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finite_method.hh
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#ifndef FINITEMETHOD
#define FINITEMETHOD
#include <Eigen/Dense>
#include <cmath>
#include "utility.hh"
using namespace Eigen;
template <int order>
class FiniteDifference{
public:
template<typename Derived>
ArrayXXf x(const ArrayBase<Derived> &var, float dx) const{
ArrayXXf result;
int nrows = var.rows(), ncols = var.cols();
if (order == 2){
result.resize(nrows, ncols);
result.row(0) = (var.row(1) - var.row(0)) / dx;
for (int i = 1; i < nrows - 1; i++)
result.row(i) = (var.row(i + 1) - var.row(i - 1)) / (2. * dx);
result.row(nrows - 1) = (var.row(nrows - 1) - var.row(nrows - 2)) / dx;
} else if (order == 1){
result.resize(nrows - 1, ncols);
for (int i = 0; i < nrows - 1; i++)
result.row(i) = (var.row(i + 1) - var.row(i)) / dx;
}
return result;
}
template<typename Derived>
ArrayXXf y(const ArrayBase<Derived> &var, float dy) const{
ArrayXXf result;
int nrows = var.rows(), ncols = var.cols();
if (order == 2){
result.resize(nrows, ncols);
result.col(0) = (var.col(1) - var.col(0)) / dy;
for (int i = 1; i < ncols - 1; i++)
result.col(i) = (var.col(i + 1) - var.col(i - 1)) / (2. * dy);
result.col(ncols - 1) = (var.col(ncols - 1) - var.col(ncols - 2)) / dy;
} else if (order == 1){
result.resize(nrows, ncols - 1);
for (int i = 0; i < ncols - 1; i++)
result.col(i) = (var.col(i + 1) - var.col(i)) / dy;
}
return result;
}
};
template <int order>
class HyperDifference{
// calculate higher order difference
protected:
static const float coeff[4][7];
public:
template<typename Derived>
ArrayXXf x(const ArrayBase<Derived> &var, float dx = 1.) const{
int r, nrows = var.rows(), ncols = var.cols();
ArrayXXf result = ArrayXXf::Zero(nrows, ncols);
for (int i = 0; i < nrows; i++){
r = MIN3(i, nrows - i - 1, order / 2);
for (int j = -r; j < r + 1; j++)
result.row(i) += coeff[r][j + 3] * var.row(i + j) * std::pow(dx, -order);
}
return result;
}
template<typename Derived>
ArrayXXf y(const ArrayBase<Derived> &var, float dy = 1.) const{
int r, nrows = var.rows(), ncols = var.cols();
ArrayXXf result = ArrayXXf::Zero(nrows, ncols);
for (int i = 0; i < ncols; i++){
r = MIN3(i, ncols - i - 1, order / 2);
for (int j = -r; j < r + 1; j++)
result.col(i) += coeff[r][j + 3] * var.col(i + j) * std::pow(dy, -order);
}
return result;
}
};
template <int order>
const float HyperDifference<order>::coeff[4][7] = {
{0, 0, 0, 0, 0, 0, 0},
{0, 0, 1, -2, 1, 0, 0},
{0, -1, 4, -6, 4, -1, 0},
{1, -6, 15, -20, 15, -6, 1}
};
template <int order>
class FiniteInterpolation{
protected:
ArrayXXf wsignx, wsigny;
static const float coeff[6][6];
public:
template<typename Derived>
ArrayXXf x(const ArrayBase<Derived> &var) const{
int r, nrows = var.rows(), ncols = var.cols();
ArrayXXf result = ArrayXXf::Zero(nrows - 1, ncols);
for (int i = 0; i < nrows - 1; i++){
r = MIN3(i + 1, nrows - i - 1, order / 2);
for (int j = -r + 1; j < r + 1; j++)
result.row(i) += coeff[2 * r - 1][j + 2] * var.row(i + j);
}
return result;
}
template<typename Derived>
ArrayXXf y(const ArrayBase<Derived> &var) const{
int r, nrows = var.rows(), ncols = var.cols();
ArrayXXf result = ArrayXXf::Zero(nrows, ncols - 1);
for (int i = 0; i < ncols - 1; i++){
r = MIN3(i + 1, ncols - i - 1, order / 2);
for (int j = -r + 1; j < r + 1; j++)
result.col(i) += coeff[2 * r - 1][j + 2] * var.col(i + j);
}
return result;
}
template<typename Deriveda, typename Derivedb>
ArrayXXf x1(const ArrayBase<Deriveda> &wind, const ArrayBase<Derivedb> &var) const{
// upwind transport
int r, nrows = nrows, ncols = ncols;
ArrayXXf result = ArrayXXf::Zero(nrows - 1, ncols);
wsignx = (wind.block(1,0,nrows - 1,ncols) > 0).select(
ArrayXXf::Zero(nrows - 1, ncols) + 1.,
ArrayXXf::Zero(nrows - 1, ncols) - 1.);
for (int i = 0; i < nrows - 1; i++){
r = MIN3(i + 1, nrows - i - 1, order / 2);
for (int j = -r + 1; j < r + 1; j++)
result.row(i) += coeff[2 * r - 1][j + 2] * var.row(i + j) +
wsignx.row(i) * coeff[2 * r - 2][j + 2] * var.row(i + j);
}
return result;
}
template<typename Deriveda, typename Derivedb>
ArrayXXf y1(const ArrayBase<Deriveda> &wind, const ArrayBase<Derivedb> &var) const{
int r, nrows = nrows, ncols = ncols;
ArrayXXf result = ArrayXXf::Zero(nrows, ncols - 1);
wsigny = (wind.block(0,1,nrows,ncols - 1) > 0).select(
ArrayXXf::Zero(nrows, ncols - 1) + 1.,
ArrayXXf::Zero(nrows, ncols - 1) - 1.);
for (int i = 0; i < ncols - 1; i++){
r = MIN3(i + 1, ncols - i - 1, order / 2);
for (int j = -r + 1; j < r + 1; j++)
result.col(i) += coeff[2 * r - 1][j + 2] * var.col(i + j) +
wsigny.col(i) * coeff[2 * r - 2][j + 2] * var.col(i + j);
}
return result;
}
};
template <int order>
const float FiniteInterpolation<order>::coeff[6][6] = {
{ 0 , 0 , 0.5 , -0.5 , 0 , 0 },
{ 0 , 0 , 0.5 , 0.5 , 0 , 0 },
{ 0 , -1./12., 1./4. , -1./4. , 1./12. , 0 },
{ 0 , -1./12., 7./12. , 7./12 , -1./12. , 0 },
{1./60, -1./12., 1./6. , -1./6. , 1./12. , -1./60.},
{1./60, -2./15., 37./60., 37./60., -2./15. , 1./60.}
};
#endif