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// Gmsh - Copyright (C) 1997-2021 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// issues on https://gitlab.onelab.info/gmsh/gmsh/issues.
#include <cmath>
#include <algorithm>
#include "pyramidalBasis.h"
#include "pointsGenerators.h"
pyramidalBasis::pyramidalBasis(int tag) : nodalBasis(tag), bergot(nullptr)
{
if(serendip && order > 2) {
Msg::Warning("Serendipity pyramid for order %i not yet implemented", order);
return;
}
bergot = new BergotBasis(order, serendip);
int num_points = points.size1();
bergotCoefficients.resize(num_points, num_points);
double *fval = new double[num_points];
// Invert the Vandermonde matrix
fullMatrix<double> VDM(num_points, num_points);
for(int j = 0; j < num_points; j++) {
bergot->f(points(j, 0), points(j, 1), points(j, 2), fval);
for(int i = 0; i < num_points; i++) VDM(i, j) = fval[i];
}
VDM.invert(bergotCoefficients);
coefficients.resize(num_points, num_points);
monomials.resize(num_points, 3);
int idx = 0;
for(int i = 0; i <= order; i++) {
for(int j = 0; j <= order; j++) {
if(bergot->validIJ(i, j)) {
for(int k = 0; k <= order - std::max(i, j); k++, idx++) {
monomials(idx, 0) = i;
monomials(idx, 1) = j;
monomials(idx, 2) = k;
for(int l = 0; l < num_points; l++) {
double oneMinW = std::max(1e-14, 1 - points(l, 2));
VDM(idx, l) = std::pow(points(l, 0), i);
VDM(idx, l) *= std::pow(points(l, 1), j);
VDM(idx, l) *= std::pow(points(l, 2), k);
VDM(idx, l) *= std::pow(oneMinW, std::max(i, j) - i - j);
}
}
}
}
}
VDM.invert(coefficients);
delete[] fval;
}
pyramidalBasis::~pyramidalBasis()
{
if(bergot) delete bergot;
}
int pyramidalBasis::getNumShapeFunctions() const { return points.size1(); }
void pyramidalBasis::f(double u, double v, double w, double *val) const
{
if(!bergot) return;
const int N = points.size1();
double *fval = new double[N];
bergot->f(u, v, w, fval);
for(int i = 0; i < N; i++) {
val[i] = 0.;
for(int j = 0; j < N; j++) val[i] += bergotCoefficients(i, j) * fval[j];
}
delete[] fval;
}
void pyramidalBasis::f(const fullMatrix<double> &coord,
fullMatrix<double> &sf) const
{
if(!bergot) return;
const int N = points.size1(), NPts = coord.size1();
sf.resize(NPts, N);
double *fval = new double[N];
for(int iPt = 0; iPt < NPts; iPt++) {
bergot->f(coord(iPt, 0), coord(iPt, 1), coord(iPt, 2), fval);
for(int i = 0; i < N; i++) {
sf(iPt, i) = 0.;
for(int j = 0; j < N; j++)
sf(iPt, i) += bergotCoefficients(i, j) * fval[j];
}
}
delete[] fval;
}
void pyramidalBasis::f(double u, double v, double w, int i, double *val) const
{
if(!bergot) return;
if(i < 0 || i >= bergotCoefficients.size1()) {
Msg::Error("Node out of range for pyramidal basis");
return;
}
const int N = points.size1();
double *fval = new double[N];
bergot->f(u, v, w, fval);
*val = 0.;
for(int j = 0; j < N; j++) *val += bergotCoefficients(i, j) * fval[j];
delete[] fval;
}
void pyramidalBasis::df(double u, double v, double w, double grads[][3]) const
{
if(!bergot) return;
const int N = points.size1();
double(*dfval)[3] = new double[N][3];
bergot->df(u, v, w, dfval);
for(int i = 0; i < N; i++) {
grads[i][0] = 0.;
grads[i][1] = 0.;
grads[i][2] = 0.;
for(int j = 0; j < N; j++) {
grads[i][0] += bergotCoefficients(i, j) * dfval[j][0];
grads[i][1] += bergotCoefficients(i, j) * dfval[j][1];
grads[i][2] += bergotCoefficients(i, j) * dfval[j][2];
}
}
delete[] dfval;
}
void pyramidalBasis::df(const fullMatrix<double> &coord,
fullMatrix<double> &dfm) const
{
if(!bergot) return;
const int N = points.size1(), NPts = coord.size1();
double(*dfv)[3] = new double[N][3];
dfm.resize(3 * NPts, N, false);
for(int iPt = 0; iPt < NPts; iPt++) {
df(coord(iPt, 0), coord(iPt, 1), coord(iPt, 2), dfv);
for(int i = 0; i < N; i++) {
dfm(3 * iPt + 0, i) = dfv[i][0];
dfm(3 * iPt + 1, i) = dfv[i][1];
dfm(3 * iPt + 2, i) = dfv[i][2];
}
}
delete[] dfv;
}
void pyramidalBasis::df(double u, double v, double w, int i,
double grad[3]) const
{
if(!bergot) return;
if(i < 0 || i >= bergotCoefficients.size1()) {
Msg::Error("Node out of range for pyramidal basis gradient");
return;
}
const int N = points.size1();
double(*dfval)[3] = new double[N][3];
bergot->df(u, v, w, dfval);
grad[0] = 0.;
grad[1] = 0.;
grad[2] = 0.;
for(int j = 0; j < N; j++) {
grad[0] += bergotCoefficients(i, j) * dfval[j][0];
grad[1] += bergotCoefficients(i, j) * dfval[j][1];
grad[2] += bergotCoefficients(i, j) * dfval[j][2];
}
delete[] dfval;
}
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