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>::
mapToReferenceSubcell( /**/ Kokkos::DynRankView<refSubcellPointValueType,refSubcellPointProperties...> refSubcellPoints,
const Kokkos::DynRankView<paramPointValueType,paramPointProperties...> paramPoints,
const ordinal_type subcellDim,
const ordinal_type subcellOrd,
const shards::CellTopology parentCell ) {
#ifdef HAVE_INTREPID2_DEBUG
INTREPID2_TEST_FOR_EXCEPTION( !hasReferenceCell(parentCell), std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::mapToReferenceSubcell): the specified cell topology does not have a reference cell.");
INTREPID2_TEST_FOR_EXCEPTION( subcellDim != 1 &&
subcellDim != 2, std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::mapToReferenceSubcell): method defined only for 1 and 2-dimensional subcells.");
INTREPID2_TEST_FOR_EXCEPTION( subcellOrd < 0 ||
subcellOrd >= parentCell.getSubcellCount(subcellDim), std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::mapToReferenceSubcell): subcell ordinal out of range.");
// refSubcellPoints is rank-2 (P,D1), D1 = cell dimension
INTREPID2_TEST_FOR_EXCEPTION( refSubcellPoints.rank() != 2, std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::mapToReferenceSubcell): refSubcellPoints must have rank 2.");
INTREPID2_TEST_FOR_EXCEPTION( refSubcellPoints.dimension(1) != parentCell.getDimension(), std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::mapToReferenceSubcell): refSubcellPoints dimension (1) does not match to parent cell dimension.");
// paramPoints is rank-2 (P,D2) with D2 = subcell dimension
INTREPID2_TEST_FOR_EXCEPTION( paramPoints.rank() != 2, std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::mapToReferenceSubcell): paramPoints must have rank 2.");
INTREPID2_TEST_FOR_EXCEPTION( paramPoints.dimension(1) != subcellDim, std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::mapToReferenceSubcell): paramPoints dimension (1) does not match to subcell dimension.");
// cross check: refSubcellPoints and paramPoints: dimension 0 must match
INTREPID2_TEST_FOR_EXCEPTION( refSubcellPoints.dimension(0) < paramPoints.dimension(0), std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::mapToReferenceSubcell): refSubcellPoints dimension (0) does not match to paramPoints dimension(0).");
#endif
const auto cellDim = parentCell.getDimension();
const auto numPts = paramPoints.dimension(0);
// Get the subcell map, i.e., the coefficients of the parametrization function for the subcell
// can i get this map from devices ?
subcellParamViewType subcellMap;
getSubcellParametrization( subcellMap,
subcellDim,
parentCell );
// subcell parameterization should be small computation (numPts is small) and it should be decorated with
// kokkos inline... let's not do this yet
// Apply the parametrization map to every point in parameter domain
switch (subcellDim) {
case 2: {
for (size_type pt=0;pt<numPts;++pt) {
const auto u = paramPoints(pt, 0);
const auto v = paramPoints(pt, 1);
// map_dim(u,v) = c_0(dim) + c_1(dim)*u + c_2(dim)*v because both Quad and Tri ref faces are affine!
for (size_type i=0;i<cellDim;++i)
refSubcellPoints(pt, i) = subcellMap(subcellOrd, i, 0) + ( subcellMap(subcellOrd, i, 1)*u +
subcellMap(subcellOrd, i, 2)*v );
}
break;
}
case 1: {
for (size_type pt=0;pt<numPts;++pt) {
const auto u = paramPoints(pt, 0);
for (size_type i=0;i<cellDim;++i)
refSubcellPoints(pt, i) = subcellMap(subcellOrd, i, 0) + ( subcellMap(subcellOrd, i, 1)*u );
}
break;
}
default: {
INTREPID2_TEST_FOR_EXCEPTION( subcellDim != 1 &&
subcellDim != 2, std::invalid_argument,
">>> ERROR (Intrepid2::CellTools::mapToReferenceSubcell): method defined only for 1 and 2-subcells");
}
}
}
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.");
}
}
}
