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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.
//
// Contributed by Ismail Badia.
// Reference : "Higher-Order Finite Element Methods"; Pavel Solin, Karel
// Segeth ,
// Ivo Dolezel , Chapman and Hall/CRC; Edition : Har/Cdr (2003).
#include "HierarchicalBasisHcurlLine.h"
HierarchicalBasisHcurlLine::HierarchicalBasisHcurlLine(int order)
{
_nvertex = 2;
_nedge = 1;
_nfaceTri = 0;
_nfaceQuad = 0;
_nVertexFunction = 0;
_nEdgeFunction = order + 1;
_nQuadFaceFunction = 0;
_nTriFaceFunction = 0;
_nBubbleFunction = 0;
_pe = order;
}
HierarchicalBasisHcurlLine::~HierarchicalBasisHcurlLine() {}
unsigned int HierarchicalBasisHcurlLine::getNumberOfOrientations() const
{
return 2; // factorial 2
}
double HierarchicalBasisHcurlLine::_affineCoordinate(int j, double u)
{
switch(j) {
case(1): return 0.5 * (1 + u);
case(2): return 0.5 * (1 - u);
default: throw std::string("j must be : 1<=j<=2");
}
}
double HierarchicalBasisHcurlLine::dotProduct(const std::vector<double> &u,
const std::vector<double> &v)
{
return u[0] * v[0] + u[1] * v[1] + u[2] * v[2];
}
void HierarchicalBasisHcurlLine::generateHcurlBasis(
double const &u, double const &v, double const &w,
std::vector<std::vector<double> > &edgeBasis,
std::vector<std::vector<double> > &faceBasis,
std::vector<std::vector<double> > &bubbleBasis)
{
double lambda1 = _affineCoordinate(1, u);
double lambda2 = _affineCoordinate(2, u);
std::vector<double> t1 = std::vector<double>(3, 0);
t1[0] = 1;
std::vector<double> n1 = std::vector<double>(3, 0);
n1[0] = 1;
std::vector<double> n2 = std::vector<double>(3, 0);
n2[0] = -1;
// Whitney functions
std::vector<double> psie_0(3, 0);
std::vector<double> psie_1(3, 0);
for(int i = 0; i < 3; i++) {
psie_0[i] = lambda1 * n2[i] / dotProduct(n2, t1) +
lambda2 * n1[i] / dotProduct(n1, t1);
psie_1[i] = lambda1 * n2[i] / dotProduct(n2, t1) -
lambda2 * n1[i] / dotProduct(n1, t1);
}
double sub = lambda1 - lambda2;
std::vector<double> legendreVector(_pe, 0);
for(unsigned int k = 0; k < legendreVector.size(); k++) {
legendreVector[k] = OrthogonalPoly::EvalLegendre(k, sub);
}
int edgeIt = 0;
for(int j = 0; j < 3; j++) { edgeBasis[edgeIt][j] = psie_0[j]; }
edgeIt++;
if(_pe >= 1) {
for(int j = 0; j < 3; j++) { edgeBasis[edgeIt][j] = psie_1[j]; }
edgeIt++;
for(int iedge = 2; iedge <= _pe; iedge++) {
for(int j = 0; j < 3; j++) {
edgeBasis[edgeIt][j] = (2 * float(iedge) - 1) / float(iedge) *
legendreVector[iedge - 1] * psie_1[j] -
(float(iedge) - 1) / float(iedge) *
legendreVector[iedge - 2] * psie_0[j];
}
edgeIt++;
}
}
}
void HierarchicalBasisHcurlLine::orientEdge(
int const &flagOrientation, int const &edgeNumber,
std::vector<std::vector<double> > &edgeFunctions,
const std::vector<std::vector<double> > &eTablePositiveFlag,
const std::vector<std::vector<double> > &eTableNegativeFlag)
{
if(flagOrientation == -1) {
for(int k = 0; k <= _pe; k++) {
edgeFunctions[k][0] = eTableNegativeFlag[k][0];
edgeFunctions[k][1] = eTableNegativeFlag[k][1];
edgeFunctions[k][2] = eTableNegativeFlag[k][2];
}
}
else {
for(int k = 0; k <= _pe; k++) {
edgeFunctions[k][0] = eTablePositiveFlag[k][0];
edgeFunctions[k][1] = eTablePositiveFlag[k][1];
edgeFunctions[k][2] = eTablePositiveFlag[k][2];
}
}
}
void HierarchicalBasisHcurlLine::orientEdgeFunctionsForNegativeFlag(
std::vector<std::vector<double> > &edgeFunctions)
{
for(int k = 0; k <= _pe; k++) {
if(k % 2 == 0) {
edgeFunctions[k][0] = edgeFunctions[k][0] * (-1);
edgeFunctions[k][1] = edgeFunctions[k][1] * (-1);
edgeFunctions[k][2] = edgeFunctions[k][2] * (-1);
}
}
}
void HierarchicalBasisHcurlLine::generateCurlBasis(
double const &u, double const &v, double const &w,
std::vector<std::vector<double> > &edgeBasis,
std::vector<std::vector<double> > &faceBasis,
std::vector<std::vector<double> > &bubbleBasis)
{
// zero for all orders
}
void HierarchicalBasisHcurlLine::getKeysInfo(std::vector<int> &functionTypeInfo,
std::vector<int> &orderInfo)
{
for(int k = 0; k <= _pe; k++) {
orderInfo[k] = k;
functionTypeInfo[k] = 1;
}
}
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