%| refer to each library part each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Solve boundary element neumann problem, Double Layer T | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openFem') +addpath('../openMsh') +addpath('../openHmx') + +% Mise en route du calcul paralelle +% matlabpool; +% parpool(8) + +% Parameters +N = 1e3 +tol = 1e-3 +typ = 'P1' +gss = 3 +X0 = [0 0 -1] + +% Spherical mesh +bnd = mshSphere(N,1); +bnd.gss = gss; + +% Radiative mesh +[x,y] = meshgrid(-3:0.1:3,-3:0.1:3); +DT = delaunayTriangulation(x(:),y(:)); +dom = msh([zeros(numel(x),1),DT.Points],DT.ConnectivityList); + +% Frequency adjusted to maximum esge size +lgt = bnd.edgLgt; +k = 1/lgt(2); +f = (k*340)/(2*pi); + +% Incident wave +PW = @(X) exp(1i*k*X*X0'); + +% Incident wave representation +figure +plot(bnd,real(PW(bnd.vtx))) +hold on +plot(dom,real(PW(dom.vtx))) +pts = bnd.ctr; +vct = bnd.nrm; +quiver3(pts(:,1),pts(:,2),pts(:,3),vct(:,1),vct(:,2),vct(:,3),'r'); +axis equal; +title('Incident wave') +xlabel('X'); ylabel('Y'); zlabel('Z'); +shading interp +hold off + + +%%% SOLVE LINEAR PROBLEM +disp('~~~~~~~~~~~~~ SOLVE LINEAR PROBLEM ~~~~~~~~~~~~~') + +% Finite elements +u = fem(typ); +v = fem(typ); + +% Finite element mass matrix --> \int_Sx psi(x)' psi(x) dx +Id = integral(bnd,u,v); + +% Green kernel function --> G(x,y) = exp(ik|x-y|)/|x-y| +Gxy1 = @(X,Y) femGreenKernel(X,Y,'gradx[exp(ikr)/r]1',k); +Gxy2 = @(X,Y) femGreenKernel(X,Y,'gradx[exp(ikr)/r]2',k); +Gxy3 = @(X,Y) femGreenKernel(X,Y,'gradx[exp(ikr)/r]3',k); + +% Finite element boundary operator --> \int_Sx \int_Sy nx.psi(x)' gradx(G(x,y)) psi(y) dx dy +tic +Dtbnd = 1/(4*pi) .* (integral(bnd,bnd,ndot(u,1),Gxy1,v,tol) + ... + integral(bnd,bnd,ndot(u,2),Gxy2,v,tol) + ... + integral(bnd,bnd,ndot(u,3),Gxy3,v,tol) ) ; +toc + +% Regularization +tic +Dtbnd = Dtbnd + 1/(4*pi) .* (femRegularize(bnd,bnd,ndot(u,1),'gradx[1/r]1',v) + ... + femRegularize(bnd,bnd,ndot(u,2),'gradx[1/r]2',v) + ... + femRegularize(bnd,bnd,ndot(u,3),'gradx[1/r]3',v) ) ; +toc + +% Operator [Id/2-Dt] +LHS = 0.5*Id - Dtbnd; + +% Structure +figure +spy(LHS) + +% LU factorization +tic +[Lh,Uh] = lu(LHS); +toc +figure +spy(Lh) +figure +spy(Uh) + +% Finite element incident wave trace --> \int_Sx psi(x) dnx(pw(x)) dx +gradxPW1 = @(X) 1i*k*X0(1) .* PW(X); +gradxPW2 = @(X) 1i*k*X0(2) .* PW(X); +gradxPW3 = @(X) 1i*k*X0(3) .* PW(X); +RHS = - (integral(bnd,ndot(u,1),gradxPW1) + ... + integral(bnd,ndot(u,2),gradxPW2) + ... + integral(bnd,ndot(u,3),gradxPW3) ); + +% Solve linear system [Id/2-Dt] * lambda = - dnP0 +tic +lambda = Uh \ (Lh \ RHS); % LHS \ RHS; +toc + + +%%% INFINITE SOLUTION +disp('~~~~~~~~~~~~~ INFINITE RADIATION ~~~~~~~~~~~~~') + +% Plane waves direction +Ninf = 1e3; +theta = 2*pi/1e3 .* (1:1e3)'; +nu = [sin(theta),zeros(size(theta)),cos(theta)]; + +% Green kernel function +xdoty = @(X,Y) X(:,1).*Y(:,1) + X(:,2).*Y(:,2) + X(:,3).*Y(:,3); +Ginf = @(X,Y) 1/(4*pi) .* exp(-1i*k*xdoty(X,Y)); + +% Finite element infinite operator --> \int_Sy exp(ik*nu.y) * psi(y) dx +Sinf = integral(nu,bnd,Ginf,v,1e-6); +figure +spy(Sinf) + +% Finite element radiation +sol = - Sinf * lambda; + +% Analytical solution +ref = sphereScattering('inf','neu',1,k,nu); +norm(ref-sol,2)/norm(ref,2) +norm(ref-sol,'inf')/norm(ref,'inf') + +% Graphical representation +figure +plot(theta,log(abs(sol)),'b',theta,log(abs(ref)),'--r') + + +%%% DOMAIN SOLUTION +disp('~~~~~~~~~~~~~ RADIATION ~~~~~~~~~~~~~') + +% Green kernel +Gxy = @(X,Y) femGreenKernel(X,Y,'[exp(ikr)/r]',k); + +% Finite element boundary operator --> \int_Sx \int_Sy psi(x)' G(x,y) psi(y) dy +tic +Sbnd = 1/(4*pi) .* integral(bnd,bnd,u,Gxy,v,tol); +toc + +% Regularization +tic +Sbnd = Sbnd + 1/(4*pi) .* femRegularize(bnd,bnd,u,'[1/r]',v); +toc + +% Finite element radiative operator --> \int_Sy G(x,y) psi(y) dy +tic +Sdom = 1/(4*pi) .* integral(dom.vtx,bnd,Gxy,v,tol); +toc + +% Regularization +tic +Sdom = Sdom + 1/(4*pi) .* femRegularize(dom.vtx,bnd,'[1/r]',v); +toc + +% Structure +figure +spy(Sdom) + +% Boundary solution +Ibnd = integral(bnd,u,v); +Psca = - Ibnd \ (Sbnd * lambda) ; +Pinc = PW(u.dof(bnd)); +Pbnd = Pinc + Psca; + +% Domain solution +Psca = - Sdom * lambda; +Pinc = PW(dom.vtx); +Pdom = Pinc + Psca; + +% Annulation sphere interieure +r = sqrt(sum(dom.vtx.^2,2)); +Pdom(r<=1.01) = Pinc(r<=1.01); + +% Graphical representation +figure +plot(bnd,abs(Pbnd)) +hold on +plot(dom,abs(Pdom)) +axis equal; +title('Total field solution') +shading interp +colorbar +hold off + + +%%% ANAYTICAL SOLUTIONS FOR COMPARISONS +% Analytical solution +Pbnd = sphereScattering('dom','neu',1,k,1.001*bnd.vtx) + PW(bnd.vtx); +Pdom = sphereScattering('dom','neu',1,k,dom.vtx) + PW(dom.vtx); + +% Solution representation +figure +plot(bnd,abs(Pbnd)) +hold on +plot(dom,abs(Pdom)) +axis equal; +title('Analytical solution') +shading interp +colorbar +hold off + +disp('Done.') diff --git a/problems/sphereScatteringN.m b/problems/sphereScatteringN.m new file mode 100644 index 0000000..2fae05c --- /dev/null +++ b/problems/sphereScatteringN.m @@ -0,0 +1,249 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. You can \ \| |/ / | +%| refer to each library part each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Solve boundary element neumann problem, Hypersingular | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openFem') +addpath('../openMsh') +addpath('../openHmx') + +% Mise en route du calcul paralelle +% matlabpool; +% parpool(8) + +% Parameters +N = 1e3 +tol = 1e-3 +typ = 'P1' +gss = 3 +X0 = [0 0 -1] + +% Spherical mesh +bnd = mshSphere(N,1); +bnd.gss = gss; + +% Radiative mesh +[x,y] = meshgrid(-3:0.1:3,-3:0.1:3); +DT = delaunayTriangulation(x(:),y(:)); +dom = msh([zeros(numel(x),1),DT.Points],DT.ConnectivityList); + +% Frequency adjusted to maximum esge size +lgt = bnd.edgLgt; +k = 1/lgt(2); +f = (k*340)/(2*pi); + +% Incident wave +PW = @(X) exp(1i*k*X*X0'); + +% Incident wave representation +figure +plot(bnd,real(PW(bnd.vtx))) +hold on +plot(dom,real(PW(dom.vtx))) +pts = bnd.ctr; +vct = bnd.nrm; +quiver3(pts(:,1),pts(:,2),pts(:,3),vct(:,1),vct(:,2),vct(:,3),'r'); +axis equal; +title('Incident wave') +xlabel('X'); ylabel('Y'); zlabel('Z'); +shading interp +% camlight +% material dull +% lighting phong +hold off + + +%%% SOLVE LINEAR PROBLEM +disp('~~~~~~~~~~~~~ SOLVE LINEAR PROBLEM ~~~~~~~~~~~~~') + +% Finite elements +u = fem(typ); +v = fem(typ); + +% Green kernel function --> G(x,y) = exp(ik|x-y|)/|x-y| +Gxy = @(X,Y) femGreenKernel(X,Y,'[exp(ikr)/r]',k); + +% Finite element boundary operator --> +% k^2 * \int_Sx \int_Sy n.psi(x) G(x,y) n.psi(y) dx dy +% - \int_Sx \int_Sy nxgrad(psi(x)) G(x,y) nxgrad(psi(y)) dx dy +tic +LHS = 1/(4*pi) .* (k^2 * integral(bnd,bnd,ndot(u),Gxy,ndot(v),tol) ... + - integral(bnd,bnd,nxgrad(u),Gxy,nxgrad(v),tol)); +toc + +% Regularization +tic +LHS = LHS + 1/(4*pi) .* (k^2 * femRegularize(bnd,bnd,ndot(u),'[1/r]',ndot(v)) ... + - femRegularize(bnd,bnd,nxgrad(u),'[1/r]',nxgrad(v))); +toc + +% Structure +figure +spy(LHS) + +% LU factorization +tic +[Lh,Uh] = lu(LHS); +toc +figure +spy(Lh) +figure +spy(Uh) + +% Finite element incident wave trace --> \int_Sx psi(x) dnx(pw(x)) dx +gradxPW1 = @(X) 1i*k*X0(1) .* PW(X); +gradxPW2 = @(X) 1i*k*X0(2) .* PW(X); +gradxPW3 = @(X) 1i*k*X0(3) .* PW(X); +RHS = - (integral(bnd,ndot(u,1),gradxPW1) + ... + integral(bnd,ndot(u,2),gradxPW2) + ... + integral(bnd,ndot(u,3),gradxPW3) ); + +% Solve linear system [H] mu = - dnP0 +tic +mu = Uh \ (Lh \ RHS); % LHS \ RHS; +toc + + +%%% INFINITE SOLUTION +disp('~~~~~~~~~~~~~ INFINITE RADIATION ~~~~~~~~~~~~~') + +% Plane waves direction +Ninf = 1e3; +theta = 2*pi/1e3 .* (1:1e3)'; +nu = [sin(theta),zeros(size(theta)),cos(theta)]; + +% Green kernel function +xdoty = @(X,Y) X(:,1).*Y(:,1) + X(:,2).*Y(:,2) + X(:,3).*Y(:,3); +Ginf1 = @(X,Y) 1/(4*pi) .* (-1i*k*X(:,1)) .* exp(-1i*k*xdoty(X,Y)); +Ginf2 = @(X,Y) 1/(4*pi) .* (-1i*k*X(:,2)) .* exp(-1i*k*xdoty(X,Y)); +Ginf3 = @(X,Y) 1/(4*pi) .* (-1i*k*X(:,3)) .* exp(-1i*k*xdoty(X,Y)); + +% Finite element infinite operator --> \int_Sy dny(exp(ik*nu.y)) * psi(y) dx +Dinf = integral(nu,bnd,Ginf1,ndot(v,1),1e-6) + ... + integral(nu,bnd,Ginf2,ndot(v,2),1e-6) + ... + integral(nu,bnd,Ginf3,ndot(v,3),1e-6) ; +figure +spy(Dinf) + +% Finite element radiation +sol = Dinf * mu; + +% Analytical solution +ref = sphereScattering('inf','neu',1,k,nu); +norm(ref-sol,2)/norm(ref,2) +norm(ref-sol,'inf')/norm(ref,'inf') + +% Graphical representation +figure +plot(theta,log(abs(sol)),'b',theta,log(abs(ref)),'--r') + + +%%% DOMAIN SOLUTION +disp('~~~~~~~~~~~~~ RADIATION ~~~~~~~~~~~~~') + +% Finite element mass matrix --> \int_Sx psi(x)' psi(x) dx +Id = integral(bnd,u,v); + +% Green kernel function --> G(x,y) = exp(ik|x-y|)/|x-y| +Gxy1 = @(X,Y) femGreenKernel(X,Y,'grady[exp(ikr)/r]1',k); +Gxy2 = @(X,Y) femGreenKernel(X,Y,'grady[exp(ikr)/r]2',k); +Gxy3 = @(X,Y) femGreenKernel(X,Y,'grady[exp(ikr)/r]3',k); + +% Finite element boundary operator --> \int_Sx \int_Sy psi(x)' grady(G(x,y)) ny.psi(y) dx dy +tic +Dbnd = 1/(4*pi) .* (integral(bnd,bnd,u,Gxy1,ndot(v,1),tol) + ... + integral(bnd,bnd,u,Gxy2,ndot(v,2),tol) + ... + integral(bnd,bnd,u,Gxy3,ndot(v,3),tol) ) ; +toc + +% Regularization +tic +Dbnd = Dbnd + 1/(4*pi) .* (femRegularize(bnd,bnd,u,'grady[1/r]1',ndot(v,1)) + ... + femRegularize(bnd,bnd,u,'grady[1/r]2',ndot(v,2)) + ... + femRegularize(bnd,bnd,u,'grady[1/r]3',ndot(v,3)) ) ; +toc + +% Finite element boundary operator --> \int_Sx \int_Sy psi(x)' grady(G(x,y)) ny.psi(y) dx dy +tic +Ddom = 1/(4*pi) .* (integral(dom.vtx,bnd,Gxy1,ndot(v,1),tol) + ... + integral(dom.vtx,bnd,Gxy2,ndot(v,2),tol) + ... + integral(dom.vtx,bnd,Gxy3,ndot(v,3),tol) ) ; +toc + +% Regularization +tic +Ddom = Ddom + 1/(4*pi) .* (femRegularize(dom.vtx,bnd,'grady[1/r]1',ndot(v,1)) + ... + femRegularize(dom.vtx,bnd,'grady[1/r]2',ndot(v,2)) + ... + femRegularize(dom.vtx,bnd,'grady[1/r]3',ndot(v,3)) ) ; +toc + +% Structure +figure +spy(Ddom) + +% Boundary solution +Psca = 0.5*mu + Id \ (Dbnd * mu) ; +Pinc = PW(u.dof(bnd)); +Pbnd = Pinc + Psca; + +% Domain solution +Psca = Ddom * mu; +Pinc = PW(dom.vtx); +Pdom = Pinc + Psca; + +% Annulation sphere interieure +r = sqrt(sum(dom.vtx.^2,2)); +Pdom(r<=1.01) = Pinc(r<=1.01); + +% Graphical representation +figure +plot(bnd,abs(Pbnd)) +hold on +plot(dom,abs(Pdom)) +axis equal; +title('Total field solution') +shading interp +colorbar +hold off + + +%%% ANAYTICAL SOLUTIONS FOR COMPARISONS +% Analytical solution +Pbnd = sphereScattering('dom','neu',1,k,1.001*bnd.vtx) + PW(bnd.vtx); +Pdom = sphereScattering('dom','neu',1,k,dom.vtx) + PW(dom.vtx); + +% Solution representation +figure +plot(bnd,abs(Pbnd)) +hold on +plot(dom,abs(Pdom)) +axis equal; +title('Analytical solution') +shading interp +colorbar +hold off + +disp('Done.') diff --git a/problems/sphereScatteringS.m b/problems/sphereScatteringS.m new file mode 100644 index 0000000..aaa2554 --- /dev/null +++ b/problems/sphereScatteringS.m @@ -0,0 +1,211 @@ +%| | +%| THE GYPSILAB TOOLBOX - v0.20 | +%| www.cmap.polytechnique.fr/~aussal/gypsilab | +%| | +%| Copyright (c) 20015-2017, Ecole polytechnique, all rights reserved. | +%| Licence Creative Commons BY-NC-SA 4.0, Attribution, NonCommercial and | +%| ShareAlike (see http://creativecommons.org/licenses/by-nc-sa/4.0/). | +%| This software is the property from Centre de Mathematiques Appliquees | +%| de l'Ecole polytechnique, route de Saclay, 91128 Palaiseau, France. | +%| _ _ _ | +%| Please acknowledge the GYPSILAB toolbox in programs | | | | | | | +%| or publications in which you use the code. You can \ \| |/ / | +%| refer to each library part each part for references. \ | | / | +%| \ / | +%| | | | +%|_______________________________________________________________|_|______| +%| Author(s) : Matthieu Aussal - CMAP, Ecole polytechnique | +%| Creation : 14.03.17 | +%| Last modif : 21.06.17 | +%| Synopsis : Solve boundary element dirichlet problem, Single Layer | +%+========================================================================+ + +% Cleaning +clear all +close all +clc + +% Library path +addpath('../openFem') +addpath('../openMsh') +addpath('../openHmx') + +% Mise en route du calcul paralelle +% matlabpool; +% parpool(8) + +% Parameters +N = 1e3 +tol = 1e-3 +typ = 'P1' +gss = 3 +X0 = [0 0 -1] + +% Spherical mesh +bnd = mshSphere(N,1); +bnd.gss = gss; + +% Radiative mesh +[x,y] = meshgrid(-3:0.1:3,-3:0.1:3); +DT = delaunayTriangulation(x(:),y(:)); +dom = msh([zeros(numel(x),1),DT.Points],DT.ConnectivityList); + +% Frequency adjusted to maximum esge size +lgt = bnd.edgLgt; +k = 1/lgt(2) +f = (k*340)/(2*pi) + +% Incident wave +PW = @(X) exp(1i*k*X*X0'); + +% Incident wave representation +figure +plot(bnd,real(PW(bnd.vtx))) +hold on +plot(dom,real(PW(dom.vtx))) +pts = bnd.ctr; +vct = bnd.nrm; +quiver3(pts(:,1),pts(:,2),pts(:,3),vct(:,1),vct(:,2),vct(:,3),'r'); +axis equal; +title('Incident wave') +xlabel('X'); ylabel('Y'); zlabel('Z'); +shading interp +hold off + + +%%% SOLVE LINEAR PROBLEM +disp('~~~~~~~~~~~~~ SOLVE LINEAR PROBLEM ~~~~~~~~~~~~~') + +% Green kernel function --> G(x,y) = exp(ik|x-y|)/|x-y| +Gxy = @(X,Y) femGreenKernel(X,Y,'[exp(ikr)/r]',k); + +% Finite elements +u = fem(typ); +v = fem(typ); + +% Finite element boundary operator --> \int_Sx \int_Sy psi(x)' G(x,y) psi(y) dx dy +tic +LHS = 1/(4*pi) .* single(integral(bnd,bnd,u,Gxy,v,tol)); +toc + +% Regularization +tic +LHS = LHS + 1/(4*pi) .* femRegularize(bnd,bnd,u,'[1/r]',v); +toc + +% Structure +figure +spy(LHS) + +% LU factorization +tic +[Lh,Uh] = lu(LHS); +toc +figure +spy(Lh) +figure +spy(Uh) + +% Finite element incident wave trace --> \int_Sx psi(x)' pw(x) dx +RHS = integral(bnd,u,PW); + +% Solve linear system [-S] * lambda = - P0 +tic +lambda = Uh \ (Lh \ RHS); % LHS \ RHS; +toc + + +%%% INFINITE SOLUTION +disp('~~~~~~~~~~~~~ INFINITE RADIATION ~~~~~~~~~~~~~') + +% Plane waves direction +Ninf = 1e3; +theta = 2*pi/1e3 .* (1:1e3)'; +nu = [sin(theta),zeros(size(theta)),cos(theta)]; + +% Green kernel function +xdoty = @(X,Y) X(:,1).*Y(:,1) + X(:,2).*Y(:,2) + X(:,3).*Y(:,3); +Ginf = @(X,Y) 1/(4*pi) .* exp(-1i*k*xdoty(X,Y)); + +% Finite element infinite operator --> \int_Sy exp(ik*nu.y) * psi(y) dx +Sinf = integral(nu,bnd,Ginf,v,1e-6); +figure +spy(Sinf) + +% Finite element radiation +sol = - Sinf * lambda; + +% Analytical solution +ref = sphereScattering('inf','dir',1,k,nu); +norm(ref-sol,2)/norm(ref,2) +norm(ref-sol,'inf')/norm(ref,'inf') + +% Graphical representation +figure +plot(theta,log(abs(sol)),'b',theta,log(abs(ref)),'--r') + + +%%% DOMAIN SOLUTION +disp('~~~~~~~~~~~~~ RADIATION ~~~~~~~~~~~~~') + +% Finite element radiative operator --> \int_Sy G(x,y) psi(y) dy +tic +Sdom = 1/(4*pi) .* integral(dom.vtx,bnd,Gxy,v,tol); +toc + +% Regularization +tic +Sreg = 1/(4*pi) .* femRegularize(dom.vtx,bnd,'[1/r]',v); +Sdom = Sdom + Sreg; +toc + +% Structure +figure +spy(Sdom) + +% Boundary solution +Ibnd = integral(bnd,u,v); +Psca = - Ibnd \ double(LHS * lambda) ; +Pinc = PW(u.dof(bnd)); +Pbnd = Pinc + Psca; + +% Domain solution +Psca = - Sdom * lambda; +Pinc = PW(dom.vtx); +Pdom = Pinc + Psca; + +% Annulation sphere interieure +r = sqrt(sum(dom.vtx.^2,2)); +Pdom(r<=1.01) = Pinc(r<=1.01); + +% Graphical representation +figure +plot(bnd,abs(Pbnd)) +hold on +plot(dom,abs(Pdom)) +axis equal; +title('Total field solution') +shading interp +colorbar +hold off + + +%%% ANAYTICAL SOLUTIONS FOR COMPARISONS +% Analytical solution +Pbnd = sphereScattering('dom','dir',1,k,1.001*bnd.vtx) + PW(bnd.vtx); +Pdom = sphereScattering('dom','dir',1,k,dom.vtx) + PW(dom.vtx); + +% Solution representation +figure +plot(bnd,abs(Pbnd)) +hold on +plot(dom,abs(Pdom)) +axis equal; +title('Analytical solution') +shading interp +colorbar +hold off + +disp('Done.') + +