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_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_TRI_Cn_FEM( const int n ,
const EPointType pointType ):
Phis( n ),
V((n+1)*(n+2)/2,(n+1)*(n+2)/2),
Vinv((n+1)*(n+2)/2,(n+1)*(n+2)/2),
latticePts( (n+1)*(n+2)/2 , 2 )
{
TEUCHOS_TEST_FOR_EXCEPTION( n <= 0, std::invalid_argument, "polynomial order must be >= 1");
const int N = (n+1)*(n+2)/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;
// construct lattice
shards::CellTopology myTri_3( shards::getCellTopologyData< shards::Triangle<3> >() );
PointTools::getLattice<Scalar,FieldContainer<Scalar> >( latticePts ,
myTri_3 ,
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);
}
}
}
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<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);
}
}
}
Basis_HDIV_TRI_In_FEM<Scalar,ArrayScalar>::Basis_HDIV_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 RT 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) . 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 (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) 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,0)
* 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,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<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( 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 (int 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 (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) = 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 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);
}
}
}
void DislocationDensity<EvalT, Traits>::
evaluateFields(typename Traits::EvalData workset)
{
Teuchos::SerialDenseMatrix<int, double> A;
Teuchos::SerialDenseMatrix<int, double> X;
Teuchos::SerialDenseMatrix<int, double> B;
Teuchos::SerialDenseSolver<int, double> solver;
A.shape(numNodes,numNodes);
X.shape(numNodes,numNodes);
B.shape(numNodes,numNodes);
// construct Identity for RHS
for (int i = 0; i < numNodes; ++i)
B(i,i) = 1.0;
for (int i=0; i < G.size() ; i++) G[i] = 0.0;
// construct the node --> point operator
for (std::size_t cell=0; cell < workset.numCells; ++cell)
{
for (std::size_t node=0; node < numNodes; ++node)
for (std::size_t qp=0; qp < numQPs; ++qp)
A(qp,node) = BF(cell,node,qp);
X = 0.0;
solver.setMatrix( Teuchos::rcp( &A, false) );
solver.setVectors( Teuchos::rcp( &X, false ), Teuchos::rcp( &B, false ) );
// Solve the system A X = B to find A_inverse
int status = 0;
status = solver.factor();
status = solver.solve();
// compute nodal Fp
nodalFp.initialize(0.0);
for (std::size_t node=0; node < numNodes; ++node)
for (std::size_t qp=0; qp < numQPs; ++qp)
for (std::size_t i=0; i < numDims; ++i)
for (std::size_t j=0; j < numDims; ++j)
nodalFp(node,i,j) += X(node,qp) * Fp(cell,qp,i,j);
// compute the curl using nodalFp
curlFp.initialize(0.0);
for (std::size_t node=0; node < numNodes; ++node)
{
for (std::size_t qp=0; qp < numQPs; ++qp)
{
curlFp(qp,0,0) += nodalFp(node,0,2) * GradBF(cell,node,qp,1) - nodalFp(node,0,1) * GradBF(cell,node,qp,2);
curlFp(qp,0,1) += nodalFp(node,1,2) * GradBF(cell,node,qp,1) - nodalFp(node,1,1) * GradBF(cell,node,qp,2);
curlFp(qp,0,2) += nodalFp(node,2,2) * GradBF(cell,node,qp,1) - nodalFp(node,2,1) * GradBF(cell,node,qp,2);
curlFp(qp,1,0) += nodalFp(node,0,0) * GradBF(cell,node,qp,2) - nodalFp(node,0,2) * GradBF(cell,node,qp,0);
curlFp(qp,1,1) += nodalFp(node,1,0) * GradBF(cell,node,qp,2) - nodalFp(node,1,2) * GradBF(cell,node,qp,0);
curlFp(qp,1,2) += nodalFp(node,2,0) * GradBF(cell,node,qp,2) - nodalFp(node,2,2) * GradBF(cell,node,qp,0);
curlFp(qp,2,0) += nodalFp(node,0,1) * GradBF(cell,node,qp,0) - nodalFp(node,0,0) * GradBF(cell,node,qp,1);
curlFp(qp,2,1) += nodalFp(node,1,1) * GradBF(cell,node,qp,0) - nodalFp(node,1,0) * GradBF(cell,node,qp,1);
curlFp(qp,2,2) += nodalFp(node,2,1) * GradBF(cell,node,qp,0) - nodalFp(node,2,0) * GradBF(cell,node,qp,1);
}
}
for (std::size_t qp=0; qp < numQPs; ++qp)
for (std::size_t i=0; i < numDims; ++i)
for (std::size_t j=0; j < numDims; ++j)
for (std::size_t k=0; k < numDims; ++k)
G(cell,qp,i,j) += Fp(cell,qp,i,k) * curlFp(qp,k,j);
}
}
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;
}
void SaddleOperator<ScalarType, MV, OP>::Apply(const SaddleContainer<ScalarType,MV>& X, SaddleContainer<ScalarType,MV>& Y) const
{
RCP<SerialDenseMatrix> Xlower = X.getLower();
RCP<SerialDenseMatrix> Ylower = Y.getLower();
if(pt_ == NO_PREC)
{
// trans does literally nothing, because the operator is symmetric
// Y.bottom = B'X.top
MVT::MvTransMv(1., *B_, *(X.upper_), *Ylower);
// Y.top = A*X.top+B*X.bottom
A_->Apply(*(X.upper_), *(Y.upper_));
MVT::MvTimesMatAddMv(1., *B_, *Xlower, 1., *(Y.upper_));
}
else if(pt_ == NONSYM)
{
// Y.bottom = -B'X.top
MVT::MvTransMv(-1., *B_, *(X.upper_), *Ylower);
// Y.top = A*X.top+B*X.bottom
A_->Apply(*(X.upper_), *(Y.upper_));
MVT::MvTimesMatAddMv(1., *B_, *Xlower, 1., *(Y.upper_));
}
else if(pt_ == BD_PREC)
{
Teuchos::SerialDenseSolver<int,ScalarType> MySolver;
// Solve A Y.X = X.X
A_->Apply(*(X.upper_),*(Y.upper_));
// So, let me tell you a funny story about how the SerialDenseSolver destroys the original matrix...
Teuchos::RCP<SerialDenseMatrix> localSchur = Teuchos::rcp(new SerialDenseMatrix(*Schur_));
// Solve the small system
MySolver.setMatrix(localSchur);
MySolver.setVectors(Ylower, Xlower);
MySolver.solve();
}
// Hermitian-Skew Hermitian splitting has some extra requirements
// We need B'B = I, which is true for standard eigenvalue problems, but not generalized
// We also need to use gmres, because our operator is no longer symmetric
else if(pt_ == HSS_PREC)
{
// std::cout << "applying preconditioner to";
// X.MvPrint(std::cout);
// Solve (H + alpha I) Y1 = X
// 1. Apply preconditioner
A_->Apply(*(X.upper_),*(Y.upper_));
// 2. Scale by 1/alpha
*Ylower = *Xlower;
Ylower->scale(1./alpha_);
// std::cout << "H preconditioning produced";
// Y.setLower(Ylower);
// Y.MvPrint(std::cout);
// Solve (S + alpha I) Y = Y1
// 1. Y_lower = (B' Y1_upper + alpha Y1_lower) / (1 + alpha^2)
Teuchos::RCP<SerialDenseMatrix> Y1_lower = Teuchos::rcp(new SerialDenseMatrix(*Ylower));
MVT::MvTransMv(1,*B_,*(Y.upper_),*Ylower);
// std::cout << "Y'b1 " << *Ylower;
Y1_lower->scale(alpha_);
// std::cout << "alpha b2 " << *Y1_lower;
*Ylower += *Y1_lower;
// std::cout << "alpha b2 + Y'b1 " << *Ylower;
Ylower->scale(1/(1+alpha_*alpha_));
// 2. Y_upper = (Y1_upper - B Y_lower) / alpha
MVT::MvTimesMatAddMv(-1/alpha_,*B_,*Ylower,1/alpha_,*(Y.upper_));
// std::cout << "preconditioning produced";
// Y.setLower(Ylower);
// Y.MvPrint(std::cout);
}
else
{
std::cout << "Not a valid preconditioner type\n";
}
Y.setLower(Ylower);
// std::cout << "result of applying operator";
// Y.MvPrint(std::cout);
}