void PointTools::
getWarpBlendLattice( /**/ Kokkos::DynRankView<pointValueType,pointProperties...> points,
const shards::CellTopology cell,
const ordinal_type order,
const ordinal_type offset ) {
switch (cell.getKey()) {
// case shards::Tetrahedron<4>::key:
// case shards::Tetrahedron<8>::key:
// case shards::Tetrahedron<10>::key: getWarpBlendLatticeTetrahedron( points, order, offset ); break;
// case shards::Triangle<3>::key:
// case shards::Triangle<4>::key:
// case shards::Triangle<6>::key: getWarpBlendLatticeTriangle ( points, order, offset ); break;
case shards::Line<2>::key:
case shards::Line<3>::key: getWarpBlendLatticeLine ( points, order, offset ); break;
default: {
INTREPID2_TEST_FOR_EXCEPTION( true , std::invalid_argument ,
">>> ERROR (Intrepid2::PointTools::getWarpBlendLattice): the specified cell type is not supported." );
}
}
}
ordinal_type
PointTools::
getLatticeSize( const shards::CellTopology cellType,
const ordinal_type order,
const ordinal_type offset ) {
#ifdef HAVE_INTREPID2_DEBUG
INTREPID2_TEST_FOR_EXCEPTION( order < 0 || offset < 0,
std::invalid_argument ,
">>> ERROR (PointTools::getLatticeSize): order and offset must be positive values." );
#endif
ordinal_type r_val = 0;
switch (cellType.getKey()) {
case shards::Tetrahedron<4>::key:
case shards::Tetrahedron<8>::key:
case shards::Tetrahedron<10>::key: {
const auto effectiveOrder = order - 4 * offset;
r_val = (effectiveOrder < 0 ? 0 :(effectiveOrder+1)*(effectiveOrder+2)*(effectiveOrder+3)/6);
break;
}
case shards::Triangle<3>::key:
case shards::Triangle<4>::key:
case shards::Triangle<6>::key: {
const auto effectiveOrder = order - 3 * offset;
r_val = (effectiveOrder < 0 ? 0 : (effectiveOrder+1)*(effectiveOrder+2)/2);
break;
}
case shards::Line<2>::key:
case shards::Line<3>::key: {
const auto effectiveOrder = order - 2 * offset;
r_val = (effectiveOrder < 0 ? 0 : (effectiveOrder+1));
break;
}
default: {
INTREPID2_TEST_FOR_EXCEPTION( true , std::invalid_argument ,
">>> ERROR (Intrepid2::PointTools::getLatticeSize): the specified cell type is not supported." );
}
}
return r_val;
}
//---------------------------------------------------------------------------//
Teuchos::RCP<Intrepid::Basis<double,Intrepid::FieldContainer<double> > >
IntrepidBasisFactory::create( const shards::CellTopology& cell_topo )
{
Teuchos::RCP<Intrepid::Basis<double,Intrepid::FieldContainer<double> > > basis;
switch( cell_topo.getKey() ){
case shards::Line<2>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_LINE_C1_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Triangle<3>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_TRI_C1_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Triangle<6>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_TRI_C2_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Quadrilateral<4>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_QUAD_C1_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Quadrilateral<9>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_QUAD_C2_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Tetrahedron<4>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_TET_C1_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Tetrahedron<10>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_TET_C2_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Hexahedron<8>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_HEX_C1_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Hexahedron<27>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_HEX_C2_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Wedge<6>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_WEDGE_C1_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Wedge<18>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_WEDGE_C2_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
case shards::Pyramid<5>::key:
case shards::Pyramid<13>::key:
case shards::Pyramid<14>::key:
basis = Teuchos::rcp(
new Intrepid::Basis_HGRAD_PYR_C1_FEM<
double,Intrepid::FieldContainer<double> >() );
break;
default:
bool topology_supported = false;
DTK_INSIST( topology_supported );
break;
}
return basis;
}
void
CellTools<SpT>::
setSubcellParametrization( subcellParamViewType &subcellParam,
const ordinal_type subcellDim,
const shards::CellTopology parentCell ) {
#ifdef HAVE_INTREPID2_DEBUG
INTREPID2_TEST_FOR_EXCEPTION( !hasReferenceCell(parentCell), std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::setSubcellParametrization): the specified cell topology does not have a reference cell.");
#endif
// subcellParametrization is rank-3 FieldContainer with dimensions (SC, PCD, COEF) where:
// - SC is the subcell count of subcells with the specified dimension in the parent cell
// - PCD is Parent Cell Dimension, which gives the number of coordinate functions in the map
// PCD = 2 for standard 2D cells and non-standard 2D cells: shell line and beam
// PCD = 3 for standard 3D cells and non-standard 3D cells: shell Tri and Quad
// - COEF is number of coefficients needed to specify a coordinate function:
// COEFF = 2 for edge parametrizations
// COEFF = 3 for both Quad and Tri face parametrizations. Because all Quad reference faces
// are affine, the coefficient of the bilinear term u*v is zero and is not stored, i.e.,
// 3 coefficients are sufficient to store Quad face parameterization maps.
//
// Edge parametrization maps [-1,1] to edge defined by (v0, v1)
// Face parametrization maps [-1,1]^2 to quadrilateral face (v0, v1, v2, v3), or
// standard 2-simplex {(0,0),(1,0),(0,1)} to traingle face (v0, v1, v2).
// This defines orientation-preserving parametrizations with respect to reference edge and
// face orientations induced by their vertex order.
// get subcellParametrization dimensions: (sc, pcd, coeff)
const auto sc = parentCell.getSubcellCount(subcellDim);
const auto pcd = parentCell.getDimension();
const auto coeff = (subcellDim == 1) ? 2 : 3;
INTREPID2_TEST_FOR_EXCEPTION( subcellDim < 1 || subcellDim > static_cast<ordinal_type>(pcd-1), std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::setSubcellParametrization): Parametrizations defined in a range between 1 and (dim-1)");
// create a view
subcellParam = subcellParamViewType("CellTools::setSubcellParametrization",
sc, pcd, coeff);
referenceNodeDataViewType
v0("CellTools::setSubcellParametrization::v0", Parameters::MaxDimension),
v1("CellTools::setSubcellParametrization::v1", Parameters::MaxDimension),
v2("CellTools::setSubcellParametrization::v1", Parameters::MaxDimension),
v3("CellTools::setSubcellParametrization::v1", Parameters::MaxDimension);
if (subcellDim == 1) {
// Edge parametrizations of 2D and 3D cells (shell lines and beams are 2D cells with edges)
for (size_type subcellOrd=0;subcellOrd<sc;++subcellOrd) {
// vertexK[0] = x_k; vertexK[1] = y_k; vertexK[2] = z_k; z_k = 0 for 2D cells
// Note that ShellLine and Beam are 2D cells!
const auto v0ord = parentCell.getNodeMap(subcellDim, subcellOrd, 0);
const auto v1ord = parentCell.getNodeMap(subcellDim, subcellOrd, 1);
getReferenceVertex(v0, parentCell, v0ord);
getReferenceVertex(v1, parentCell, v1ord);
// x(t) = (x0 + x1)/2 + t*(x1 - x0)/2
subcellParam(subcellOrd, 0, 0) = (v0[0] + v1[0])/2.0;
subcellParam(subcellOrd, 0, 1) = (v1[0] - v0[0])/2.0;
// y(t) = (y0 + y1)/2 + t*(y1 - y0)/2
subcellParam(subcellOrd, 1, 0) = (v0[1] + v1[1])/2.0;
subcellParam(subcellOrd, 1, 1) = (v1[1] - v0[1])/2.0;
if( pcd == 3 ) {
// z(t) = (z0 + z1)/2 + t*(z1 - z0)/2
subcellParam(subcellOrd, 2, 0) = (v0[2] + v1[2])/2.0;
subcellParam(subcellOrd, 2, 1) = (v1[2] - v0[2])/2.0;
}
}
}
else if (subcellDim == 2) {
// Face parametrizations of 3D cells: (shell Tri and Quad are 3D cells with faces)
// A 3D cell can have both Tri and Quad faces, but because they are affine images of the
// parametrization domain, 3 coefficients are enough to store them in both cases.
for (size_type subcellOrd=0;subcellOrd<sc;++subcellOrd) {
switch (parentCell.getKey(subcellDim,subcellOrd)) {
case shards::Triangle<3>::key:
case shards::Triangle<4>::key:
case shards::Triangle<6>::key: {
const auto v0ord = parentCell.getNodeMap(subcellDim, subcellOrd, 0);
const auto v1ord = parentCell.getNodeMap(subcellDim, subcellOrd, 1);
const auto v2ord = parentCell.getNodeMap(subcellDim, subcellOrd, 2);
getReferenceVertex(v0, parentCell, v0ord);
getReferenceVertex(v1, parentCell, v1ord);
getReferenceVertex(v2, parentCell, v2ord);
// x(u,v) = x0 + (x1 - x0)*u + (x2 - x0)*v
subcellParam(subcellOrd, 0, 0) = v0[0];
subcellParam(subcellOrd, 0, 1) = v1[0] - v0[0];
subcellParam(subcellOrd, 0, 2) = v2[0] - v0[0];
// y(u,v) = y0 + (y1 - y0)*u + (y2 - y0)*v
subcellParam(subcellOrd, 1, 0) = v0[1];
subcellParam(subcellOrd, 1, 1) = v1[1] - v0[1];
subcellParam(subcellOrd, 1, 2) = v2[1] - v0[1];
// z(u,v) = z0 + (z1 - z0)*u + (z2 - z0)*v
subcellParam(subcellOrd, 2, 0) = v0[2];
subcellParam(subcellOrd, 2, 1) = v1[2] - v0[2];
subcellParam(subcellOrd, 2, 2) = v2[2] - v0[2];
break;
}
case shards::Quadrilateral<4>::key:
case shards::Quadrilateral<8>::key:
case shards::Quadrilateral<9>::key: {
const auto v0ord = parentCell.getNodeMap(subcellDim, subcellOrd, 0);
const auto v1ord = parentCell.getNodeMap(subcellDim, subcellOrd, 1);
const auto v2ord = parentCell.getNodeMap(subcellDim, subcellOrd, 2);
const auto v3ord = parentCell.getNodeMap(subcellDim, subcellOrd, 3);
getReferenceVertex(v0, parentCell, v0ord);
getReferenceVertex(v1, parentCell, v1ord);
getReferenceVertex(v2, parentCell, v2ord);
getReferenceVertex(v3, parentCell, v3ord);
// x(u,v) = (x0+x1+x2+x3)/4+u*(-x0+x1+x2-x3)/4+v*(-x0-x1+x2+x3)/4+uv*(0=x0-x1+x2-x3)/4
subcellParam(subcellOrd, 0, 0) = ( v0[0] + v1[0] + v2[0] + v3[0])/4.0;
subcellParam(subcellOrd, 0, 1) = (-v0[0] + v1[0] + v2[0] - v3[0])/4.0;
subcellParam(subcellOrd, 0, 2) = (-v0[0] - v1[0] + v2[0] + v3[0])/4.0;
// y(u,v) = (y0+y1+y2+y3)/4+u*(-y0+y1+y2-y3)/4+v*(-y0-y1+y2+y3)/4+uv*(0=y0-y1+y2-y3)/4
subcellParam(subcellOrd, 1, 0) = ( v0[1] + v1[1] + v2[1] + v3[1])/4.0;
subcellParam(subcellOrd, 1, 1) = (-v0[1] + v1[1] + v2[1] - v3[1])/4.0;
subcellParam(subcellOrd, 1, 2) = (-v0[1] - v1[1] + v2[1] + v3[1])/4.0;
// z(u,v) = (z0+z1+z2+z3)/4+u*(-z0+z1+z2-z3)/4+v*(-z0-z1+z2+z3)/4+uv*(0=z0-z1+z2-z3)/4
subcellParam(subcellOrd, 2, 0) = ( v0[2] + v1[2] + v2[2] + v3[2])/4.0;
subcellParam(subcellOrd, 2, 1) = (-v0[2] + v1[2] + v2[2] - v3[2])/4.0;
subcellParam(subcellOrd, 2, 2) = (-v0[2] - v1[2] + v2[2] + v3[2])/4.0;
break;
}
default: {
INTREPID2_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::setSubcellParametrization): parametrization not defined for the specified face topology.");
}
}
}
}
}
void
CellTools<SpT>::
getSubcellParametrization( subcellParamViewType &subcellParam,
const ordinal_type subcellDim,
const shards::CellTopology parentCell ) {
#ifdef HAVE_INTREPID2_DEBUG
INTREPID2_TEST_FOR_EXCEPTION( !hasReferenceCell(parentCell), std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::getSubcellParametrization): the specified cell topology does not have a reference cell.");
#endif
if (!isSubcellParametrizationSet_)
setSubcellParametrization();
// Select subcell parametrization according to its parent cell type
const auto pcd = parentCell.getDimension(); // parent cell dim
INTREPID2_TEST_FOR_EXCEPTION( subcellDim < 1 || subcellDim > static_cast<ordinal_type>(pcd-1), std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::getSubcellParametrization): Parametrizations defined in a range between 1 and (dim-1)");
switch (parentCell.getKey() ) {
case shards::Tetrahedron<4>::key:
case shards::Tetrahedron<8>::key:
case shards::Tetrahedron<10>::key:
case shards::Tetrahedron<11>::key: subcellParam = ( subcellDim == 2 ? subcellParamData_.tetFaces : subcellParamData_.tetEdges ); break;
case shards::Hexahedron<8>::key:
case shards::Hexahedron<20>::key:
case shards::Hexahedron<27>::key: subcellParam = ( subcellDim == 2 ? subcellParamData_.hexFaces : subcellParamData_.hexEdges ); break;
case shards::Pyramid<5>::key:
case shards::Pyramid<13>::key:
case shards::Pyramid<14>::key: subcellParam = ( subcellDim == 2 ? subcellParamData_.pyrFaces : subcellParamData_.pyrEdges ); break;
case shards::Wedge<6>::key:
case shards::Wedge<15>::key:
case shards::Wedge<18>::key: subcellParam = ( subcellDim == 2 ? subcellParamData_.wedgeFaces : subcellParamData_.wedgeEdges ); break;
case shards::Triangle<3>::key:
case shards::Triangle<4>::key:
case shards::Triangle<6>::key: subcellParam = subcellParamData_.triEdges; break;
case shards::Quadrilateral<4>::key:
case shards::Quadrilateral<8>::key:
case shards::Quadrilateral<9>::key: subcellParam = subcellParamData_.quadEdges; break;
// case shards::ShellTriangle<3>::key:
// case shards::ShellTriangle<6>::key: subcellParam = ( subcellDim == 2 ? subcellParamData_.shellTriFaces : subcellParamData_.shellTriEdges ); break;
// case shards::ShellQuadrilateral<4>::key:
// case shards::ShellQuadrilateral<8>::key:
// case shards::ShellQuadrilateral<9>::key: subcellParam = ( subcellDim == 2 ? subcellParamData_.shellQuadFaces : subcellParamData_.shellQuadEdges ); break;
case shards::ShellLine<2>::key:
case shards::ShellLine<3>::key:
case shards::Beam<2>::key:
case shards::Beam<3>::key: subcellParam = subcellParamData_.lineEdges; break;
default: {
INTREPID2_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::getSubcellParametrization): invalid cell topology.");
}
}
}