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laghos_solver.cpp
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// Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
// reserved. See files LICENSE and NOTICE for details.
//
// This file is part of CEED, a collection of benchmarks, miniapps, software
// libraries and APIs for efficient high-order finite element and spectral
// element discretizations for exascale applications. For more information and
// source code availability see http://github.com/ceed.
//
// The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
// a collaborative effort of two U.S. Department of Energy organizations (Office
// of Science and the National Nuclear Security Administration) responsible for
// the planning and preparation of a capable exascale ecosystem, including
// software, applications, hardware, advanced system engineering and early
// testbed platforms, in support of the nation's exascale computing imperative.
#include "general/forall.hpp"
#include "laghos_solver.hpp"
#include "linalg/kernels.hpp"
#include <unordered_map>
#ifdef MFEM_USE_MPI
namespace mfem
{
namespace hydrodynamics
{
void VisualizeField(socketstream &sock, const char *vishost, int visport,
ParGridFunction &gf, const char *title,
int x, int y, int w, int h, bool vec)
{
gf.HostRead();
ParMesh &pmesh = *gf.ParFESpace()->GetParMesh();
MPI_Comm comm = pmesh.GetComm();
int num_procs, myid;
MPI_Comm_size(comm, &num_procs);
MPI_Comm_rank(comm, &myid);
bool newly_opened = false;
int connection_failed;
do
{
if (myid == 0)
{
if (!sock.is_open() || !sock)
{
sock.open(vishost, visport);
sock.precision(8);
newly_opened = true;
}
sock << "solution\n";
}
pmesh.PrintAsOne(sock);
gf.SaveAsOne(sock);
if (myid == 0 && newly_opened)
{
const char* keys = (gf.FESpace()->GetMesh()->Dimension() == 2)
? "mAcRjl" : "mmaaAcl";
sock << "window_title '" << title << "'\n"
<< "window_geometry "
<< x << " " << y << " " << w << " " << h << "\n"
<< "keys " << keys;
if ( vec ) { sock << "vvv"; }
sock << std::endl;
}
if (myid == 0)
{
connection_failed = !sock && !newly_opened;
}
MPI_Bcast(&connection_failed, 1, MPI_INT, 0, comm);
}
while (connection_failed);
}
static void Rho0DetJ0Vol(const int dim, const int NE,
const IntegrationRule &ir,
ParMesh *pmesh,
ParFiniteElementSpace &L2,
const ParGridFunction &rho0,
QuadratureData &qdata,
double &volume);
LagrangianHydroOperator::LagrangianHydroOperator(const int size,
ParFiniteElementSpace &h1,
ParFiniteElementSpace &l2,
const Array<int> &ess_tdofs,
Coefficient &rho0_coeff,
ParGridFunction &rho0_gf,
ParGridFunction &gamma_gf,
const int source,
const double cfl,
const bool visc,
const bool vort,
const bool p_assembly,
const double cgt,
const int cgiter,
double ftz,
const int oq) :
TimeDependentOperator(size),
H1(h1), L2(l2), H1c(H1.GetParMesh(), H1.FEColl(), 1),
pmesh(H1.GetParMesh()),
H1Vsize(H1.GetVSize()),
H1TVSize(H1.TrueVSize()),
H1GTVSize(H1.GlobalTrueVSize()),
L2Vsize(L2.GetVSize()),
L2TVSize(L2.TrueVSize()),
L2GTVSize(L2.GlobalTrueVSize()),
block_offsets(4),
x_gf(&H1),
ess_tdofs(ess_tdofs),
dim(pmesh->Dimension()),
NE(pmesh->GetNE()),
l2dofs_cnt(L2.GetFE(0)->GetDof()),
h1dofs_cnt(H1.GetFE(0)->GetDof()),
source_type(source), cfl(cfl),
use_viscosity(visc),
use_vorticity(vort),
p_assembly(p_assembly),
cg_rel_tol(cgt), cg_max_iter(cgiter),ftz_tol(ftz),
gamma_gf(gamma_gf),
Mv(&H1), Mv_spmat_copy(),
Me(l2dofs_cnt, l2dofs_cnt, NE),
Me_inv(l2dofs_cnt, l2dofs_cnt, NE),
ir(IntRules.Get(pmesh->GetElementBaseGeometry(0),
(oq > 0) ? oq : 3 * H1.GetOrder(0) + L2.GetOrder(0) - 1)),
Q1D(int(floor(0.7 + pow(ir.GetNPoints(), 1.0 / dim)))),
qdata(dim, NE, ir.GetNPoints()),
qdata_is_current(false),
forcemat_is_assembled(false),
Force(&L2, &H1),
ForcePA(nullptr), VMassPA(nullptr), EMassPA(nullptr),
VMassPA_Jprec(nullptr),
CG_VMass(H1.GetParMesh()->GetComm()),
CG_EMass(L2.GetParMesh()->GetComm()),
timer(p_assembly ? L2TVSize : 1),
qupdate(nullptr),
X(H1c.GetTrueVSize()),
B(H1c.GetTrueVSize()),
one(L2Vsize),
rhs(H1Vsize),
e_rhs(L2Vsize),
rhs_c_gf(&H1c),
dvc_gf(&H1c)
{
block_offsets[0] = 0;
block_offsets[1] = block_offsets[0] + H1Vsize;
block_offsets[2] = block_offsets[1] + H1Vsize;
block_offsets[3] = block_offsets[2] + L2Vsize;
one.UseDevice(true);
one = 1.0;
if (p_assembly)
{
qupdate = new QUpdate(dim, NE, Q1D, visc, vort, cfl,
&timer, gamma_gf, ir, H1, L2);
ForcePA = new ForcePAOperator(qdata, H1, L2, ir);
VMassPA = new MassPAOperator(H1c, ir, rho0_coeff);
EMassPA = new MassPAOperator(L2, ir, rho0_coeff);
// Inside the above constructors for mass, there is reordering of the mesh
// nodes which is performed on the host. Since the mesh nodes are a
// subvector, so we need to sync with the rest of the base vector (which
// is assumed to be in the memory space used by the mfem::Device).
H1.GetParMesh()->GetNodes()->ReadWrite();
// Attributes 1/2/3 correspond to fixed-x/y/z boundaries, i.e.,
// we must enforce v_x/y/z = 0 for the velocity components.
const int bdr_attr_max = H1.GetMesh()->bdr_attributes.Max();
Array<int> ess_bdr(bdr_attr_max);
for (int c = 0; c < dim; c++)
{
ess_bdr = 0;
ess_bdr[c] = 1;
H1c.GetEssentialTrueDofs(ess_bdr, c_tdofs[c]);
c_tdofs[c].Read();
}
X.UseDevice(true);
B.UseDevice(true);
rhs.UseDevice(true);
e_rhs.UseDevice(true);
}
else
{
// Standard local assembly and inversion for energy mass matrices.
// 'Me' is used in the computation of the internal energy
// which is used twice: once at the start and once at the end of the run.
MassIntegrator mi(rho0_coeff, &ir);
for (int e = 0; e < NE; e++)
{
DenseMatrixInverse inv(&Me(e));
const FiniteElement &fe = *L2.GetFE(e);
ElementTransformation &Tr = *L2.GetElementTransformation(e);
mi.AssembleElementMatrix(fe, Tr, Me(e));
inv.Factor();
inv.GetInverseMatrix(Me_inv(e));
}
// Standard assembly for the velocity mass matrix.
VectorMassIntegrator *vmi = new VectorMassIntegrator(rho0_coeff, &ir);
Mv.AddDomainIntegrator(vmi);
Mv.Assemble();
Mv_spmat_copy = Mv.SpMat();
}
// Values of rho0DetJ0 and Jac0inv at all quadrature points.
// Initial local mesh size (assumes all mesh elements are the same).
int Ne, ne = NE;
double Volume, vol = 0.0;
if (dim > 1 && p_assembly)
{
Rho0DetJ0Vol(dim, NE, ir, pmesh, L2, rho0_gf, qdata, vol);
}
else
{
const int NQ = ir.GetNPoints();
Vector rho_vals(NQ);
for (int e = 0; e < NE; e++)
{
rho0_gf.GetValues(e, ir, rho_vals);
ElementTransformation &Tr = *H1.GetElementTransformation(e);
for (int q = 0; q < NQ; q++)
{
const IntegrationPoint &ip = ir.IntPoint(q);
Tr.SetIntPoint(&ip);
DenseMatrixInverse Jinv(Tr.Jacobian());
Jinv.GetInverseMatrix(qdata.Jac0inv(e*NQ + q));
const double rho0DetJ0 = Tr.Weight() * rho_vals(q);
qdata.rho0DetJ0w(e*NQ + q) = rho0DetJ0 * ir.IntPoint(q).weight;
}
}
for (int e = 0; e < NE; e++) { vol += pmesh->GetElementVolume(e); }
}
MPI_Allreduce(&vol, &Volume, 1, MPI_DOUBLE, MPI_SUM, pmesh->GetComm());
MPI_Allreduce(&ne, &Ne, 1, MPI_INT, MPI_SUM, pmesh->GetComm());
switch (pmesh->GetElementBaseGeometry(0))
{
case Geometry::SEGMENT: qdata.h0 = Volume / Ne; break;
case Geometry::SQUARE: qdata.h0 = sqrt(Volume / Ne); break;
case Geometry::TRIANGLE: qdata.h0 = sqrt(2.0 * Volume / Ne); break;
case Geometry::CUBE: qdata.h0 = pow(Volume / Ne, 1./3.); break;
case Geometry::TETRAHEDRON: qdata.h0 = pow(6.0 * Volume / Ne, 1./3.); break;
default: MFEM_ABORT("Unknown zone type!");
}
qdata.h0 /= (double) H1.GetOrder(0);
if (p_assembly)
{
// Setup the preconditioner of the velocity mass operator.
// BC are handled by the VMassPA, so ess_tdofs here can be empty.
Array<int> empty_tdofs;
VMassPA_Jprec = new OperatorJacobiSmoother(VMassPA->GetBF(), empty_tdofs);
CG_VMass.SetPreconditioner(*VMassPA_Jprec);
CG_VMass.SetOperator(*VMassPA);
CG_VMass.SetRelTol(cg_rel_tol);
CG_VMass.SetAbsTol(0.0);
CG_VMass.SetMaxIter(cg_max_iter);
CG_VMass.SetPrintLevel(-1);
CG_EMass.SetOperator(*EMassPA);
CG_EMass.iterative_mode = false;
CG_EMass.SetRelTol(cg_rel_tol);
CG_EMass.SetAbsTol(0.0);
CG_EMass.SetMaxIter(cg_max_iter);
CG_EMass.SetPrintLevel(-1);
}
else
{
ForceIntegrator *fi = new ForceIntegrator(qdata);
fi->SetIntRule(&ir);
Force.AddDomainIntegrator(fi);
// Make a dummy assembly to figure out the sparsity.
Force.Assemble(0);
Force.Finalize(0);
}
}
LagrangianHydroOperator::~LagrangianHydroOperator()
{
delete qupdate;
if (p_assembly)
{
delete EMassPA;
delete VMassPA;
delete VMassPA_Jprec;
delete ForcePA;
}
}
void LagrangianHydroOperator::Mult(const Vector &S, Vector &dS_dt) const
{
// Make sure that the mesh positions correspond to the ones in S. This is
// needed only because some mfem time integrators don't update the solution
// vector at every intermediate stage (hence they don't change the mesh).
UpdateMesh(S);
// The monolithic BlockVector stores the unknown fields as follows:
// (Position, Velocity, Specific Internal Energy).
Vector* sptr = const_cast<Vector*>(&S);
ParGridFunction v;
const int VsizeH1 = H1.GetVSize();
v.MakeRef(&H1, *sptr, VsizeH1);
// Set dx_dt = v (explicit).
ParGridFunction dx;
dx.MakeRef(&H1, dS_dt, 0);
dx = v;
SolveVelocity(S, dS_dt);
SolveEnergy(S, v, dS_dt);
qdata_is_current = false;
}
void LagrangianHydroOperator::SolveVelocity(const Vector &S,
Vector &dS_dt) const
{
UpdateQuadratureData(S);
AssembleForceMatrix();
// The monolithic BlockVector stores the unknown fields as follows:
// (Position, Velocity, Specific Internal Energy).
ParGridFunction dv;
dv.MakeRef(&H1, dS_dt, H1Vsize);
dv = 0.0;
ParGridFunction accel_src_gf;
if (source_type == 2)
{
accel_src_gf.SetSpace(&H1);
RTCoefficient accel_coeff(dim);
accel_src_gf.ProjectCoefficient(accel_coeff);
accel_src_gf.Read();
}
if (p_assembly)
{
timer.sw_force.Start();
ForcePA->Mult(one, rhs);
timer.sw_force.Stop();
rhs.Neg();
// Partial assembly solve for each velocity component
const int size = H1c.GetVSize();
const Operator *Pconf = H1c.GetProlongationMatrix();
for (int c = 0; c < dim; c++)
{
dvc_gf.MakeRef(&H1c, dS_dt, H1Vsize + c*size);
rhs_c_gf.MakeRef(&H1c, rhs, c*size);
if (Pconf) { Pconf->MultTranspose(rhs_c_gf, B); }
else { B = rhs_c_gf; }
if (source_type == 2)
{
ParGridFunction accel_comp;
accel_comp.MakeRef(&H1c, accel_src_gf, c*size);
Vector AC;
accel_comp.GetTrueDofs(AC);
Vector BA(AC.Size());
VMassPA->MultFull(AC, BA);
B += BA;
}
H1c.GetRestrictionMatrix()->Mult(dvc_gf, X);
VMassPA->SetEssentialTrueDofs(c_tdofs[c]);
VMassPA->EliminateRHS(B);
timer.sw_cgH1.Start();
CG_VMass.Mult(B, X);
timer.sw_cgH1.Stop();
timer.H1iter += CG_VMass.GetNumIterations();
if (Pconf) { Pconf->Mult(X, dvc_gf); }
else { dvc_gf = X; }
// We need to sync the subvector 'dvc_gf' with its base vector
// because it may have been moved to a different memory space.
dvc_gf.GetMemory().SyncAlias(dS_dt.GetMemory(), dvc_gf.Size());
}
}
else
{
timer.sw_force.Start();
Force.Mult(one, rhs);
timer.sw_force.Stop();
rhs.Neg();
if (source_type == 2)
{
Vector rhs_accel(rhs.Size());
Mv_spmat_copy.Mult(accel_src_gf, rhs_accel);
rhs += rhs_accel;
}
HypreParMatrix A;
Mv.FormLinearSystem(ess_tdofs, dv, rhs, A, X, B);
CGSolver cg(H1.GetParMesh()->GetComm());
HypreSmoother prec;
prec.SetType(HypreSmoother::Jacobi, 1);
cg.SetPreconditioner(prec);
cg.SetOperator(A);
cg.SetRelTol(cg_rel_tol);
cg.SetAbsTol(0.0);
cg.SetMaxIter(cg_max_iter);
cg.SetPrintLevel(-1);
timer.sw_cgH1.Start();
cg.Mult(B, X);
timer.sw_cgH1.Stop();
timer.H1iter += cg.GetNumIterations();
Mv.RecoverFEMSolution(X, rhs, dv);
}
}
void LagrangianHydroOperator::SolveEnergy(const Vector &S, const Vector &v,
Vector &dS_dt) const
{
UpdateQuadratureData(S);
AssembleForceMatrix();
// The monolithic BlockVector stores the unknown fields as follows:
// (Position, Velocity, Specific Internal Energy).
ParGridFunction de;
de.MakeRef(&L2, dS_dt, H1Vsize*2);
de = 0.0;
// Solve for energy, assemble the energy source if such exists.
LinearForm *e_source = nullptr;
if (source_type == 1) // 2D Taylor-Green.
{
// Needed since the Assemble() defaults to PA.
L2.GetMesh()->DeleteGeometricFactors();
e_source = new LinearForm(&L2);
TaylorCoefficient coeff;
DomainLFIntegrator *d = new DomainLFIntegrator(coeff, &ir);
e_source->AddDomainIntegrator(d);
e_source->Assemble();
}
Array<int> l2dofs;
if (p_assembly)
{
timer.sw_force.Start();
ForcePA->MultTranspose(v, e_rhs);
timer.sw_force.Stop();
if (e_source) { e_rhs += *e_source; }
timer.sw_cgL2.Start();
CG_EMass.Mult(e_rhs, de);
timer.sw_cgL2.Stop();
const HYPRE_Int cg_num_iter = CG_EMass.GetNumIterations();
timer.L2iter += (cg_num_iter==0) ? 1 : cg_num_iter;
// Move the memory location of the subvector 'de' to the memory
// location of the base vector 'dS_dt'.
de.GetMemory().SyncAlias(dS_dt.GetMemory(), de.Size());
}
else // not p_assembly
{
timer.sw_force.Start();
Force.MultTranspose(v, e_rhs);
timer.sw_force.Stop();
if (e_source) { e_rhs += *e_source; }
Vector loc_rhs(l2dofs_cnt), loc_de(l2dofs_cnt);
for (int e = 0; e < NE; e++)
{
L2.GetElementDofs(e, l2dofs);
e_rhs.GetSubVector(l2dofs, loc_rhs);
timer.sw_cgL2.Start();
Me_inv(e).Mult(loc_rhs, loc_de);
timer.sw_cgL2.Stop();
timer.L2iter += 1;
de.SetSubVector(l2dofs, loc_de);
}
}
delete e_source;
}
void LagrangianHydroOperator::UpdateMesh(const Vector &S) const
{
Vector* sptr = const_cast<Vector*>(&S);
x_gf.MakeRef(&H1, *sptr, 0);
H1.GetParMesh()->NewNodes(x_gf, false);
}
double LagrangianHydroOperator::GetTimeStepEstimate(const Vector &S) const
{
UpdateMesh(S);
UpdateQuadratureData(S);
double glob_dt_est;
const MPI_Comm comm = H1.GetParMesh()->GetComm();
MPI_Allreduce(&qdata.dt_est, &glob_dt_est, 1, MPI_DOUBLE, MPI_MIN, comm);
return glob_dt_est;
}
void LagrangianHydroOperator::ResetTimeStepEstimate() const
{
qdata.dt_est = std::numeric_limits<double>::infinity();
}
void LagrangianHydroOperator::ComputeDensity(ParGridFunction &rho) const
{
rho.SetSpace(&L2);
DenseMatrix Mrho(l2dofs_cnt);
Vector rhs(l2dofs_cnt), rho_z(l2dofs_cnt);
Array<int> dofs(l2dofs_cnt);
DenseMatrixInverse inv(&Mrho);
MassIntegrator mi(&ir);
DensityIntegrator di(qdata);
di.SetIntRule(&ir);
for (int e = 0; e < NE; e++)
{
const FiniteElement &fe = *L2.GetFE(e);
ElementTransformation &eltr = *L2.GetElementTransformation(e);
di.AssembleRHSElementVect(fe, eltr, rhs);
mi.AssembleElementMatrix(fe, eltr, Mrho);
inv.Factor();
inv.Mult(rhs, rho_z);
L2.GetElementDofs(e, dofs);
rho.SetSubVector(dofs, rho_z);
}
}
double ComputeVolumeIntegral(const ParFiniteElementSpace &pfes,
const int DIM, const int NE, const int NQ,
const int Q1D, const int VDIM, const double norm,
const Vector& mass, const Vector& f)
{
MFEM_VERIFY(pfes.GetNE() > 0, "Empty local mesh should have been handled!");
MFEM_VERIFY(DIM==1 || DIM==2 || DIM==3, "Unsuported dimension!");
const bool use_tensors = UsesTensorBasis(pfes);
const int QX = use_tensors ? Q1D : NQ,
QY = use_tensors ? Q1D : 1,
QZ = use_tensors ? Q1D : 1;
auto f_vals = mfem::Reshape(f.Read(), VDIM, NQ, NE);
Vector integrand(NE*NQ);
auto I = Reshape(integrand.Write(), NQ, NE);
if (DIM == 1)
{
MFEM_FORALL(e, NE,
{
for (int q = 0; q < NQ; ++q)
{
double vmag = 0;
for (int k = 0; k < VDIM; k++)
{
vmag += pow(f_vals(k,q,e), norm);
}
I(q,e) = vmag;
}
});
}
else if (DIM == 2)
{
MFEM_FORALL_2D(e, NE, QX, QY, 1,
{
MFEM_FOREACH_THREAD(qy,y,QY)
{
MFEM_FOREACH_THREAD(qx,x,QX)
{
const int q = qx + qy * QX;
double vmag = 0.0;
for (int k = 0; k < VDIM; k++)
{
vmag += pow(f_vals(k, q, e), norm);
}
I(q, e) = vmag;
}
}
});
}
else if (DIM == 3)
{
MFEM_FORALL_3D(e, NE, QX, QY, QZ,
{
MFEM_FOREACH_THREAD(qz,z,QZ)
{
MFEM_FOREACH_THREAD(qy,y,QY)
{
MFEM_FOREACH_THREAD(qx,x,QX)
{
const int q = qx + (qy + qz * QY) * QX;
double vmag = 0;
for (int k = 0; k < VDIM; k++)
{
vmag += pow(f_vals(k, q, e), norm);
}
I(q, e) = vmag;
}
}
}
});
}
return integrand * mass;
}
double LagrangianHydroOperator::InternalEnergy(const ParGridFunction &gf) const
{
double glob_ie = 0.0, internal_energy = 0.0;
if (L2.GetNE() > 0) // UsesTensorBasis does not handle empty local mesh
{
auto L2ordering =
UsesTensorBasis(L2) ?
ElementDofOrdering::LEXICOGRAPHIC : ElementDofOrdering::NATIVE;
// get the restriction and interpolator objects
auto L2qi = L2.GetQuadratureInterpolator(ir);
L2qi->SetOutputLayout(QVectorLayout::byVDIM);
auto L2r = L2.GetElementRestriction(L2ordering);
const int NQ = ir.GetNPoints();
const int ND = L2.GetFE(0)->GetDof();
Vector e_vec(NE*ND), q_val(NE*NQ);
// Get internal energy at the quadrature points
L2r->Mult(gf, e_vec);
L2qi->Values(e_vec, q_val);
internal_energy =
ComputeVolumeIntegral(L2, dim, NE, NQ, Q1D, 1, 1.0, qdata.rho0DetJ0w, q_val);
}
MPI_Allreduce(&internal_energy, &glob_ie, 1, MPI_DOUBLE, MPI_SUM,
L2.GetParMesh()->GetComm());
return glob_ie;
}
double LagrangianHydroOperator::KineticEnergy(const ParGridFunction &v) const
{
double glob_ke = 0.0, kinetic_energy = 0.0;
if (H1.GetNE() > 0) // UsesTensorBasis does not handle empty local mesh
{
auto H1ordering =
UsesTensorBasis(H1) ?
ElementDofOrdering::LEXICOGRAPHIC : ElementDofOrdering::NATIVE;
// get the restriction and interpolator objects
auto h1_interpolator = H1.GetQuadratureInterpolator(ir);
h1_interpolator->SetOutputLayout(QVectorLayout::byVDIM);
auto H1r = H1.GetElementRestriction(H1ordering);
const int NQ = ir.GetNPoints();
const int ND = H1.GetFE(0)->GetDof();
Vector e_vec(dim*NE*ND), q_val(dim*NE*NQ);
// Get internal energy at the quadrature points
H1r->Mult(v, e_vec);
h1_interpolator->Values(e_vec, q_val);
// Get the IE, initial weighted mass
kinetic_energy =
ComputeVolumeIntegral(H1, dim, NE, NQ, Q1D, dim, 2.0, qdata.rho0DetJ0w, q_val);
}
MPI_Allreduce(&kinetic_energy, &glob_ke, 1, MPI_DOUBLE, MPI_SUM,
H1.GetParMesh()->GetComm());
return 0.5*glob_ke;
}
void LagrangianHydroOperator::PrintTimingData(bool IamRoot, int steps,
const bool fom) const
{
const MPI_Comm com = H1.GetComm();
double my_rt[5], T[5];
my_rt[0] = timer.sw_cgH1.RealTime();
my_rt[1] = timer.sw_cgL2.RealTime();
my_rt[2] = timer.sw_force.RealTime();
my_rt[3] = timer.sw_qdata.RealTime();
my_rt[4] = my_rt[0] + my_rt[2] + my_rt[3];
MPI_Reduce(my_rt, T, 5, MPI_DOUBLE, MPI_MAX, 0, com);
HYPRE_Int mydata[3], alldata[3];
mydata[0] = timer.L2dof * timer.L2iter;
mydata[1] = timer.quad_tstep;
mydata[2] = NE;
MPI_Reduce(mydata, alldata, 3, HYPRE_MPI_INT, MPI_SUM, 0, com);
if (IamRoot)
{
using namespace std;
// FOM = (FOM1 * T1 + FOM2 * T2 + FOM3 * T3) / (T1 + T2 + T3)
const HYPRE_Int H1iter = p_assembly ? (timer.H1iter/dim) : timer.H1iter;
const double FOM1 = 1e-6 * H1GTVSize * H1iter / T[0];
const double FOM2 = 1e-6 * steps * (H1GTVSize + L2GTVSize) / T[2];
const double FOM3 = 1e-6 * alldata[1] * ir.GetNPoints() / T[3];
const double FOM = (FOM1 * T[0] + FOM2 * T[2] + FOM3 * T[3]) / T[4];
const double FOM0 = 1e-6 * steps * (H1GTVSize + L2GTVSize) / T[4];
cout << endl;
cout << "CG (H1) total time: " << T[0] << endl;
cout << "CG (H1) rate (megadofs x cg_iterations / second): "
<< FOM1 << endl;
cout << endl;
cout << "CG (L2) total time: " << T[1] << endl;
cout << "CG (L2) rate (megadofs x cg_iterations / second): "
<< 1e-6 * alldata[0] / T[1] << endl;
cout << endl;
cout << "Forces total time: " << T[2] << endl;
cout << "Forces rate (megadofs x timesteps / second): "
<< FOM2 << endl;
cout << endl;
cout << "UpdateQuadData total time: " << T[3] << endl;
cout << "UpdateQuadData rate (megaquads x timesteps / second): "
<< FOM3 << endl;
cout << endl;
cout << "Major kernels total time (seconds): " << T[4] << endl;
cout << "Major kernels total rate (megadofs x time steps / second): "
<< FOM << endl;
if (!fom) { return; }
const int QPT = ir.GetNPoints();
const HYPRE_Int GNZones = alldata[2];
const long ndofs = 2*H1GTVSize + L2GTVSize + QPT*GNZones;
cout << endl;
cout << "| Ranks " << "| Zones "
<< "| H1 dofs " << "| L2 dofs "
<< "| QP " << "| N dofs "
<< "| FOM0 "
<< "| FOM1 " << "| T1 "
<< "| FOM2 " << "| T2 "
<< "| FOM3 " << "| T3 "
<< "| FOM " << "| TT "
<< "|" << endl;
cout << setprecision(3);
cout << "| " << setw(6) << H1.GetNRanks()
<< "| " << setw(8) << GNZones
<< "| " << setw(8) << H1GTVSize
<< "| " << setw(8) << L2GTVSize
<< "| " << setw(3) << QPT
<< "| " << setw(9) << ndofs
<< "| " << setw(7) << FOM0
<< "| " << setw(7) << FOM1
<< "| " << setw(5) << T[0]
<< "| " << setw(7) << FOM2
<< "| " << setw(5) << T[2]
<< "| " << setw(7) << FOM3
<< "| " << setw(5) << T[3]
<< "| " << setw(7) << FOM
<< "| " << setw(5) << T[4]
<< "| " << endl;
}
}
// Smooth transition between 0 and 1 for x in [-eps, eps].
MFEM_HOST_DEVICE inline double smooth_step_01(double x, double eps)
{
const double y = (x + eps) / (2.0 * eps);
if (y < 0.0) { return 0.0; }
if (y > 1.0) { return 1.0; }
return (3.0 - 2.0 * y) * y * y;
}
void LagrangianHydroOperator::UpdateQuadratureData(const Vector &S) const
{
if (qdata_is_current) { return; }
qdata_is_current = true;
forcemat_is_assembled = false;
if (dim > 1 && p_assembly) { return qupdate->UpdateQuadratureData(S, qdata); }
// This code is only for the 1D/FA mode
timer.sw_qdata.Start();
const int nqp = ir.GetNPoints();
ParGridFunction x, v, e;
Vector* sptr = const_cast<Vector*>(&S);
x.MakeRef(&H1, *sptr, 0);
v.MakeRef(&H1, *sptr, H1.GetVSize());
e.MakeRef(&L2, *sptr, 2*H1.GetVSize());
Vector e_vals;
DenseMatrix Jpi(dim), sgrad_v(dim), Jinv(dim), stress(dim), stressJiT(dim);
// Batched computations are needed, because hydrodynamic codes usually
// involve expensive computations of material properties. Although this
// miniapp uses simple EOS equations, we still want to represent the batched
// cycle structure.
int nzones_batch = 3;
const int nbatches = NE / nzones_batch + 1; // +1 for the remainder.
int nqp_batch = nqp * nzones_batch;
double *gamma_b = new double[nqp_batch],
*rho_b = new double[nqp_batch],
*e_b = new double[nqp_batch],
*p_b = new double[nqp_batch],
*cs_b = new double[nqp_batch];
// Jacobians of reference->physical transformations for all quadrature points
// in the batch.
DenseTensor *Jpr_b = new DenseTensor[nzones_batch];
for (int b = 0; b < nbatches; b++)
{
int z_id = b * nzones_batch; // Global index over zones.
// The last batch might not be full.
if (z_id == NE) { break; }
else if (z_id + nzones_batch > NE)
{
nzones_batch = NE - z_id;
nqp_batch = nqp * nzones_batch;
}
double min_detJ = std::numeric_limits<double>::infinity();
for (int z = 0; z < nzones_batch; z++)
{
ElementTransformation *T = H1.GetElementTransformation(z_id);
Jpr_b[z].SetSize(dim, dim, nqp);
e.GetValues(z_id, ir, e_vals);
for (int q = 0; q < nqp; q++)
{
const IntegrationPoint &ip = ir.IntPoint(q);
T->SetIntPoint(&ip);
Jpr_b[z](q) = T->Jacobian();
const double detJ = Jpr_b[z](q).Det();
min_detJ = fmin(min_detJ, detJ);
const int idx = z * nqp + q;
// Assuming piecewise constant gamma that moves with the mesh.
gamma_b[idx] = gamma_gf(z_id);
rho_b[idx] = qdata.rho0DetJ0w(z_id*nqp + q) / detJ / ip.weight;
e_b[idx] = fmax(0.0, e_vals(q));
}
++z_id;
}
// Batched computation of material properties.
ComputeMaterialProperties(nqp_batch, gamma_b, rho_b, e_b, p_b, cs_b);
z_id -= nzones_batch;
for (int z = 0; z < nzones_batch; z++)
{
ElementTransformation *T = H1.GetElementTransformation(z_id);
for (int q = 0; q < nqp; q++)
{
const IntegrationPoint &ip = ir.IntPoint(q);
T->SetIntPoint(&ip);
// Note that the Jacobian was already computed above. We've chosen
// not to store the Jacobians for all batched quadrature points.
const DenseMatrix &Jpr = Jpr_b[z](q);
CalcInverse(Jpr, Jinv);
const double detJ = Jpr.Det(), rho = rho_b[z*nqp + q],
p = p_b[z*nqp + q], sound_speed = cs_b[z*nqp + q];
stress = 0.0;
for (int d = 0; d < dim; d++) { stress(d, d) = -p; }
double visc_coeff = 0.0;
if (use_viscosity)
{
// Compression-based length scale at the point. The first
// eigenvector of the symmetric velocity gradient gives the
// direction of maximal compression. This is used to define the
// relative change of the initial length scale.
v.GetVectorGradient(*T, sgrad_v);
double vorticity_coeff = 1.0;
if (use_vorticity)
{
const double grad_norm = sgrad_v.FNorm();
const double div_v = fabs(sgrad_v.Trace());
vorticity_coeff = (grad_norm > 0.0) ? div_v / grad_norm : 1.0;
}
sgrad_v.Symmetrize();
double eig_val_data[3], eig_vec_data[9];
if (dim==1)
{
eig_val_data[0] = sgrad_v(0, 0);
eig_vec_data[0] = 1.;
}
else { sgrad_v.CalcEigenvalues(eig_val_data, eig_vec_data); }
Vector compr_dir(eig_vec_data, dim);
// Computes the initial->physical transformation Jacobian.
mfem::Mult(Jpr, qdata.Jac0inv(z_id*nqp + q), Jpi);
Vector ph_dir(dim); Jpi.Mult(compr_dir, ph_dir);
// Change of the initial mesh size in the compression direction.
const double h = qdata.h0 * ph_dir.Norml2() /
compr_dir.Norml2();
// Measure of maximal compression.
const double mu = eig_val_data[0];
visc_coeff = 2.0 * rho * h * h * fabs(mu);
// The following represents a "smooth" version of the statement
// "if (mu < 0) visc_coeff += 0.5 rho h sound_speed". Note that
// eps must be scaled appropriately if a different unit system is
// being used.
const double eps = 1e-12;
visc_coeff += 0.5 * rho * h * sound_speed * vorticity_coeff *
(1.0 - smooth_step_01(mu - 2.0 * eps, eps));
stress.Add(visc_coeff, sgrad_v);
}
// Time step estimate at the point. Here the more relevant length
// scale is related to the actual mesh deformation; we use the min
// singular value of the ref->physical Jacobian. In addition, the
// time step estimate should be aware of the presence of shocks.
const double h_min =
Jpr.CalcSingularvalue(dim-1) / (double) H1.GetOrder(0);
const double inv_dt = sound_speed / h_min +
2.5 * visc_coeff / rho / h_min / h_min;
if (min_detJ < 0.0)
{
// This will force repetition of the step with smaller dt.
qdata.dt_est = 0.0;
}
else
{
if (inv_dt>0.0)
{
qdata.dt_est = fmin(qdata.dt_est, cfl*(1.0/inv_dt));
}
}
// Quadrature data for partial assembly of the force operator.
MultABt(stress, Jinv, stressJiT);
stressJiT *= ir.IntPoint(q).weight * detJ;
for (int vd = 0 ; vd < dim; vd++)
{
for (int gd = 0; gd < dim; gd++)
{
qdata.stressJinvT(vd)(z_id*nqp + q, gd) =
stressJiT(vd, gd);
}
}
}
++z_id;
}
}
delete [] gamma_b;
delete [] rho_b;
delete [] e_b;
delete [] p_b;
delete [] cs_b;
delete [] Jpr_b;
timer.sw_qdata.Stop();
timer.quad_tstep += NE;
}
/// Trace of a square matrix
template<int H, int W, typename T>
MFEM_HOST_DEVICE inline
double Trace(const T * __restrict__ data)
{
double t = 0.0;
for (int i = 0; i < W; i++) { t += data[i+i*H]; }
return t;
}
template<int H, int W, typename T>
MFEM_HOST_DEVICE static inline
void SFNorm(double &scale_factor, double &scaled_fnorm2,
const T * __restrict__ data)
{
int i;
constexpr int hw = H * W;
T max_norm = 0.0, entry, fnorm2;
for (i = 0; i < hw; i++)
{
entry = fabs(data[i]);
if (entry > max_norm)
{
max_norm = entry;
}
}
if (max_norm == 0.0)
{
scale_factor = scaled_fnorm2 = 0.0;
return;
}
fnorm2 = 0.0;
for (i = 0; i < hw; i++)
{
entry = data[i] / max_norm;
fnorm2 += entry * entry;
}
scale_factor = max_norm;
scaled_fnorm2 = fnorm2;
}
/// Compute the Frobenius norm of the matrix
template<int H, int W, typename T>
MFEM_HOST_DEVICE inline
double FNorm(const T * __restrict__ data)
{
double s, n2;
SFNorm<H,W>(s, n2, data);
return s*sqrt(n2);
}
template<int DIM> MFEM_HOST_DEVICE static inline
void QUpdateBody(const int NE, const int e,
const int NQ, const int q,
const bool use_viscosity,
const bool use_vorticity,
const double h0,
const double h1order,
const double cfl,
const double infinity,
double* __restrict__ Jinv,
double* __restrict__ stress,
double* __restrict__ sgrad_v,
double* __restrict__ eig_val_data,
double* __restrict__ eig_vec_data,
double* __restrict__ compr_dir,
double* __restrict__ Jpi,
double* __restrict__ ph_dir,
double* __restrict__ stressJiT,
const double* __restrict__ d_gamma,
const double* __restrict__ d_weights,
const double* __restrict__ d_Jacobians,
const double* __restrict__ d_rho0DetJ0w,
const double* __restrict__ d_e_quads,
const double* __restrict__ d_grad_v_ext,
const double* __restrict__ d_Jac0inv,