Basis_HGRAD_LINE_Hermite_FEM<Scalar,ArrayScalar>::Basis_HGRAD_LINE_Hermite_FEM() :
latticePts_(2,1) {
this->basisCardinality_ = 4; // Four basis functions
this->basisDegree_ = 3; // Cubic polynomials
this->basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() );
this->basisType_ = BASIS_FEM_DEFAULT;
this->basisCoordinates_ = COORDINATES_CARTESIAN;
this->basisTagsAreSet_ = false;
latticePts_(0,0) = -1.0;
latticePts_(1,0) = 1.0;
setupVandermonde();
} // no-arg constructor
void Basis_HGRAD_LINE_Cn_FEM<Scalar,ArrayScalar>::getDofCoords( ArrayScalar & dofCoords ) const
{
for (int i=0;i<latticePts_.dimension(0);i++)
{
for (int j=0;j<latticePts_.dimension(1);j++)
{
dofCoords(i,j) = latticePts_(i,j);
}
}
return;
}
Basis_HGRAD_LINE_Hermite_FEM<Scalar,ArrayScalar>::Basis_HGRAD_LINE_Hermite_FEM( const ArrayScalar &pts) :
latticePts_( pts.dimension(0), 1 ) {
int n = pts.dimension(0);
this->basisCardinality_ = 2*n;
this->basisDegree_ = 2*n-1;
this->basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() );
this->basisType_ = BASIS_FEM_DEFAULT;
this->basisCoordinates_ = COORDINATES_CARTESIAN;
this->basisTagsAreSet_ = false;
for( int i=0; i<n-1; ++i ) {
TEUCHOS_TEST_FOR_EXCEPTION( pts(i,0) >= pts(i+1,0), std::runtime_error ,
"Intrepid::Basis_HGRAD_LINE_Hermite_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-1;i++) {
latticePts_(i,0) = pts(i,0);
}
if (std::abs(pts(n-1,0)-1.0) < INTREPID_TOL) {
latticePts_(n-1,0) = 1.0;
}
else {
latticePts_(n-1,0) = pts(n-1,0);
}
setupVandermonde();
} // Constructor with points given
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_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);
}
}
}
void Basis_HGRAD_LINE_Cn_FEM<Scalar, ArrayScalar>::initializeTags() {
// Basis-dependent initializations
int tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
int posScDim = 0; // position in the tag, counting from 0, of the subcell dim
int posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
int posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
// An array with local DoF tags assigned to the basis functions, in the order of their local enumeration
int *tags = new int[ tagSize * this->getCardinality() ];
int internal_dof;
int edge_dof;
const int n = this->getDegree();
// now we check the points for association
if (latticePts_(0,0) == -1.0) {
tags[0] = 0;
tags[1] = 0;
tags[2] = 0;
tags[3] = 1;
edge_dof = 1;
internal_dof = n-1;
}
else {
tags[0] = 1;
tags[1] = 0;
tags[2] = 0;
tags[3] = n+1;
edge_dof = 0;
internal_dof = n+1;
}
for (int i=1;i<n;i++) {
tags[4*i] = 1;
tags[4*i+1] = 0;
tags[4*i+2] = -edge_dof + i;
tags[4*i+3] = internal_dof;
}
if (latticePts_(n,0) == 1.0) {
tags[4*n] = 0;
tags[4*n+1] = 1;
tags[4*n+2] = 0;
tags[4*n+3] = 1;
}
else {
tags[4*n] = 1;
tags[4*n+1] = 0;
tags[4*n+2] = n;
tags[4*n+3] = n;
}
Intrepid2::setOrdinalTagData(this -> tagToOrdinal_,
this -> ordinalToTag_,
tags,
this -> basisCardinality_,
tagSize,
posScDim,
posScOrd,
posDfOrd);
delete []tags;
}
void Basis_HGRAD_LINE_Hermite_FEM<Scalar, ArrayScalar>::initializeTags() {
// Basis-dependent intializations
int tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
int posScDim = 0; // position in the tag, counting from 0, of the subcell dim
int posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
int posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
// An array with local DoF tags assigned to the basis functions, in the order of their local enumeration
int C = this->getCardinality();
tags_.reserve( tagSize * C );
int n = C/2;
int hasLeftVertex = static_cast<int>( latticePts_(0 , 0) == -1.0 );
int hasRightVertex = static_cast<int>( latticePts_(n-1, 0) == 1.0 );
int internal_dof = C - 2*(hasLeftVertex+hasRightVertex);
if( hasLeftVertex ) {
// Value interpolant
tags_[0] = 0; // this is a vertex (interval end point)
tags_[1] = 0; // this is the first subcell
tags_[2] = 0; // this is the first DoF for this vertex
tags_[3] = 2; // this vertex has 2 DoF
// Derivative interpolant
tags_[4] = 0; // this is a vertex (interval end point)
tags_[5] = 0; // this is the first subcell
tags_[6] = 1; // this is the second DoF for this vertex
tags_[7] = 2; // this vertex has 2 DoF
}
else { // no left vertex
// Value interpolant
tags_[0] = 1; // this point is on a line
tags_[1] = 0; // no subcells
tags_[2] = 0; // this is the first DoF for this line
tags_[3] = C-2*hasRightVertex; // this cell has 2n DoF
// Derivative interpolant
tags_[4] = 1; // this point is on a line
tags_[5] = 0; // no subcells
tags_[6] = 1; // this is the second DoF for this line
tags_[7] = C-2*hasRightVertex; // this cell has 2n DoF
}
if( hasRightVertex ) {
int i0 = C-2;
int i1 = C-1;
// Value interpolant
tags_[4*i0 ] = 0;
tags_[4*i0+1] = hasLeftVertex;
tags_[4*i0+2] = 0;
tags_[4*i0+3] = 2;
// Derivative interpolant
tags_[4*i1 ] = 0;
tags_[4*i1+1] = hasLeftVertex;
tags_[4*i1+2] = 1;
tags_[4*i1+3] = 2;
}
else { // no right vertex
int i0 = C-2;
int i1 = C-1;
// Value interpolant
tags_[4*i0 ] = 1;
tags_[4*i0+1] = 0;
tags_[4*i0+2] = internal_dof-2;
tags_[4*i0+3] = internal_dof;
// Derivative interpolant
tags_[4*i1 ] = 1;
tags_[4*i1+1] = 0;
tags_[4*i1+2] = internal_dof-1;
tags_[4*i1+3] = internal_dof;
}
for( int i=1; i<n-1; ++i ) {
int i0 = 2*i; int i1 = 2*i+1;
// Value interpolant
tags_[4*i0 ] = 1; // Points on a line (1 dimensional)
tags_[4*i0+1] = 0;
tags_[4*i0+2] = i0 - 2*hasLeftVertex;
tags_[4*i0+3] = internal_dof;
// Derivative interpolant
tags_[4*i1 ] = 1;
tags_[4*i1+1] = 0;
tags_[4*i1+2] = i1 - 2*hasLeftVertex;
tags_[4*i1+3] = internal_dof;
}
// Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
Intrepid::setOrdinalTagData(this -> tagToOrdinal_,
this -> ordinalToTag_,
tags_.data(),
this -> basisCardinality_,
tagSize,
posScDim,
posScOrd,
posDfOrd);
}
