Basis_HGRAD_QUAD_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_QUAD_Cn_FEM( const int order,
const EPointType &pointType ):
ptsx_( order+1 , 1 ) ,
ptsy_( order+1 , 1 )
{
Array<Array<RCP<Basis<Scalar,ArrayScalar> > > > bases(1);
bases[0].resize(2);
bases[0][0] = Teuchos::rcp( new Basis_HGRAD_LINE_Cn_FEM<Scalar,ArrayScalar>( order , pointType ) );
bases[0][1] = Teuchos::rcp( new Basis_HGRAD_LINE_Cn_FEM<Scalar,ArrayScalar>( order , pointType ) );
this->setBases( bases );
this->basisCardinality_ = (order+1)*(order+1);
this->basisDegree_ = order;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
// fill up the pt arrays with calls to the lattice
EPointType pt = (pointType==POINTTYPE_EQUISPACED)?pointType:POINTTYPE_WARPBLEND;
PointTools::getLattice<Scalar,ArrayScalar >( ptsx_ ,
shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >()) ,
order ,
0 ,
pt );
for (int i=0;i<order+1;i++)
{
ptsy_(i,0) = ptsx_(i,0);
}
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HDIV_HEX_In_FEM<Scalar,ArrayScalar>::Basis_HDIV_HEX_In_FEM( int order ,
const ArrayScalar & ptsClosed ,
const ArrayScalar & ptsOpen):
closedBasis_( order , ptsClosed ),
openBasis_( order-1 , ptsOpen ),
closedPts_( ptsClosed ),
openPts_( ptsOpen )
{
this -> basisDegree_ = order;
this -> basisCardinality_ = 3 * closedBasis_.getCardinality() * openBasis_.getCardinality() * openBasis_.getCardinality();
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
Array<Array<RCP<Basis<Scalar,ArrayScalar > > > > bases(3);
bases[0].resize(3); bases[1].resize(3); bases[2].resize(3);
bases[0][0] = rcp( &closedBasis_ , false );
bases[0][1] = rcp( &openBasis_ , false );
bases[0][2] = rcp( &openBasis_ , false );
bases[1][0] = rcp( &openBasis_ , false );
bases[1][1] = rcp( &closedBasis_ , false );
bases[1][2] = rcp( &openBasis_ , false );
bases[2][0] = rcp( &openBasis_ , false );
bases[2][1] = rcp( &openBasis_ , false );
bases[2][2] = rcp( &closedBasis_ , false );
this->setBases( bases );
initializeTags();
this->basisTagsAreSet_ = true;
}
void TagExtractor::findStartEndPositions(const QString &tag)
{
initializeTags(tag);
starts = findAll(startTag);
ends = findAll(endTag);
}
Basis_HGRAD_LINE_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_LINE_Cn_FEM( const int n ,
const EPointType &pointType ):
latticePts_( n+1 , 1 ),
Phis_( n ),
V_(n+1,n+1),
Vinv_(n+1,n+1)
{
const int N = n+1;
this -> basisCardinality_ = N;
this -> basisDegree_ = n;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
switch(pointType) {
case POINTTYPE_EQUISPACED:
PointTools::getLattice<Scalar,ArrayScalar >( latticePts_ , this->basisCellTopology_ , n , 0 , POINTTYPE_EQUISPACED );
break;
case POINTTYPE_SPECTRAL:
case POINTTYPE_WARPBLEND:
PointTools::getLattice<Scalar,ArrayScalar >( latticePts_ , this->basisCellTopology_ , n , 0 , POINTTYPE_WARPBLEND );
break;
case POINTTYPE_SPECTRAL_OPEN:
PointTools::getGaussPoints<Scalar,ArrayScalar >( latticePts_ , n );
break;
default:
TEUCHOS_TEST_FOR_EXCEPTION( true , std::invalid_argument , "Basis_HGRAD_LINE_Cn_FEM:: invalid point type" );
break;
}
// form Vandermonde matrix. Actually, this is the transpose of the VDM,
// so we transpose on copy below.
Phis_.getValues( V_ , latticePts_ , OPERATOR_VALUE );
// now I need to copy V into a Teuchos array to do the inversion
Teuchos::SerialDenseMatrix<int,Scalar> Vsdm(N,N);
for (int i=0;i<N;i++) {
for (int j=0;j<N;j++) {
Vsdm(i,j) = V_(i,j);
}
}
// invert the matrix
Teuchos::SerialDenseSolver<int,Scalar> solver;
solver.setMatrix( rcp( &Vsdm , false ) );
solver.invert( );
// now I need to copy the inverse into Vinv
for (int i=0;i<N;i++) {
for (int j=0;j<N;j++) {
Vinv_(i,j) = Vsdm(j,i);
}
}
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HGRAD_TRI_C1_FEM<Scalar,ArrayScalar>::Basis_HGRAD_TRI_C1_FEM()
{
this -> basisCardinality_ = 3;
this -> basisDegree_ = 1;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
this -> basisType_ = BASIS_FEM_DEFAULT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HGRAD_QUAD_C2_FEM<Scalar, ArrayScalar>::Basis_HGRAD_QUAD_C2_FEM()
{
this -> basisCardinality_ = 9;
this -> basisDegree_ = 2;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
this -> basisType_ = BASIS_FEM_DEFAULT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HCURL_HEX_I1_FEM<Scalar,ArrayScalar>::Basis_HCURL_HEX_I1_FEM()
{
this -> basisCardinality_ = 12;
this -> basisDegree_ = 1;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() );
this -> basisType_ = BASIS_FEM_DEFAULT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HGRAD_TET_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_TET_Cn_FEM( const int n ,
const EPointType pointType ):
Phis( n ),
V((n+1)*(n+2)*(n+3)/6,(n+1)*(n+2)*(n+3)/6),
Vinv((n+1)*(n+2)*(n+3)/6,(n+1)*(n+2)*(n+3)/6),
latticePts( (n+1)*(n+2)*(n+3)/6 , 3 )
{
const int N = (n+1)*(n+2)*(n+3)/6;
this -> basisCardinality_ = N;
this -> basisDegree_ = n;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Tetrahedron<4> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
// construct lattice
PointTools::getLattice<Scalar,ArrayScalar >( latticePts ,
this->getBaseCellTopology() ,
n ,
0 ,
pointType );
// form Vandermonde matrix. Actually, this is the transpose of the VDM,
// so we transpose on copy below.
Phis.getValues( V , latticePts , OPERATOR_VALUE );
// now I need to copy V into a Teuchos array to do the inversion
Teuchos::SerialDenseMatrix<int,Scalar> Vsdm(N,N);
for (int i=0;i<N;i++) {
for (int j=0;j<N;j++) {
Vsdm(i,j) = V(i,j);
}
}
// invert the matrix
Teuchos::SerialDenseSolver<int,Scalar> solver;
solver.setMatrix( rcp( &Vsdm , false ) );
solver.invert( );
// now I need to copy the inverse into Vinv
for (int i=0;i<N;i++) {
for (int j=0;j<N;j++) {
Vinv(i,j) = Vsdm(j,i);
}
}
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HGRAD_LINE_Cn_FEM_JACOBI<Scalar,ArrayScalar>::Basis_HGRAD_LINE_Cn_FEM_JACOBI(int order, Scalar alpha, Scalar beta) {
this -> basisCardinality_ = order+1;
this -> basisDegree_ = order;
this -> jacobiAlpha_ = alpha;
this -> jacobiBeta_ = beta;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Line<> >() );
this -> basisType_ = BASIS_FEM_HIERARCHICAL;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HDIV_HEX_In_FEM<Scalar,ArrayScalar>::Basis_HDIV_HEX_In_FEM( int order , const EPointType &pointType ):
closedBasis_( order , pointType==POINTTYPE_SPECTRAL?POINTTYPE_SPECTRAL:POINTTYPE_EQUISPACED ),
openBasis_( order-1 , pointType==POINTTYPE_SPECTRAL?POINTTYPE_SPECTRAL_OPEN:POINTTYPE_EQUISPACED ),
closedPts_( order+1 , 1 ),
openPts_( order , 1 )
{
this -> basisDegree_ = order;
this -> basisCardinality_ = 3 * closedBasis_.getCardinality() * openBasis_.getCardinality() * openBasis_.getCardinality();
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
PointTools::getLattice<Scalar,ArrayScalar >( closedPts_ ,
shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >()) ,
order ,
0 ,
pointType==POINTTYPE_SPECTRAL?POINTTYPE_WARPBLEND:POINTTYPE_EQUISPACED );
if (pointType == POINTTYPE_SPECTRAL)
{
PointTools::getGaussPoints<Scalar,ArrayScalar >( openPts_ ,
order - 1 );
}
else
{
PointTools::getLattice<Scalar,ArrayScalar >( openPts_ ,
shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >()) ,
order - 1,
0 ,
POINTTYPE_EQUISPACED );
}
Array<Array<RCP<Basis<Scalar,ArrayScalar > > > > bases(3);
bases[0].resize(3); bases[1].resize(3); bases[2].resize(3);
bases[0][0] = rcp( &closedBasis_ , false );
bases[0][1] = rcp( &openBasis_ , false );
bases[0][2] = rcp( &openBasis_ , false );
bases[1][0] = rcp( &openBasis_ , false );
bases[1][1] = rcp( &closedBasis_ , false );
bases[1][2] = rcp( &openBasis_ , false );
bases[2][0] = rcp( &openBasis_ , false );
bases[2][1] = rcp( &openBasis_ , false );
bases[2][2] = rcp( &closedBasis_ , false );
this->setBases( bases );
initializeTags();
this->basisTagsAreSet_ = true;
}
QString TagExtractor::getFirstInTag(const QString &tag)
{
initializeTags(tag);
int start = contents.indexOf(startTag, 0);
int end = contents.indexOf(endTag, 0);
QString contents;
if(start != -1 && end != -1)
contents = extract(start, end);
return contents;
}
Basis_HGRAD_HEX_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_HEX_Cn_FEM( const int orderx ,
const int ordery ,
const int orderz ,
const ArrayScalar &pts_x ,
const ArrayScalar &pts_y ,
const ArrayScalar &pts_z ):
ptsx_( pts_x.dimension(0) , 1 ),
ptsy_( pts_y.dimension(0) , 1 ),
ptsz_( pts_z.dimension(0) , 1 )
{
for (int i=0;i<pts_x.dimension(0);i++)
{
ptsx_(i,0) = pts_x(i,0);
}
for (int i=0;i<pts_y.dimension(0);i++)
{
ptsy_(i,0) = pts_y(i,0);
}
for (int i=0;i<pts_z.dimension(0);i++)
{
ptsz_(i,0) = pts_z(i,0);
}
Array<Array<RCP<Basis<Scalar,ArrayScalar> > > > bases(1);
bases[0].resize(3);
bases[0][0] = Teuchos::rcp( new Basis_HGRAD_LINE_Cn_FEM< Scalar , ArrayScalar >( orderx , pts_x ) );
bases[0][1] = Teuchos::rcp( new Basis_HGRAD_LINE_Cn_FEM< Scalar , ArrayScalar >( ordery , pts_y ) );
bases[0][2] = Teuchos::rcp( new Basis_HGRAD_LINE_Cn_FEM< Scalar , ArrayScalar >( orderz , pts_z ) );
this->setBases( bases );
this->basisCardinality_ = (orderx+1)*(ordery+1)*(orderz+1);
if (orderx >= ordery && orderx >= orderz ) {
this->basisDegree_ = orderx;
}
else if (ordery >= orderx && ordery >= orderz) {
this->basisDegree_ = ordery;
}
else {
this->basisDegree_ = orderz;
}
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HGRAD_HEX_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_HEX_Cn_FEM( const int order ,
const EPointType & pointType ):
ptsx_( order+1 , 1 ),
ptsy_( order+1 , 1 ),
ptsz_( order+1 , 1 )
{
Array<Array<RCP<Basis<Scalar,ArrayScalar> > > > bases(1);
bases[0].resize(3);
bases[0][0] = Teuchos::rcp( new Basis_HGRAD_LINE_Cn_FEM< Scalar , ArrayScalar >( order , pointType ) );
// basis is same in each direction, so I only need to instantiate it once!
bases[0][1] = bases[0][0];
bases[0][2] = bases[0][0];
this->setBases( bases );
this->basisCardinality_ = (order+1)*(order+1)*(order+1);
this->basisDegree_ = order;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
// get points
EPointType pt = (pointType==POINTTYPE_EQUISPACED)?pointType:POINTTYPE_WARPBLEND;
PointTools::getLattice<Scalar,ArrayScalar >( ptsx_ ,
shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >()) ,
order ,
0 ,
pt );
for (int i=0;i<order+1;i++)
{
ptsy_(i,0) = ptsx_(i,0);
ptsz_(i,0) = ptsx_(i,0);
}
initializeTags();
this->basisTagsAreSet_ = true;
}
void Basis_HGRAD_LINE_Hermite_FEM<Scalar,ArrayScalar>::setupVandermonde( bool factor ) {
initializeTags();
int nBf = this->getCardinality();
int n = nBf/2;
V_.shape(nBf,nBf);
// Make containers to store the Legendre polynomials and their derivatives
// at a given point
ArrayScalar P ( nBf );
ArrayScalar Px( nBf );
// Loop over grid points
for( int i=0; i<n; ++i ) {
recurrence(P,Px,latticePts_(i,0));
// Loop over basis functions
for(int j=0; j<nBf; ++j ) {
V_(j, i ) = P (j);
V_(j, i+n) = Px(j);
}
}
solver_.setMatrix(Teuchos::rcpFromRef(V_));
if(factor) {
solver_.factorWithEquilibration(true);
solver_.factor();
isFactored_ = true;
}
else {
isFactored_ = false;
}
}
Basis_HGRAD_QUAD_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_QUAD_Cn_FEM( const int orderx , const int ordery,
const ArrayScalar &pts_x ,
const ArrayScalar &pts_y ):
ptsx_( pts_x.dimension(0) , 1 ) ,
ptsy_( pts_y.dimension(0) , 1 )
{
Array<Array<RCP<Basis<Scalar,ArrayScalar> > > > bases(1);
bases[0].resize(2);
bases[0][0] = Teuchos::rcp( new Basis_HGRAD_LINE_Cn_FEM<Scalar,ArrayScalar>( orderx , pts_x ) );
bases[0][1] = Teuchos::rcp( new Basis_HGRAD_LINE_Cn_FEM<Scalar,ArrayScalar>( ordery , pts_y ) );
this->setBases( bases );
this->basisCardinality_ = (orderx+1)*(ordery+1);
if (orderx > ordery) {
this->basisDegree_ = orderx;
}
else {
this->basisDegree_ = ordery;
}
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
for (int i=0;i<pts_x.dimension(0);i++)
{
ptsx_(i,0) = pts_x(i,0);
}
for (int i=0;i<pts_y.dimension(0);i++)
{
ptsy_(i,0) = pts_y(i,0);
}
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HDIV_TRI_In_FEM<Scalar,ArrayScalar>::Basis_HDIV_TRI_In_FEM( const ordinal_type n ,
const EPointType pointType ):
Phis( n ),
coeffs( (n+1)*(n+2) , n*(n+2) )
{
const ordinal_type N = n*(n+2);
this -> basisCardinality_ = N;
this -> basisDegree_ = n;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
const ordinal_type littleN = n*(n+1); // dim of (P_{n-1})^2 -- smaller space
const ordinal_type bigN = (n+1)*(n+2); // dim of (P_{n})^2 -- larger space
const ordinal_type scalarSmallestN = (n-1)*n / 2;
const ordinal_type scalarLittleN = littleN/2;
const ordinal_type scalarBigN = bigN/2;
// first, need to project the basis for RT space onto the
// orthogonal basis of degree n
// get coefficients of PkHx
Teuchos::SerialDenseMatrix<ordinal_type,Scalar> V1(bigN, N);
// basis for the space is
// { (phi_i,0) }_{i=0}^{scalarLittleN-1} ,
// { (0,phi_i) }_{i=0}^{scalarLittleN-1} ,
// { (x,y) . phi_i}_{i=scalarLittleN}^{scalarBigN-1}
// columns of V1 are expansion of this basis in terms of the basis
// for P_{n}^2
// these two loops get the first two sets of basis functions
for (ordinal_type i=0;i<scalarLittleN;i++) {
V1(i,i) = 1.0;
V1(scalarBigN+i,scalarLittleN+i) = 1.0;
}
// now I need to integrate { (x,y) phi } against the big basis
// first, get a cubature rule.
CubatureDirectTriDefault<Scalar,ArrayScalar > myCub( 2 * n );
ArrayScalar cubPoints( myCub.getNumPoints() , 2 );
ArrayScalar cubWeights( myCub.getNumPoints() );
myCub.getCubature( cubPoints , cubWeights );
// tabulate the scalar orthonormal basis at cubature points
ArrayScalar phisAtCubPoints( scalarBigN , myCub.getNumPoints() );
Phis.getValues( phisAtCubPoints , cubPoints , OPERATOR_VALUE );
// now do the integration
for (ordinal_type i=0;i<n;i++) {
for (ordinal_type j=0;j<scalarBigN;j++) { // ordinal_type (x,y) phi_i \cdot (phi_j,0)
V1(j,littleN+i) = 0.0;
for (ordinal_type k=0;k<myCub.getNumPoints();k++) {
V1(j,littleN+i) +=
cubWeights(k) * cubPoints(k,0)
* phisAtCubPoints(scalarSmallestN+i,k)
* phisAtCubPoints(j,k);
}
}
for (ordinal_type j=0;j<scalarBigN;j++) { // ordinal_type (x,y) phi_i \cdot (0,phi_j)
V1(j+scalarBigN,littleN+i) = 0.0;
for (ordinal_type k=0;k<myCub.getNumPoints();k++) {
V1(j+scalarBigN,littleN+i) +=
cubWeights(k) * cubPoints(k,1)
* phisAtCubPoints(scalarSmallestN+i,k)
* phisAtCubPoints(j,k);
}
}
}
//std::cout << V1 << "\n";
// next, apply the RT nodes (rows) to the basis for (P_n)^2 (columns)
Teuchos::SerialDenseMatrix<ordinal_type,Scalar> V2(N , bigN);
// first 3 * degree nodes are normals at each edge
// get the points on the line
ArrayScalar linePts( n , 1 );
if (pointType == POINTTYPE_WARPBLEND) {
CubatureDirectLineGauss<Scalar> edgeRule( n );
ArrayScalar edgeCubWts( n );
edgeRule.getCubature( linePts , edgeCubWts );
}
else if (pointType == POINTTYPE_EQUISPACED ) {
shards::CellTopology linetop(shards::getCellTopologyData<shards::Line<2> >() );
PointTools::getLattice<Scalar,ArrayScalar >( linePts ,
linetop ,
n+1 , 1 ,
POINTTYPE_EQUISPACED );
}
// holds the image of the line points
ArrayScalar edgePts( n , 2 );
ArrayScalar phisAtEdgePoints( scalarBigN , n );
// these are scaled by the appropriate edge lengths.
const Scalar nx[] = {0.0,1.0,-1.0};
const Scalar ny[] = {-1.0,1.0,0.0};
for (ordinal_type i=0;i<3;i++) { // loop over edges
CellTools<Scalar>::mapToReferenceSubcell( edgePts ,
linePts ,
1 ,
i ,
this->basisCellTopology_ );
Phis.getValues( phisAtEdgePoints , edgePts , OPERATOR_VALUE );
// loop over points (rows of V2)
for (ordinal_type j=0;j<n;j++) {
// loop over orthonormal basis functions (columns of V2)
for (ordinal_type k=0;k<scalarBigN;k++) {
V2(n*i+j,k) = nx[i] * phisAtEdgePoints(k,j);
V2(n*i+j,k+scalarBigN) = ny[i] * phisAtEdgePoints(k,j);
}
}
}
// next map the points to each edge
// remaining nodes are divided into two pieces: point value of x
// components and point values of y components. These are
// evaluated at the interior of a lattice of degree + 1, For then
// the degree == 1 space corresponds classicaly to RT0 and so gets
// no internal nodes, and degree == 2 corresponds to RT1 and needs
// one internal node per vector component.
const ordinal_type numInternalPoints = PointTools::getLatticeSize( this->getBaseCellTopology() ,
n + 1 ,
1 );
if (numInternalPoints > 0) {
ArrayScalar internalPoints( numInternalPoints , 2 );
PointTools::getLattice<Scalar,ArrayScalar >( internalPoints ,
this->getBaseCellTopology() ,
n + 1 ,
1 ,
pointType );
ArrayScalar phisAtInternalPoints( scalarBigN , numInternalPoints );
Phis.getValues( phisAtInternalPoints , internalPoints , OPERATOR_VALUE );
// copy values into right positions of V2
for (ordinal_type i=0;i<numInternalPoints;i++) {
for (ordinal_type j=0;j<scalarBigN;j++) {
// x component
V2(3*n+i,j) = phisAtInternalPoints(j,i);
// y component
V2(3*n+numInternalPoints+i,scalarBigN+j) = phisAtInternalPoints(j,i);
}
}
}
// std::cout << "Nodes on big basis\n";
// std::cout << V2 << "\n";
// std::cout << "End nodes\n";
Teuchos::SerialDenseMatrix<ordinal_type,Scalar> Vsdm( N , N );
// multiply V2 * V1 --> V
Vsdm.multiply( Teuchos::NO_TRANS , Teuchos::NO_TRANS , 1.0 , V2 , V1 , 0.0 );
// std::cout << "Vandermonde:\n";
// std::cout << Vsdm << "\n";
// std::cout << "End Vandermonde\n";
Teuchos::SerialDenseSolver<ordinal_type,Scalar> solver;
solver.setMatrix( rcp( &Vsdm , false ) );
solver.invert( );
Teuchos::SerialDenseMatrix<ordinal_type,Scalar> Csdm( bigN , N );
Csdm.multiply( Teuchos::NO_TRANS , Teuchos::NO_TRANS , 1.0 , V1 , Vsdm , 0.0 );
// std::cout << Csdm << "\n";
for (ordinal_type i=0;i<bigN;i++) {
for (ordinal_type j=0;j<N;j++) {
coeffs(i,j) = Csdm(i,j);
}
}
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HCURL_TRI_In_FEM<Scalar,ArrayScalar>::Basis_HCURL_TRI_In_FEM( const int n ,
const EPointType pointType ):
Phis_( n ),
coeffs_( (n+1)*(n+2) , n*(n+2) )
{
const int N = n*(n+2);
this -> basisCardinality_ = N;
this -> basisDegree_ = n;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
const int littleN = n*(n+1); // dim of (P_{n-1})^2 -- smaller space
const int bigN = (n+1)*(n+2); // dim of (P_{n})^2 -- larger space
const int scalarSmallestN = (n-1)*n / 2;
const int scalarLittleN = littleN/2;
const int scalarBigN = bigN/2;
// first, need to project the basis for Nedelec space onto the
// orthogonal basis of degree n
// get coefficients of PkHx
Teuchos::SerialDenseMatrix<int,Scalar> V1(bigN, N);
// basis for the space is
// { (phi_i,0) }_{i=0}^{scalarLittleN-1} ,
// { (0,phi_i) }_{i=0}^{scalarLittleN-1} ,
// { (x,y) \times phi_i}_{i=scalarLittleN}^{scalarBigN-1}
// { (x,y) \times phi = (y phi , -x \phi)
// columns of V1 are expansion of this basis in terms of the basis
// for P_{n}^2
// these two loops get the first two sets of basis functions
for (int i=0;i<scalarLittleN;i++) {
V1(i,i) = 1.0;
V1(scalarBigN+i,scalarLittleN+i) = 1.0;
}
// now I need to integrate { (x,y) \times phi } against the big basis
// first, get a cubature rule.
CubatureDirectTriDefault<Scalar,ArrayScalar > myCub( 2 * n );
ArrayScalar cubPoints( myCub.getNumPoints() , 2 );
ArrayScalar cubWeights( myCub.getNumPoints() );
myCub.getCubature( cubPoints , cubWeights );
// tabulate the scalar orthonormal basis at cubature points
ArrayScalar phisAtCubPoints( scalarBigN , myCub.getNumPoints() );
Phis_.getValues( phisAtCubPoints , cubPoints , OPERATOR_VALUE );
// now do the integration
for (int i=0;i<n;i++) {
for (int j=0;j<scalarBigN;j++) { // int (x,y) phi_i \cdot (phi_j,0)
V1(j,littleN+i) = 0.0;
for (int k=0;k<myCub.getNumPoints();k++) {
V1(j,littleN+i) -=
cubWeights(k) * cubPoints(k,1)
* phisAtCubPoints(scalarSmallestN+i,k)
* phisAtCubPoints(j,k);
}
}
for (int j=0;j<scalarBigN;j++) { // int (x,y) phi_i \cdot (0,phi_j)
V1(j+scalarBigN,littleN+i) = 0.0;
for (int k=0;k<myCub.getNumPoints();k++) {
V1(j+scalarBigN,littleN+i) +=
cubWeights(k) * cubPoints(k,0)
* phisAtCubPoints(scalarSmallestN+i,k)
* phisAtCubPoints(j,k);
}
}
}
//std::cout << V1 << "\n";
// next, apply the RT nodes (rows) to the basis for (P_n)^2 (columns)
Teuchos::SerialDenseMatrix<int,Scalar> V2(N , bigN);
// first 3 * degree nodes are normals at each edge
// get the points on the line
ArrayScalar linePts( n , 1 );
if (pointType == POINTTYPE_WARPBLEND) {
CubatureDirectLineGauss<Scalar> edgeRule( 2*n - 1 );
ArrayScalar edgeCubWts( n );
edgeRule.getCubature( linePts , edgeCubWts );
}
else if (pointType == POINTTYPE_EQUISPACED ) {
shards::CellTopology linetop(shards::getCellTopologyData<shards::Line<2> >() );
PointTools::getLattice<Scalar,ArrayScalar >( linePts ,
linetop ,
n+1 , 1 ,
POINTTYPE_EQUISPACED );
}
ArrayScalar edgePts( n , 2 );
ArrayScalar phisAtEdgePoints( scalarBigN , n );
ArrayScalar edgeTan(2);
for (int i=0;i<3;i++) { // loop over edges
CellTools<Scalar>::getReferenceEdgeTangent( edgeTan ,
i ,
this->basisCellTopology_ );
/* multiply by 2.0 to account for a Jacobian in Pavel's definition */
for (int j=0;j<2;j++) {
edgeTan(j) *= 2.0;
}
CellTools<Scalar>::mapToReferenceSubcell( edgePts ,
linePts ,
1 ,
i ,
this->basisCellTopology_ );
Phis_.getValues( phisAtEdgePoints , edgePts , OPERATOR_VALUE );
// loop over points (rows of V2)
for (int j=0;j<n;j++) {
// loop over orthonormal basis functions (columns of V2)
for (int k=0;k<scalarBigN;k++) {
V2(n*i+j,k) = edgeTan(0) * phisAtEdgePoints(k,j);
V2(n*i+j,k+scalarBigN) = edgeTan(1) * phisAtEdgePoints(k,j);
}
}
}
// remaining nodes are x- and y- components at internal points, if n > 1
// this code is exactly the same as it is for HDIV
const int numInternalPoints = PointTools::getLatticeSize( this->getBaseCellTopology() ,
n + 1 ,
1 );
if (numInternalPoints > 0) {
ArrayScalar internalPoints( numInternalPoints , 2 );
PointTools::getLattice<Scalar,ArrayScalar >( internalPoints ,
this->getBaseCellTopology() ,
n + 1 ,
1 ,
pointType );
ArrayScalar phisAtInternalPoints( scalarBigN , numInternalPoints );
Phis_.getValues( phisAtInternalPoints , internalPoints , OPERATOR_VALUE );
// copy values into right positions of V2
for (int i=0;i<numInternalPoints;i++) {
for (int j=0;j<scalarBigN;j++) {
// x component
V2(3*n+i,j) = phisAtInternalPoints(j,i);
// y component
V2(3*n+numInternalPoints+i,scalarBigN+j) = phisAtInternalPoints(j,i);
}
}
}
// std::cout << "Nodes on big basis\n";
// std::cout << V2 << "\n";
// std::cout << "End nodes\n";
Teuchos::SerialDenseMatrix<int,Scalar> Vsdm( N , N );
// multiply V2 * V1 --> V
Vsdm.multiply( Teuchos::NO_TRANS , Teuchos::NO_TRANS , 1.0 , V2 , V1 , 0.0 );
// std::cout << "Vandermonde:\n";
// std::cout << Vsdm << "\n";
// std::cout << "End Vandermonde\n";
Teuchos::SerialDenseSolver<int,Scalar> solver;
solver.setMatrix( rcp( &Vsdm , false ) );
solver.invert( );
Teuchos::SerialDenseMatrix<int,Scalar> Csdm( bigN , N );
Csdm.multiply( Teuchos::NO_TRANS , Teuchos::NO_TRANS , 1.0 , V1 , Vsdm , 0.0 );
// std::cout << Csdm << "\n";
for (int i=0;i<bigN;i++) {
for (int j=0;j<N;j++) {
coeffs_(i,j) = Csdm(i,j);
}
}
initializeTags();
this->basisTagsAreSet_ = true;
}
Basis_HGRAD_LINE_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_LINE_Cn_FEM( const int n ,
const ArrayScalar &pts ):
latticePts_( n+1 , 1 ),
Phis_( n ),
V_(n+1,n+1),
Vinv_(n+1,n+1)
{
const int N = n+1;
this -> basisCardinality_ = N;
this -> basisDegree_ = n;
this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() );
this -> basisType_ = BASIS_FEM_FIAT;
this -> basisCoordinates_ = COORDINATES_CARTESIAN;
this -> basisTagsAreSet_ = false;
// check validity of points
for (int i=0;i<n;i++) {
TEUCHOS_TEST_FOR_EXCEPTION( pts(i,0) >= pts(i+1,0) ,
std::runtime_error ,
"Intrepid2::Basis_HGRAD_LINE_Cn_FEM Illegal points given to constructor" );
}
// copy points int latticePts, correcting endpoints if needed
if (std::abs(pts(0,0)+1.0) < INTREPID_TOL) {
latticePts_(0,0) = -1.0;
}
else {
latticePts_(0,0) = pts(0,0);
}
for (int i=1;i<n;i++) {
latticePts_(i,0) = pts(i,0);
}
if (std::abs(pts(n,0)-1.0) < INTREPID_TOL) {
latticePts_(n,0) = 1.0;
}
else {
latticePts_(n,0) = pts(n,0);
}
// form Vandermonde matrix. Actually, this is the transpose of the VDM,
// so we transpose on copy below.
Phis_.getValues( V_ , latticePts_ , OPERATOR_VALUE );
// now I need to copy V into a Teuchos array to do the inversion
Teuchos::SerialDenseMatrix<int,Scalar> Vsdm(N,N);
for (int i=0;i<N;i++) {
for (int j=0;j<N;j++) {
Vsdm(i,j) = V_(i,j);
}
}
// invert the matrix
Teuchos::SerialDenseSolver<int,Scalar> solver;
solver.setMatrix( rcp( &Vsdm , false ) );
solver.invert( );
// now I need to copy the inverse into Vinv
for (int i=0;i<N;i++) {
for (int j=0;j<N;j++) {
Vinv_(i,j) = Vsdm(j,i);
}
}
initializeTags();
this->basisTagsAreSet_ = true;
}
