A stateless class for operations on cell data. Provides methods for: More...

#include <Intrepid2_CellTools.hpp>

Public Member Functions
	CellTools ()=default
	Default constructor.

	~CellTools ()=default
	Destructor.

template<typename InCellViewType , typename InputViewType>
void	checkPointwiseInclusion (InCellViewType inCell, const InputViewType points, const shards::CellTopology cellTopo, const typename ScalarTraits< typename InputViewType::value_type >::scalar_type threshold)

template<typename Scalar >
void	setJacobianDividedByDet (Data< Scalar, DeviceType > &jacobianDividedByDet, const Data< Scalar, DeviceType > &jacobian, const Data< Scalar, DeviceType > &jacobianDetInv)

template<typename PhysPointViewType , typename RefPointViewType , typename WorksetType , typename HGradBasisPtrType >
void	mapToPhysicalFrame (PhysPointViewType physPoints, const RefPointViewType refPoints, const WorksetType worksetCell, const HGradBasisPtrType basis)

template<typename refSubcellViewType , typename paramViewType >
void	mapToReferenceSubcell (refSubcellViewType refSubcellPoints, const paramViewType paramPoints, const ordinal_type subcellDim, const ordinal_type subcellOrd, const shards::CellTopology parentCell)

template<typename refSubcellViewType , typename paramViewType >
void	mapToReferenceSubcell (refSubcellViewType refSubcellPoints, const paramViewType paramPoints, const typename RefSubcellParametrization< DeviceType >::ConstViewType subcellParametrization, const ordinal_type subcellOrd)

template<typename refSubcellViewType , typename paramViewType , typename ordViewType >
void	mapToReferenceSubcell (refSubcellViewType refSubcellPoints, const paramViewType paramPoints, const typename RefSubcellParametrization< DeviceType >::ConstViewType subcellParametrization, const ordViewType subcellOrd)

Static Public Member Functions
static bool	hasReferenceCell (const shards::CellTopology cellTopo)
	Checks if a cell topology has reference cell. More...

template<typename JacobianViewType , typename PointViewType , typename WorksetType , typename HGradBasisType >
static void	setJacobian (JacobianViewType jacobian, const PointViewType points, const WorksetType worksetCell, const Teuchos::RCP< HGradBasisType > basis, const int startCell=0, const int endCell=-1)
	Computes the Jacobian matrix DF of the reference-to-physical frame map F. More...

template<typename JacobianViewType , typename BasisGradientsType , typename WorksetType >
static void	setJacobian (JacobianViewType jacobian, const WorksetType worksetCell, const BasisGradientsType gradients, const int startCell=0, const int endCell=-1)
	Computes the Jacobian matrix DF of the reference-to-physical frame map F. More...

template<typename JacobianViewType , typename PointViewType , typename WorksetCellViewType >
static void	setJacobian (JacobianViewType jacobian, const PointViewType points, const WorksetCellViewType worksetCell, const shards::CellTopology cellTopo)
	Computes the Jacobian matrix DF of the reference-to-physical frame map F. More...

template<typename JacobianInvViewType , typename JacobianViewType >
static void	setJacobianInv (JacobianInvViewType jacobianInv, const JacobianViewType jacobian)
	Computes the inverse of the Jacobian matrix DF of the reference-to-physical frame map F. More...

template<typename JacobianDetViewType , typename JacobianViewType >
static void	setJacobianDet (JacobianDetViewType jacobianDet, const JacobianViewType jacobian)
	Computes the determinant of the Jacobian matrix DF of the reference-to-physical frame map F. More...

template<class PointScalar >
static Data< PointScalar, DeviceType >	allocateJacobianDet (const Data< PointScalar, DeviceType > &jacobian)
	Allocates and returns a Data container suitable for storing determinants corresponding to the Jacobians in the Data container provided. More...

template<class PointScalar >
static Data< PointScalar, DeviceType >	allocateJacobianInv (const Data< PointScalar, DeviceType > &jacobian)
	Allocates and returns a Data container suitable for storing inverses corresponding to the Jacobians in the Data container provided. More...

template<class PointScalar >
static void	setJacobianDet (Data< PointScalar, DeviceType > &jacobianDet, const Data< PointScalar, DeviceType > &jacobian)
	Computes determinants corresponding to the Jacobians in the Data container provided. More...

template<class PointScalar >
static void	setJacobianDetInv (Data< PointScalar, DeviceType > &jacobianDetInv, const Data< PointScalar, DeviceType > &jacobian)
	Computes reciprocals of determinants corresponding to the Jacobians in the Data container provided. More...

template<class PointScalar >
static void	setJacobianInv (Data< PointScalar, DeviceType > &jacobianInv, const Data< PointScalar, DeviceType > &jacobian)
	Computes determinants corresponding to the Jacobians in the Data container provided. More...

template<class PointScalar >
static void	setJacobianDividedByDet (Data< PointScalar, DeviceType > &jacobianDividedByDet, const Data< PointScalar, DeviceType > &jacobian, const Data< PointScalar, DeviceType > &jacobianDetInv)
	Multiplies the Jacobian with shape (C,P,D,D) by the reciprocals of the determinants, with shape (C,P), entrywise. More...

template<typename cellCenterValueType , class... cellCenterProperties>
static void	getReferenceCellCenter (Kokkos::DynRankView< cellCenterValueType, cellCenterProperties...> cellCenter, const shards::CellTopology cell)
	Computes the Cartesian coordinates of reference cell barycenter. More...

template<typename cellVertexValueType , class... cellVertexProperties>
static void	getReferenceVertex (Kokkos::DynRankView< cellVertexValueType, cellVertexProperties...> cellVertex, const shards::CellTopology cell, const ordinal_type vertexOrd)
	Retrieves the Cartesian coordinates of a reference cell vertex. More...

template<typename subcellVertexValueType , class... subcellVertexProperties>
static void	getReferenceSubcellVertices (Kokkos::DynRankView< subcellVertexValueType, subcellVertexProperties...> subcellVertices, const ordinal_type subcellDim, const ordinal_type subcellOrd, const shards::CellTopology parentCell)
	Retrieves the Cartesian coordinates of all vertices of a reference subcell. More...

template<typename cellNodeValueType , class... cellNodeProperties>
static void	getReferenceNode (Kokkos::DynRankView< cellNodeValueType, cellNodeProperties...> cellNode, const shards::CellTopology cell, const ordinal_type nodeOrd)
	Retrieves the Cartesian coordinates of a reference cell node. More...

template<typename SubcellNodeViewType >
static void	getReferenceSubcellNodes (SubcellNodeViewType subcellNodes, const ordinal_type subcellDim, const ordinal_type subcellOrd, const shards::CellTopology parentCell)
	Retrieves the Cartesian coordinates of all nodes of a reference subcell. More...

template<typename RefEdgeTangentViewType >
static void	getReferenceEdgeTangent (RefEdgeTangentViewType refEdgeTangent, const ordinal_type edgeOrd, const shards::CellTopology parentCell)
	Computes constant tangent vectors to edges of 2D or 3D reference cells. More...

template<typename RefFaceTanViewType >
static void	getReferenceFaceTangents (RefFaceTanViewType refFaceTanU, RefFaceTanViewType refFaceTanV, const ordinal_type faceOrd, const shards::CellTopology parentCell)
	Computes pairs of constant tangent vectors to faces of a 3D reference cells. More...

template<typename RefSideNormalViewType >
static void	getReferenceSideNormal (RefSideNormalViewType refSideNormal, const ordinal_type sideOrd, const shards::CellTopology parentCell)
	Computes constant normal vectors to sides of 2D or 3D reference cells. More...

template<typename RefFaceNormalViewType >
static void	getReferenceFaceNormal (RefFaceNormalViewType refFaceNormal, const ordinal_type faceOrd, const shards::CellTopology parentCell)
	Computes constant normal vectors to faces of 3D reference cell. More...

template<typename edgeTangentValueType , class... edgeTangentProperties, typename worksetJacobianValueType , class... worksetJacobianProperties>
static void	getPhysicalEdgeTangents (Kokkos::DynRankView< edgeTangentValueType, edgeTangentProperties...> edgeTangents, const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...> worksetJacobians, const ordinal_type worksetEdgeOrd, const shards::CellTopology parentCell)
	Computes non-normalized tangent vectors to physical edges in an edge workset $\{\mathcal{E}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of edge worksets). More...

template<typename edgeTangentValueType , class... edgeTangentProperties, typename worksetJacobianValueType , class... worksetJacobianProperties, typename edgeOrdValueType , class... edgeOrdProperties>
static void	getPhysicalEdgeTangents (Kokkos::DynRankView< edgeTangentValueType, edgeTangentProperties...> edgeTangents, const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...> worksetJacobians, const Kokkos::DynRankView< edgeOrdValueType, edgeOrdProperties...> worksetEdgeOrds, const shards::CellTopology parentCell)
	Computes non-normalized tangent vectors to physical edges in an edge workset $\{\mathcal{E}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of edge worksets). More...

template<typename faceTanValueType , class... faceTanProperties, typename worksetJacobianValueType , class... worksetJacobianProperties>
static void	getPhysicalFaceTangents (Kokkos::DynRankView< faceTanValueType, faceTanProperties...> faceTanU, Kokkos::DynRankView< faceTanValueType, faceTanProperties...> faceTanV, const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...> worksetJacobians, const ordinal_type worksetFaceOrd, const shards::CellTopology parentCell)
	Computes non-normalized tangent vector pairs to physical faces in a face workset $\{\mathcal{F}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of face worksets). More...

template<typename faceTanValueType , class... faceTanProperties, typename worksetJacobianValueType , class... worksetJacobianProperties, typename faceOrdValueType , class... faceOrdProperties>
static void	getPhysicalFaceTangents (Kokkos::DynRankView< faceTanValueType, faceTanProperties...> faceTanU, Kokkos::DynRankView< faceTanValueType, faceTanProperties...> faceTanV, const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...> worksetJacobians, const Kokkos::DynRankView< faceOrdValueType, faceOrdProperties...> worksetFaceOrds, const shards::CellTopology parentCell)
	Computes non-normalized tangent vector pairs to physical faces in a face workset $\{\mathcal{F}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of face worksets). More...

template<typename sideNormalValueType , class... sideNormalProperties, typename worksetJacobianValueType , class... worksetJacobianProperties>
static void	getPhysicalSideNormals (Kokkos::DynRankView< sideNormalValueType, sideNormalProperties...> sideNormals, const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...> worksetJacobians, const ordinal_type worksetSideOrd, const shards::CellTopology parentCell)
	Computes non-normalized normal vectors to physical sides in a side workset $\{\mathcal{S}_{c,i}\}_{c=0}^{N}$ . More...

template<typename sideNormalValueType , class... sideNormalProperties, typename worksetJacobianValueType , class... worksetJacobianProperties, typename edgeOrdValueType , class... edgeOrdProperties>
static void	getPhysicalSideNormals (Kokkos::DynRankView< sideNormalValueType, sideNormalProperties...> sideNormals, const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...> worksetJacobians, const Kokkos::DynRankView< edgeOrdValueType, edgeOrdProperties...> worksetSideOrds, const shards::CellTopology parentCell)
	Computes non-normalized normal vectors to physical sides in a side workset $\{\mathcal{S}_{c,i}\}_{c=0}^{N}$ . It is similar to the CellTools::getPhysicalSideNormals function above, with the difference that the side ordinal can change from point to point, and it is provided by the rank-2 input array worksetSideOrds, indexed by (C,P). More...

template<typename faceNormalValueType , class... faceNormalProperties, typename worksetJacobianValueType , class... worksetJacobianProperties>
static void	getPhysicalFaceNormals (Kokkos::DynRankView< faceNormalValueType, faceNormalProperties...> faceNormals, const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...> worksetJacobians, const ordinal_type worksetFaceOrd, const shards::CellTopology parentCell)
	Computes non-normalized normal vectors to physical faces in a face workset $\{\mathcal{F}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of face worksets). More...

template<typename faceNormalValueType , class... faceNormalProperties, typename worksetJacobianValueType , class... worksetJacobianProperties, typename faceOrdValueType , class... faceOrdProperties>
static void	getPhysicalFaceNormals (Kokkos::DynRankView< faceNormalValueType, faceNormalProperties...> faceNormals, const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...> worksetJacobians, const Kokkos::DynRankView< faceOrdValueType, faceOrdProperties...> worksetFaceOrds, const shards::CellTopology parentCell)
	Computes non-normalized normal vectors to physical faces in a face workset $\{\mathcal{F}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of face worksets). It is similar to the CellTools::getPhysicalSideNormals function above, with the difference that the side ordinal can change from point to point, and it is provided by the rank-2 input array worksetSideOrds, indexed by (C,P). More...

template<typename PhysPointValueType , typename RefPointValueType , typename WorksetType , typename HGradBasisPtrType >
static void	mapToPhysicalFrame (PhysPointValueType physPoints, const RefPointValueType refPoints, const WorksetType worksetCell, const HGradBasisPtrType basis)
	Computes F, the reference-to-physical frame map. More...

template<typename PhysPointViewType , typename RefPointViewType , typename WorksetCellViewType >
static void	mapToPhysicalFrame (PhysPointViewType physPoints, const RefPointViewType refPoints, const WorksetCellViewType worksetCell, const shards::CellTopology cellTopo)
	Computes F, the reference-to-physical frame map. More...

template<typename refSubcellViewType , typename paramPointViewType >
static void	mapToReferenceSubcell (refSubcellViewType refSubcellPoints, const paramPointViewType paramPoints, const ordinal_type subcellDim, const ordinal_type subcellOrd, const shards::CellTopology parentCell)
	Computes parameterization maps of 1- and 2-subcells of reference cells. More...

template<typename refSubcellViewType , typename paramPointViewType >
static void	mapToReferenceSubcell (refSubcellViewType refSubcellPoints, const paramPointViewType paramPoints, const typename RefSubcellParametrization< DeviceType >::ConstViewType subcellParametrization, const ordinal_type subcellOrd)
	Computes parameterization maps of 1- and 2-subcells of reference cells. More...

template<typename refSubcellViewType , typename paramPointViewType , typename ordViewType >
static void	mapToReferenceSubcell (refSubcellViewType refSubcellPoints, const paramPointViewType paramPoints, const typename RefSubcellParametrization< DeviceType >::ConstViewType subcellParametrization, const ordViewType subcellOrd)
	Computes parameterization maps of 1- and 2-subcells of reference cells. More...

template<typename refPointValueType , class... refPointProperties, typename physPointValueType , class... physPointProperties, typename worksetCellValueType , class... worksetCellProperties>
static void	mapToReferenceFrame (Kokkos::DynRankView< refPointValueType, refPointProperties...> refPoints, const Kokkos::DynRankView< physPointValueType, physPointProperties...> physPoints, const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...> worksetCell, const shards::CellTopology cellTopo)
	Computes $F^{-1}_{c}$ , the inverse of the reference-to-physical frame map using a default initial guess. More...

template<typename refPointValueType , class... refPointProperties, typename initGuessValueType , class... initGuessProperties, typename physPointValueType , class... physPointProperties, typename worksetCellValueType , class... worksetCellProperties, typename HGradBasisPtrType >
static void	mapToReferenceFrameInitGuess (Kokkos::DynRankView< refPointValueType, refPointProperties...> refPoints, const Kokkos::DynRankView< initGuessValueType, initGuessProperties...> initGuess, const Kokkos::DynRankView< physPointValueType, physPointProperties...> physPoints, const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...> worksetCell, const HGradBasisPtrType basis)
	Computation of $F^{-1}_{c}$ , the inverse of the reference-to-physical frame map using user-supplied initial guess. More...

template<typename refPointValueType , class... refPointProperties, typename initGuessValueType , class... initGuessProperties, typename physPointValueType , class... physPointProperties, typename worksetCellValueType , class... worksetCellProperties>
static void	mapToReferenceFrameInitGuess (Kokkos::DynRankView< refPointValueType, refPointProperties...> refPoints, const Kokkos::DynRankView< initGuessValueType, initGuessProperties...> initGuess, const Kokkos::DynRankView< physPointValueType, physPointProperties...> physPoints, const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...> worksetCell, const shards::CellTopology cellTopo)
	Computation of $F^{-1}_{c}$ , the inverse of the reference-to-physical frame map using user-supplied initial guess. More...

template<typename subcvCoordValueType , class... subcvCoordProperties, typename cellCoordValueType , class... cellCoordProperties>
static void	getSubcvCoords (Kokkos::DynRankView< subcvCoordValueType, subcvCoordProperties...> subcvCoords, const Kokkos::DynRankView< cellCoordValueType, cellCoordProperties...> cellCoords, const shards::CellTopology primaryCell)
	Computes coordinates of sub-control volumes in each primary cell. More...

template<typename PointViewType >
static bool	checkPointInclusion (const PointViewType point, const shards::CellTopology cellTopo, const typename ScalarTraits< typename PointViewType::value_type >::scalar_type thres=threshold< typename ScalarTraits< typename PointViewType::value_type >::scalar_type >())
	Checks if a point belongs to a reference cell. More...

template<unsigned cellTopologyKey, typename OutputViewType , typename InputViewType >
static void	checkPointwiseInclusion (OutputViewType inCell, const InputViewType points, const typename ScalarTraits< typename InputViewType::value_type >::scalar_type thresh=threshold< typename ScalarTraits< typename InputViewType::value_type >::scalar_type >())
	Checks every point for inclusion in the reference cell of a given topology. The points can belong to a global set and stored in a rank-2 view (P,D) , or to multiple sets indexed by a cell ordinal and stored in a rank-3 view (C,P,D). The cell topology key is a template argument. Requires cell topology with a reference cell. More...

template<typename InCellViewType , typename PointViewType >
static void	checkPointwiseInclusion (InCellViewType inCell, const PointViewType points, const shards::CellTopology cellTopo, const typename ScalarTraits< typename PointViewType::value_type >::scalar_type thres=threshold< typename ScalarTraits< typename PointViewType::value_type >::scalar_type >())
	Checks every point in multiple sets indexed by a cell ordinal for inclusion in the reference cell of a given topology. Requires cell topology with a reference cell. More...

template<typename inCellValueType , class... inCellProperties, typename pointValueType , class... pointProperties, typename cellWorksetValueType , class... cellWorksetProperties>
static void	checkPointwiseInclusion (Kokkos::DynRankView< inCellValueType, inCellProperties...> inCell, const Kokkos::DynRankView< pointValueType, pointProperties...> points, const Kokkos::DynRankView< cellWorksetValueType, cellWorksetProperties...> cellWorkset, const shards::CellTopology cellTopo, const typename ScalarTraits< pointValueType >::scalar_type thres=threshold< typename ScalarTraits< pointValueType >::scalar_type >())
	Checks every points for inclusion in physical cells from a cell workset. The points can belong to a global set and stored in a rank-2 (P,D) view, or to multiple sets indexed by a cell ordinal and stored in a rank-3 (C,P,D) view cells in a cell workset. More...

Private Types
using	ExecSpaceType = typename DeviceType::execution_space

using	MemSpaceType = typename DeviceType::memory_space

Static Private Member Functions
template<typename outputValueType , typename pointValueType >
static Teuchos::RCP< Basis < DeviceType, outputValueType, pointValueType > >	createHGradBasis (const shards::CellTopology cellTopo)
	Generates default HGrad basis based on cell topology. More...

Detailed Description

template<typename DeviceType>
class Intrepid2::CellTools< DeviceType >

A stateless class for operations on cell data. Provides methods for:

computing Jacobians of reference-to-physical frame mappings, their inverses and determinants
application of the reference-to-physical frame mapping and its inverse
parametrizations of edges and faces of reference cells needed for edge and face integrals,
computation of edge and face tangents and face normals on both reference and physical frames
inclusion tests for point sets in reference and physical cells.

Definition at line 77 of file Intrepid2_CellTools.hpp.

Member Function Documentation

template<typename DeviceType >

template<class PointScalar >

Data< PointScalar, DeviceType > Intrepid2::CellTools< DeviceType >::allocateJacobianDet ( const Data< PointScalar, DeviceType > & jacobian )

static

Allocates and returns a Data container suitable for storing determinants corresponding to the Jacobians in the Data container provided.

Parameters

jacobian [in] - data with shape (C,P,D,D), as returned by CellGeometry::allocateJacobianData()

Returns: Data container with shape (C,P)

Definition at line 92 of file Intrepid2_CellToolsDefJacobian.hpp.

References Intrepid2::Data< DataScalar, DeviceType >::getExtents(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView1(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView3(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView4(), and Intrepid2::Data< DataScalar, DeviceType >::getVariationTypes().

template<typename DeviceType >

template<class PointScalar >

Data< PointScalar, DeviceType > Intrepid2::CellTools< DeviceType >::allocateJacobianInv ( const Data< PointScalar, DeviceType > & jacobian )

static

Allocates and returns a Data container suitable for storing inverses corresponding to the Jacobians in the Data container provided.

Parameters

jacobian [in] - data with shape (C,P,D,D), as returned by CellGeometry::allocateJacobianData()

Returns: Data container with shape (C,P,D,D)

Definition at line 126 of file Intrepid2_CellToolsDefJacobian.hpp.

References Intrepid2::Data< DataScalar, DeviceType >::getExtents(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView1(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView2(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView3(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView4(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingViewRank(), Intrepid2::Data< DataScalar, DeviceType >::getVariationTypes(), and INTREPID2_TEST_FOR_EXCEPTION_DEVICE_SAFE.

template<typename DeviceType >

template<typename PointViewType >

bool Intrepid2::CellTools< DeviceType >::checkPointInclusion	(	const PointViewType	point,
		const shards::CellTopology	cellTopo,
		const typename ScalarTraits< typename PointViewType::value_type >::scalar_type	thres = `threshold<typename ScalarTraits<typename PointViewType::value_type>::scalar_type>()`
	)

static

Checks if a point belongs to a reference cell.

Requires cell topology with a reference cell.

Parameters

point	[in] - rank-1 view (D) of the point tested for inclusion
cellTopo	[in] - cell topology
threshold	[in] - "tightness" of the inclusion test

Returns: true if the point is in the closure of the specified reference cell and false otherwise.

Definition at line 37 of file Intrepid2_CellToolsDefInclusion.hpp.

template<typename DeviceType >

template<unsigned cellTopologyKey, typename OutputViewType , typename InputViewType >

void Intrepid2::CellTools< DeviceType >::checkPointwiseInclusion	(	OutputViewType	inCell,
		const InputViewType	points,
		const typename ScalarTraits< typename InputViewType::value_type >::scalar_type	thresh = `threshold<typename ScalarTraits<typename InputViewType::value_type>::scalar_type>()`
	)

static

Checks every point for inclusion in the reference cell of a given topology. The points can belong to a global set and stored in a rank-2 view (P,D) , or to multiple sets indexed by a cell ordinal and stored in a rank-3 view (C,P,D). The cell topology key is a template argument. Requires cell topology with a reference cell.

Parameters

inCell	[out] - rank-1 view (P) or rank-2 view (C,P). On return, its entries will be set to 1 or 0 depending on whether points are included in cells
point	[in] - rank-2 view (P,D) or rank-3 view (C,P,D) with reference coordinates of the points tested for inclusion
threshold	[in] - "tightness" of the inclusion test

Definition at line 131 of file Intrepid2_CellToolsDefInclusion.hpp.

template<typename DeviceType >

template<typename InCellViewType , typename PointViewType >

static void Intrepid2::CellTools< DeviceType >::checkPointwiseInclusion	(	InCellViewType	inCell,
		const PointViewType	points,
		const shards::CellTopology	cellTopo,
		const typename ScalarTraits< typename PointViewType::value_type >::scalar_type	thres = `threshold< typename ScalarTraits< typename PointViewType::value_type >::scalar_type >()`
	)

static

Checks every point in multiple sets indexed by a cell ordinal for inclusion in the reference cell of a given topology. Requires cell topology with a reference cell.

Parameters

inRefCell	[out] - rank-2 view (C,P) with results from the pointwise inclusion test
refPoints	[in] - rank-3 view (C,P,D)
cellTopo	[in] - cell topology
threshold	[in] - "tightness" of the inclusion test

template<typename DeviceType >

template<typename inCellValueType , class... inCellProperties, typename pointValueType , class... pointProperties, typename cellWorksetValueType , class... cellWorksetProperties>

void Intrepid2::CellTools< DeviceType >::checkPointwiseInclusion	(	Kokkos::DynRankView< inCellValueType, inCellProperties...>	inCell,
		const Kokkos::DynRankView< pointValueType, pointProperties...>	points,
		const Kokkos::DynRankView< cellWorksetValueType, cellWorksetProperties...>	cellWorkset,
		const shards::CellTopology	cellTopo,
		const typename ScalarTraits< pointValueType >::scalar_type	thres = `threshold<typename ScalarTraits<pointValueType>::scalar_type>()`
	)

static

Checks every points for inclusion in physical cells from a cell workset. The points can belong to a global set and stored in a rank-2 (P,D) view, or to multiple sets indexed by a cell ordinal and stored in a rank-3 (C,P,D) view cells in a cell workset.

Parameters

inCell	[out] - rank-2 view (P,D) with results from the pointwise inclusion test
points	[in] - rank-2 view (P,D) or rank-3 view (C,P,D) with the physical points
cellWorkset	[in] - rank-3 view with dimensions (C,N,D) with the nodes of the cell workset
cellTopo	[in] - cell topology
threshold	[in] - tolerance for inclusion tests on the input points

Definition at line 216 of file Intrepid2_CellToolsDefInclusion.hpp.

References Intrepid2::RealSpaceTools< DeviceType >::clone().

template<typename DeviceType >

template<typename outputValueType , typename pointValueType >

static Teuchos::RCP<Basis<DeviceType,outputValueType,pointValueType> > Intrepid2::CellTools< DeviceType >::createHGradBasis ( const shards::CellTopology cellTopo )

inlinestaticprivate

Generates default HGrad basis based on cell topology.

Parameters

cellTopo [in] - cell topology

Definition at line 100 of file Intrepid2_CellTools.hpp.

template<typename DeviceType >

template<typename edgeTangentValueType , class... edgeTangentProperties, typename worksetJacobianValueType , class... worksetJacobianProperties>

void Intrepid2::CellTools< DeviceType >::getPhysicalEdgeTangents	(	Kokkos::DynRankView< edgeTangentValueType, edgeTangentProperties...>	edgeTangents,
		const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...>	worksetJacobians,
		const ordinal_type	worksetEdgeOrd,
		const shards::CellTopology	parentCell
	)

static

Computes non-normalized tangent vectors to physical edges in an edge workset $\{\mathcal{E}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of edge worksets).

For every edge in the workset the tangents are computed at the points ${\bf x}_p = F_c(\hat{\Phi}_i(t_p))\in\mathcal{E}_{c,i}$ that are images of points from R=[-1,1] on edge $\mathcal{E}_{c,i}$ . Returns rank-3 array with dimensions (C,P,D1), D1=2 or D1=3 such that

${edgeTangents}(c,p,d) = DF_c(\hat{\Phi}_i(t_p))\cdot {\partial{\hat{\Phi}}_{i}(t_p)\over\partial t}\,; \qquad t_p \in R$

In this formula:

is Jacobian of parent cell ${\mathcal C}$ that owns physical edge ${\mathcal E}_{c,i}$ ;
${\partial{\hat{\Phi}}_{i}/\partial t}$ is the (constant) tangent to reference edge $\hat{\mathcal E}_i$ ; see Intrepid2::CellTools::getReferenceEdgeTangent that has the same local ordinal as the edges in the workset;
$\hat{\Phi}_i R\mapsto\hat{\mathcal E}_i$ is parametrization of reference edge $\hat{\mathcal E}_i$ ;

Warning: worksetJacobians must contain the values of $DF_c(\hat{\Phi}_i(t_p))$ , where $t_p \in R=[-1,1]$ , i.e., Jacobians of the parent cells evaluated at points that are located on reference edge $\hat{\mathcal E}_i$ having the same local ordinal as the edges in the workset.

Parameters

edgeTangents	[out] - rank-3 array (C,P,D1) with tangents on workset edges
worksetJacobians	[in] - rank-4 array (C,P,D1,D1) with Jacobians evaluated at ref. edge points
worksetEdgeOrd	[in] - edge ordinal, relative to ref. cell, of the edge workset
parentCell	[in] - cell topology of the parent reference cell

Definition at line 372 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RealSpaceTools< DeviceType >::matvec().

Referenced by Intrepid2::FunctionSpaceTools< DeviceType >::computeEdgeMeasure().

template<typename DeviceType >

template<typename edgeTangentValueType , class... edgeTangentProperties, typename worksetJacobianValueType , class... worksetJacobianProperties, typename edgeOrdValueType , class... edgeOrdProperties>

void Intrepid2::CellTools< DeviceType >::getPhysicalEdgeTangents	(	Kokkos::DynRankView< edgeTangentValueType, edgeTangentProperties...>	edgeTangents,
		const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...>	worksetJacobians,
		const Kokkos::DynRankView< edgeOrdValueType, edgeOrdProperties...>	worksetEdgeOrds,
		const shards::CellTopology	parentCell
	)

static

Computes non-normalized tangent vectors to physical edges in an edge workset $\{\mathcal{E}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of edge worksets).

It is similar to the CellTools::getPhysicalEdgeTangents function above, with the difference that the edge ordinal can change from point to point, and it is provided by the rank-2 input array worksetEdgeOrds, indexed by (C,P).

Parameters

edgeTangents	[out] - rank-3 array (C,P,D1) with tangents on workset edges
worksetJacobians	[in] - rank-4 array (C,P,D1,D1) with Jacobians evaluated at ref. edge points
worksetEdgeOrds	[in] - rank-2 array (C,P) with edge ordinals, relative to ref. cell, of the edge workset
parentCell	[in] - cell topology of the parent reference cell

Definition at line 454 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RefSubcellParametrization< DeviceType >::get(), and Intrepid2::RealSpaceTools< DeviceType >::matvec().

template<typename DeviceType >

template<typename faceNormalValueType , class... faceNormalProperties, typename worksetJacobianValueType , class... worksetJacobianProperties>

void Intrepid2::CellTools< DeviceType >::getPhysicalFaceNormals	(	Kokkos::DynRankView< faceNormalValueType, faceNormalProperties...>	faceNormals,
		const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...>	worksetJacobians,
		const ordinal_type	worksetFaceOrd,
		const shards::CellTopology	parentCell
	)

static

Computes non-normalized normal vectors to physical faces in a face workset $\{\mathcal{F}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of face worksets).

For every face in the workset the normals are computed at the points ${\bf x}_p = F_c(\hat{\Phi}_i(u_p,v_p))\in\mathcal{F}_{c,i}$ that are images of points from the parametrization domain R on face $\mathcal{F}_{c,i}$ . Returns rank-3 array with dimensions (C,P,D), D=3, such that

${faceNormals}(c,p,d) = \left( DF_c(\hat{\Phi}_i(u_p, v_p))\cdot {\partial\hat{\Phi}_i\over\partial u}\right) \times \left( DF_c(\hat{\Phi}_i(u_p, v_p))\cdot {\partial\hat{\Phi}_i\over\partial v}\right) \,; \qquad (u_p, v_p) \in R \,.$

In this formula:

is Jacobian of parent cell ${\mathcal C}$ that owns physical face ${\mathcal F}_{c,i}$ ;
${\partial\hat{\Phi}_i/\partial u}, {\partial\hat{\Phi}_i/\partial v}$ are the (constant) tangents on reference face $\hat{\mathcal F}_i$ ; see Intrepid2::CellTools::getReferenceFaceTangents; that has the same local ordinal as the faces in the workset;
$\hat{\Phi}_i : R\mapsto \hat{\mathcal F}_i$ is parametrization of reference face $\hat{\mathcal F}_i$ ;
R is the parametrization domain for reference face $\hat{\mathcal F}_i$ :
$R = \left\{\begin{array}{rl} \{(0,0),(1,0),(0,1)\} & \mbox{if $\hat{\mathcal F}_i$ is Triangle} \\[1ex] [-1,1]\times [-1,1] & \mbox{if $\hat{\mathcal F}_i$ is Quadrilateral} \end{array}\right.$

Warning: worksetJacobians must contain the values of $DF_c(\hat{\Phi}_i(u_p,v_p))$ , where $(u_p,v_p)\in R$ , i.e., Jacobians of the parent cells evaluated at points that are located on reference face $\hat{\mathcal F}_i$ having the same local ordinal as the faces in the workset.

Parameters

faceNormals	[out] - rank-3 array (C,P,D), normals at workset faces
worksetJacobians	[in] - rank-4 array (C,P,D,D) with Jacobians at ref. face points
worksetFaceOrd	[in] - face ordinal, relative to ref. cell, of the face workset
parentCell	[in] - cell topology of the parent reference cell

Definition at line 813 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RealSpaceTools< DeviceType >::vecprod().

Referenced by Intrepid2::FunctionSpaceTools< DeviceType >::computeFaceMeasure().

template<typename DeviceType >

template<typename faceNormalValueType , class... faceNormalProperties, typename worksetJacobianValueType , class... worksetJacobianProperties, typename faceOrdValueType , class... faceOrdProperties>

void Intrepid2::CellTools< DeviceType >::getPhysicalFaceNormals	(	Kokkos::DynRankView< faceNormalValueType, faceNormalProperties...>	faceNormals,
		const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...>	worksetJacobians,
		const Kokkos::DynRankView< faceOrdValueType, faceOrdProperties...>	worksetFaceOrds,
		const shards::CellTopology	parentCell
	)

static

Computes non-normalized normal vectors to physical faces in a face workset $\{\mathcal{F}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of face worksets). It is similar to the CellTools::getPhysicalSideNormals function above, with the difference that the side ordinal can change from point to point, and it is provided by the rank-2 input array worksetSideOrds, indexed by (C,P).

Parameters

faceNormals	[out] - rank-3 array (C,P,D), normals at workset faces
worksetJacobians	[in] - rank-4 array (C,P,D,D) with Jacobians at ref. face points
worksetFaceOrds	[in] - rank-2 array (C,P) with face ordinals, relative to ref. cell, of the face workset
parentCell	[in] - cell topology of the parent reference cell

Definition at line 875 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RealSpaceTools< DeviceType >::vecprod().

template<typename DeviceType >

template<typename faceTanValueType , class... faceTanProperties, typename worksetJacobianValueType , class... worksetJacobianProperties>

void Intrepid2::CellTools< DeviceType >::getPhysicalFaceTangents	(	Kokkos::DynRankView< faceTanValueType, faceTanProperties...>	faceTanU,
		Kokkos::DynRankView< faceTanValueType, faceTanProperties...>	faceTanV,
		const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...>	worksetJacobians,
		const ordinal_type	worksetFaceOrd,
		const shards::CellTopology	parentCell
	)

static

Computes non-normalized tangent vector pairs to physical faces in a face workset $\{\mathcal{F}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of face worksets).

For every face in the workset the tangents are computed at the points ${\bf x}_p = F_c(\hat{\Phi}_i(u_p,v_p))\in\mathcal{F}_{c,i}$ that are images of points from the parametrization domain R on face $\mathcal{F}_{c,i}$ . Returns 2 rank-3 arrays with dimensions (C,P,D), D=3 such that

${faceTanU}(c,p,d) = DF_c(\hat{\Phi}_i(u_p, v_p))\cdot {\partial\hat{\Phi}_i\over\partial u};\qquad {faceTanV}(c,p,d) = DF_c(\hat{\Phi}_i(u_p, v_p))\cdot {\partial\hat{\Phi}_{i}\over\partial v}\,; \qquad (u_p, v_p) \in R \,.$

In this formula:

is Jacobian of parent cell ${\mathcal C}$ that owns physical face ${\mathcal F}_{c,i}$ ;
${\partial\hat{\Phi}_i/\partial u}, {\partial\hat{\Phi}_i/\partial v}$ are the (constant) tangents on reference face $\hat{\mathcal F}_i$ ; see Intrepid2::CellTools::getReferenceFaceTangents; that has the same local ordinal as the faces in the workset;
$\hat{\Phi}_i : R\mapsto \hat{\mathcal F}_i$ is parametrization of reference face $\hat{\mathcal F}_i$ ;
R is the parametrization domain for reference face $\hat{\mathcal F}_i$ :
$R = \left\{\begin{array}{rl} \{(0,0),(1,0),(0,1)\} & \mbox{if $\hat{\mathcal F}_i$ is Triangle} \\[1ex] [-1,1]\times [-1,1] & \mbox{if $\hat{\mathcal F}_i$ is Quadrilateral} \end{array}\right.$

Warning: worksetJacobians must contain the values of $DF_c(\hat{\Phi}_i(u_p,v_p))$ , where $(u_p,v_p)\in R$ , i.e., Jacobians of the parent cells evaluated at points that are located on reference face $\hat{\mathcal F}_i$ having the same local ordinal as the faces in the workset.

Parameters

faceTanU	[out] - rank-3 array (C,P,D), image of ref. face u-tangent at workset faces
faceTanV	[out] - rank-3 array (C,P,D), image of ref. face u-tangent at workset faces
worksetJacobians	[in] - rank-4 array (C,P,D,D) with Jacobians at ref. face points
worksetFaceOrd	[in] - face ordinal, relative to ref. cell, of the face workset
parentCell	[in] - cell topology of the parent reference cell

Definition at line 518 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RealSpaceTools< DeviceType >::matvec().

template<typename DeviceType >

template<typename faceTanValueType , class... faceTanProperties, typename worksetJacobianValueType , class... worksetJacobianProperties, typename faceOrdValueType , class... faceOrdProperties>

void Intrepid2::CellTools< DeviceType >::getPhysicalFaceTangents	(	Kokkos::DynRankView< faceTanValueType, faceTanProperties...>	faceTanU,
		Kokkos::DynRankView< faceTanValueType, faceTanProperties...>	faceTanV,
		const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...>	worksetJacobians,
		const Kokkos::DynRankView< faceOrdValueType, faceOrdProperties...>	worksetFaceOrds,
		const shards::CellTopology	parentCell
	)

static

Computes non-normalized tangent vector pairs to physical faces in a face workset $\{\mathcal{F}_{c,i}\}_{c=0}^{N}$ ; (see Subcell worksets for definition of face worksets).

It is similar to the CellTools::getPhysicalFaceTangents function above, with the difference that the face ordinal can change from point to point, and it is provided by the rank-2 input array worksetFaceOrds, indexed by (C,P).

Parameters

faceTanU	[out] - rank-3 array (C,P,D), image of ref. face u-tangent at workset faces
faceTanV	[out] - rank-3 array (C,P,D), image of ref. face u-tangent at workset faces
worksetJacobians	[in] - rank-4 array (C,P,D,D) with Jacobians at ref. face points
worksetFaceOrds	[in] - rank-2 array (C,P) with face ordinals, relative to ref. cell, of the face workset
parentCell	[in] - cell topology of the parent reference cell

Definition at line 614 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RefSubcellParametrization< DeviceType >::get(), and Intrepid2::RealSpaceTools< DeviceType >::matvec().

template<typename DeviceType >

template<typename sideNormalValueType , class... sideNormalProperties, typename worksetJacobianValueType , class... worksetJacobianProperties>

void Intrepid2::CellTools< DeviceType >::getPhysicalSideNormals	(	Kokkos::DynRankView< sideNormalValueType, sideNormalProperties...>	sideNormals,
		const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...>	worksetJacobians,
		const ordinal_type	worksetSideOrd,
		const shards::CellTopology	parentCell
	)

static

Computes non-normalized normal vectors to physical sides in a side workset $\{\mathcal{S}_{c,i}\}_{c=0}^{N}$ .

For every side in the workset the normals are computed at the points ${\bf x}_p = F_c(\hat{\Phi}_i(P_p))\in\mathcal{S}_{c,i}$ that are images of points from the parametrization domain R on side $\mathcal{S}_{c,i}$ . A side is defined as a subcell of dimension one less than that of its parent cell. Therefore, sides of 2D cells are 1-subcells (edges) and sides of 3D cells are 2-subcells (faces).

Returns rank-3 array with dimensions (C,P,D), D = 2 or 3, such that

${sideNormals}(c,p,d) = \left\{\begin{array}{crl} \displaystyle \left(DF_c(\hat{\Phi}_i(t_p))\cdot {\partial{\hat{\Phi}}_{i}(t_p)\over\partial t}\right)^{\perp} & t_p\in R & \mbox{for 2D parent cells} \\[2ex] \displaystyle \left( DF_c(\hat{\Phi}_i(u_p, v_p))\cdot {\partial\hat{\Phi}_i\over\partial u}\right) \times \left( DF_c(\hat{\Phi}_i(u_p, v_p))\cdot {\partial\hat{\Phi}_i\over\partial v}\right) \,; & (u_p, v_p) \in R & \mbox{for 3D parent cells} \end{array}\right.$

In this formula:

is Jacobian of parent cell ${\mathcal C}$ that owns physical side ${\mathcal S}_{c,i}$ ;
For 2D cells: ${\partial{\hat{\Phi}}_{i}/\partial t}$ is the (constant) tangent to reference side (edge) $\hat{\mathcal S}_i$ ; see Intrepid2::CellTools::getReferenceEdgeTangent, that has the same local ordinal as the sides in the workset;
For 3D cells: ${\partial\hat{\Phi}_i/\partial u}, {\partial\hat{\Phi}_i/\partial v}$ are the (constant) tangents on reference side (face) $\hat{\mathcal S}_i$ ; see Intrepid2::CellTools::getReferenceFaceTangents, that has the same local ordinal as the sides in the workset;
$\hat{\Phi}_i : R\mapsto \hat{\mathcal S}_i$ is parametrization of reference side $\hat{\mathcal S}_i$ ;
R is the parametrization domain for reference side $\hat{\mathcal S}_i$ . For 2D parent cells R=[-1,1] and for 3D parent cells
$R = \left\{\begin{array}{rl} \{(0,0),(1,0),(0,1)\} & \mbox{if $\hat{\mathcal S}_i$ is Triangle} \\[1ex] [-1,1]\times [-1,1] & \mbox{if $\hat{\mathcal S}_i$ is Quadrilateral} \end{array}\right.$

Remarks

For 3D cells the physical side normals coincides with the face normals computed by Intrepid2::CellTools::getPhysicalFaceNormals and these two methods are completely equivalent.
For 2D cells the physical side normals are defined by ${\bf n}=(t_2,-t_1)$ where ${\bf t}=(t_1,t_2)$ are the physical edge tangents computed by Intrepid2::CellTools::getPhysicalEdgeTangents. Therefore, the pairs $({\bf n},{\bf t})$ are positively oriented.

Warning: worksetJacobians must contain the values of $DF_c(\hat{\Phi}_i(P_p))$ , where $P_p\in R$ , i.e., Jacobians of the parent cells evaluated at points that are located on reference side $\hat{\mathcal S}_i$ having the same local ordinal as the sides in the workset.

Parameters

sideNormals	[out] - rank-3 array (C,P,D), normals at workset sides
worksetJacobians	[in] - rank-4 array (C,P,D,D) with Jacobians at ref. side points
worksetSideOrd	[in] - side ordinal, relative to ref. cell, of the side workset
parentCell	[in] - cell topology of the parent reference cell

Definition at line 715 of file Intrepid2_CellToolsDefNodeInfo.hpp.

Referenced by Intrepid2::CubatureControlVolumeSide< DeviceType, pointValueType, weightValueType >::getCubature().

template<typename DeviceType >

template<typename sideNormalValueType , class... sideNormalProperties, typename worksetJacobianValueType , class... worksetJacobianProperties, typename edgeOrdValueType , class... edgeOrdProperties>

void Intrepid2::CellTools< DeviceType >::getPhysicalSideNormals	(	Kokkos::DynRankView< sideNormalValueType, sideNormalProperties...>	sideNormals,
		const Kokkos::DynRankView< worksetJacobianValueType, worksetJacobianProperties...>	worksetJacobians,
		const Kokkos::DynRankView< edgeOrdValueType, edgeOrdProperties...>	worksetSideOrds,
		const shards::CellTopology	parentCell
	)

static

Computes non-normalized normal vectors to physical sides in a side workset $\{\mathcal{S}_{c,i}\}_{c=0}^{N}$ . It is similar to the CellTools::getPhysicalSideNormals function above, with the difference that the side ordinal can change from point to point, and it is provided by the rank-2 input array worksetSideOrds, indexed by (C,P).

Parameters

sideNormals	[out] - rank-3 array (C,P,D), normals at workset sides
worksetJacobians	[in] - rank-4 array (C,P,D,D) with Jacobians at ref. side points
worksetSideOrds	[in] - rank-2 array (C,P) with side ordinals, relative to ref. cell, of the side workset
parentCell	[in] - cell topology of the parent reference cell

Definition at line 766 of file Intrepid2_CellToolsDefNodeInfo.hpp.

template<typename DeviceType >

template<typename cellCenterValueType , class... cellCenterProperties>

void Intrepid2::CellTools< DeviceType >::getReferenceCellCenter	(	Kokkos::DynRankView< cellCenterValueType, cellCenterProperties...>	cellCenter,
		const shards::CellTopology	cell
	)

static

Computes the Cartesian coordinates of reference cell barycenter.

Requires cell topology with a reference cell.

Parameters

cellCenter	[out] - coordinates of the specified reference cell center
cell	[in] - cell topology

Definition at line 36 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RefCellCenter< DeviceType >::get().

Referenced by Intrepid2::Basis_HVOL_C0_FEM< DeviceType, outputValueType, pointValueType >::Basis_HVOL_C0_FEM().

template<typename DeviceType >

template<typename RefEdgeTangentViewType >

void Intrepid2::CellTools< DeviceType >::getReferenceEdgeTangent	(	RefEdgeTangentViewType	refEdgeTangent,
		const ordinal_type	edgeOrd,
		const shards::CellTopology	parentCell
	)

static

Computes constant tangent vectors to edges of 2D or 3D reference cells.

Returns rank-1 array with dimension (D), D=2 or D=3; such that

${refEdgeTangent}(*) = \hat{\bf t}_i = {\partial\hat{\Phi}_i(t)\over\partial t}\,,$

where $\hat{\Phi}_i : R =[-1,1]\mapsto \hat{\mathcal E}_i$ is the parametrization map of the specified reference edge $\hat{\mathcal E}_i$ , given by

$\hat{\Phi}_i(t) = \left\{\begin{array}{ll} (\hat{x}(t),\hat{y}(t),\hat{z}(t)) & \mbox{for 3D parent cells} \\[1ex] (\hat{x}(t),\hat{y}(t)) & \mbox{for 2D parent cells} \\[1ex] \end{array}\right.$

The length of computed edge tangents is one-half the length of their associated edges:

$|\hat{\bf t}_i | = {1\over 2} |\hat{\mathcal E}_i |\,.$

Because the edges of all reference cells are always affine images of [-1,1], the edge tangent is constant vector field.

Parameters

refEdgeTangent	[out] - rank-1 array (D) with the edge tangent; D = cell dimension
edgeOrd	[in] - ordinal of the edge whose tangent is computed
parentCell	[in] - cell topology of the parent reference cell

Definition at line 211 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RefSubcellParametrization< DeviceType >::get().

Referenced by Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::Basis_HCURL_TET_In_FEM(), Intrepid2::Basis_HCURL_TRI_In_FEM< DeviceType, outputValueType, pointValueType >::Basis_HCURL_TRI_In_FEM(), Intrepid2::ProjectionTools< DeviceType >::getHCurlBasisCoeffs(), Intrepid2::ProjectionTools< DeviceType >::getHGradBasisCoeffs(), and Intrepid2::ProjectionTools< DeviceType >::getL2BasisCoeffs().

template<typename DeviceType >

template<typename RefFaceNormalViewType >

void Intrepid2::CellTools< DeviceType >::getReferenceFaceNormal	(	RefFaceNormalViewType	refFaceNormal,
		const ordinal_type	faceOrd,
		const shards::CellTopology	parentCell
	)

static

Computes constant normal vectors to faces of 3D reference cell.

Returns rank-1 array with dimension (D), D=3 such that

${refFaceNormal}(*) = \hat{\bf n}_i = {\partial\hat{\Phi}_{i}\over\partial u} \times {\partial\hat{\Phi}_{i}\over\partial v}$

where $\hat{\Phi}_i: R \mapsto \hat{\mathcal F}_i$ is the parametrization map of the specified reference face $\hat{\mathcal F}_i$ given by

$\hat{\Phi}_i(u,v) =(\hat{x}(u,v),\hat{y}(u,v),\hat{z}(u,v))$

and

$R = \left\{\begin{array}{rl} \{(0,0),(1,0),(0,1)\} & \mbox{if ${\mathcal F}$ is Triangle} \\[1ex] [-1,1]\times [-1,1] & \mbox{if ${\mathcal F}$ is Quadrilateral} \,. \end{array}\right.$

The length of computed face normals is proportional to face area:

$|\hat{\bf n}_i | = \left\{\begin{array}{rl} 2 \mbox{Area}(\hat{\mathcal F}_i) & \mbox{if $\hat{\mathcal F}_i$ is Triangle} \\[1ex] \mbox{Area}(\hat{\mathcal F}_i) & \mbox{if $\hat{\mathcal F}_i$ is Quadrilateral} \,. \end{array}\right.$

Because the faces of all reference cells are always affine images of R , the coordinate functions $\hat{x},\hat{y},\hat{z}$ of the parametrization map are linear and the face normal is a constant vector.

Remarks: The method Intrepid2::CellTools::getReferenceFaceTangents computes the reference face tangents ${\partial\hat{\Phi}_{i}/\partial u}$ and ${\partial\hat{\Phi}_{i}/\partial v}$ .

Parameters

refFaceNormal	[out] - rank-1 array (D) with (constant) face normal
faceOrd	[in] - ordinal of the face whose normal is computed
parentCell	[in] - cell topology of the parent reference cell

Definition at line 335 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RealSpaceTools< DeviceType >::vecprod().

Referenced by Intrepid2::ProjectionTools< DeviceType >::getHCurlBasisCoeffs(), and Intrepid2::ProjectionTools< DeviceType >::getHGradBasisCoeffs().

template<typename DeviceType >

template<typename RefFaceTanViewType >

void Intrepid2::CellTools< DeviceType >::getReferenceFaceTangents	(	RefFaceTanViewType	refFaceTanU,
		RefFaceTanViewType	refFaceTanV,
		const ordinal_type	faceOrd,
		const shards::CellTopology	parentCell
	)

static

Computes pairs of constant tangent vectors to faces of a 3D reference cells.

Returns 2 rank-1 arrays with dimension (D), D=3, such that

${refFaceTanU}(*) = \hat{\bf t}_{i,u} = {\partial\hat{\Phi}_i(u,v)\over\partial u} = \left({\partial\hat{x}(u,v)\over\partial u}, {\partial\hat{y}(u,v)\over\partial u}, {\partial\hat{z}(u,v)\over\partial u} \right) ;$

${refFaceTanV}(*) = \hat{\bf t}_{i,v} = {\partial\hat{\Phi}_i(u,v)\over \partial v} = \left({\partial\hat{x}(u,v)\over\partial v}, {\partial\hat{y}(u,v)\over\partial v}, {\partial\hat{z}(u,v)\over\partial v} \right)\,;$

where $\hat{\Phi}_i: R \mapsto \hat{\mathcal F}_i$ is the parametrization map of the specified reference face $\hat{\mathcal F}_i$ given by

$\hat{\Phi}_i(u,v) =(\hat{x}(u,v),\hat{y}(u,v),\hat{z}(u,v))$

and

$R = \left\{\begin{array}{rl} \{(0,0),(1,0),(0,1)\} & \mbox{if $\hat{\mathcal F}_i$ is Triangle} \\[1ex] [-1,1]\times [-1,1] & \mbox{if $\hat{\mathcal F}_i$ is Quadrilateral} \,. \end{array}\right.$

Because the faces of all reference cells are always affine images of R , the coordinate functions $\hat{x},\hat{y},\hat{z}$ of the parametrization map are linear and the face tangents are constant vectors.

Parameters

refFaceTanU	[out] - rank-1 array (D) with (constant) tangent in u-direction
refFaceTanV	[out] - rank-1 array (D) with (constant) tangent in v-direction
faceOrd	[in] - ordinal of the face whose tangents are computed
parentCell	[in] - cell topology of the parent 3D reference cell

Definition at line 249 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RefSubcellParametrization< DeviceType >::get().

Referenced by Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::Basis_HCURL_TET_In_FEM().

template<typename DeviceType >

template<typename cellNodeValueType , class... cellNodeProperties>

void Intrepid2::CellTools< DeviceType >::getReferenceNode	(	Kokkos::DynRankView< cellNodeValueType, cellNodeProperties...>	cellNode,
		const shards::CellTopology	cell,
		const ordinal_type	nodeOrd
	)

static

Retrieves the Cartesian coordinates of a reference cell node.

Returns Cartesian coordinates of a reference cell node. Requires cell topology with a reference cell. Node coordinates are always returned as an (x,y,z)-triple regardlesss of the actual topological cell dimension. The unused coordinates are set to zero, e.g., node 0 of Line<2> is returned as {-1,0,0}.

Remarks: Because the nodes of a cell with a base topology coincide with its vertices, for cells with base topology this method is equivalent to Intrepid2::CellTools::getReferenceVertex.

Parameters

cellNode	[out] - coordinates of the specified reference vertex
cell	[in] - cell topology of the cell
vertexOrd	[in] - node ordinal

Definition at line 139 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RefCellNodes< DeviceType >::get().

template<typename DeviceType >

template<typename RefSideNormalViewType >

void Intrepid2::CellTools< DeviceType >::getReferenceSideNormal	(	RefSideNormalViewType	refSideNormal,
		const ordinal_type	sideOrd,
		const shards::CellTopology	parentCell
	)

static

Computes constant normal vectors to sides of 2D or 3D reference cells.

A side is defined as a subcell of dimension one less than that of its parent cell. Therefore, sides of 2D cells are 1-subcells (edges) and sides of 3D cells are 2-subcells (faces).

Returns rank-1 array with dimension (D), D = 2 or 3 such that

${refSideNormal}(*) = \hat{\bf n}_i = \left\{\begin{array}{rl} \displaystyle \left({\partial\hat{\Phi}_i(t)\over\partial t}\right)^{\perp} & \mbox{for 2D parent cells} \\[2ex] \displaystyle {\partial\hat{\Phi}_{i}\over\partial u} \times {\partial\hat{\Phi}_{i}\over\partial v} & \mbox{for 3D parent cells} \end{array}\right.$

where $(u_1,u_2)^\perp = (u_2, -u_1)$ , and $\hat{\Phi}_i: R \mapsto \hat{\mathcal S}_i$ is the parametrization map of the specified reference side $\hat{\mathcal S}_i$ given by

$\hat{\Phi}_i(u,v) = \left\{\begin{array}{rl} (\hat{x}(t),\hat{y}(t)) & \mbox{for 2D parent cells} \\[1ex] (\hat{x}(u,v),\hat{y}(u,v),\hat{z}(u,v)) & \mbox{for 3D parent cells} \end{array}\right.$

For sides of 2D cells R=[-1,1] and for sides of 3D cells

$R = \left\{\begin{array}{rl} \{(0,0),(1,0),(0,1)\} & \mbox{if $\hat{\mathcal S}_i$ is Triangle} \\[1ex] [-1,1]\times [-1,1] & \mbox{if $\hat{\mathcal S}_i$ is Quadrilateral} \,. \end{array}\right.$

For 3D cells the length of computed side normals is proportional to side area:

$|\hat{\bf n}_i | = \left\{\begin{array}{rl} 2 \mbox{Area}(\hat{\mathcal F}_i) & \mbox{if $\hat{\mathcal F}_i$ is Triangle} \\[1ex] \mbox{Area}(\hat{\mathcal F}_i) & \mbox{if $\hat{\mathcal F}_i$ is Quadrilateral} \,. \end{array}\right.$

For 2D cells the length of computed side normals is proportional to side length:

$|\hat{\bf n}_i | = {1\over 2} |\hat{\mathcal F}_i |\,.$

Because the sides of all reference cells are always affine images of R , the coordinate functions $\hat{x},\hat{y},\hat{z}$ of the parametrization maps are linear and the side normal is a constant vector.

Remarks

For 3D cells the reference side normal coincides with the face normal computed by Intrepid2::CellTools::getReferenceFaceNormal and these two methods are completely equivalent.
For 2D cells the reference side normal is defined by $\hat{{\bf n}}= \hat{\bf t}^\perp = (t_2,-t_1)$ where $\hat{{\bf t}}=(t_1,t_2)$ is the tangent vector computed by Intrepid2::CellTools::getReferenceEdgeTangent. Therefore, the pair $(\hat{{\bf n}},\hat{{\bf t}})$ is positively oriented.

Parameters

refSideNormal	[out] - rank-1 array (D) with (constant) side normal
sideOrd	[in] - ordinal of the side whose normal is computed
parentCell	[in] - cell topology of the parent reference cell

Definition at line 294 of file Intrepid2_CellToolsDefNodeInfo.hpp.

Referenced by Intrepid2::Basis_HDIV_TET_In_FEM< DeviceType, outputValueType, pointValueType >::Basis_HDIV_TET_In_FEM(), Intrepid2::Basis_HDIV_TRI_In_FEM< DeviceType, outputValueType, pointValueType >::Basis_HDIV_TRI_In_FEM(), Intrepid2::ProjectionTools< DeviceType >::getHDivBasisCoeffs(), and Intrepid2::ProjectionTools< DeviceType >::getL2BasisCoeffs().

template<typename DeviceType >

template<typename SubcellNodeViewType >

void Intrepid2::CellTools< DeviceType >::getReferenceSubcellNodes	(	SubcellNodeViewType	subcellNodes,
		const ordinal_type	subcellDim,
		const ordinal_type	subcellOrd,
		const shards::CellTopology	parentCell
	)

static

Retrieves the Cartesian coordinates of all nodes of a reference subcell.

Returns rank-2 array with the Cartesian coordinates of the nodes of the specified reference cell subcell. Requires cell topology with a reference cell.

Parameters

subcellNodes	[out] - rank-2 (N,D) array with the Cartesian coordinates of the reference subcell nodes
subcellDim	[in] - dimension of the subcell; 0 <= subcellDim <= parentCell dimension
subcellOrd	[in] - ordinal of the subcell
parentCell	[in] - topology of the cell that owns the subcell

Remarks: When subcellDim = dimension of the parentCell this method returns the Cartesian coordinates of the nodes of the reference cell itself. Note that this requires subcellOrd=0.

Definition at line 169 of file Intrepid2_CellToolsDefNodeInfo.hpp.

template<typename DeviceType >

template<typename subcellVertexValueType , class... subcellVertexProperties>

void Intrepid2::CellTools< DeviceType >::getReferenceSubcellVertices	(	Kokkos::DynRankView< subcellVertexValueType, subcellVertexProperties...>	subcellVertices,
		const ordinal_type	subcellDim,
		const ordinal_type	subcellOrd,
		const shards::CellTopology	parentCell
	)

static

Retrieves the Cartesian coordinates of all vertices of a reference subcell.

Returns rank-2 array with the Cartesian coordinates of the vertices of the specified reference cell subcell. Requires cell topology with a reference cell.

Parameters

subcellVertices	[out] - rank-2 (V,D) array with the Cartesian coordinates of the reference subcell vertices
subcellDim	[in] - dimension of the subcell; 0 <= subcellDim <= parentCell dimension
subcellOrd	[in] - ordinal of the subcell
parentCell	[in] - topology of the cell that owns the subcell

Remarks: When subcellDim = dimension of the parentCell this method returns the Cartesian coordinates of the vertices of the reference cell itself. Note that this requires subcellOrd=0.

Definition at line 103 of file Intrepid2_CellToolsDefNodeInfo.hpp.

template<typename DeviceType >

template<typename cellVertexValueType , class... cellVertexProperties>

void Intrepid2::CellTools< DeviceType >::getReferenceVertex	(	Kokkos::DynRankView< cellVertexValueType, cellVertexProperties...>	cellVertex,
		const shards::CellTopology	cell,
		const ordinal_type	vertexOrd
	)

static

Retrieves the Cartesian coordinates of a reference cell vertex.

Requires cell topology with a reference cell.

Parameters

cellVertex	[out] - coordinates of the specified reference cell vertex
cell	[in] - cell topology of the cell
vertexOrd	[in] - vertex ordinal

Definition at line 68 of file Intrepid2_CellToolsDefNodeInfo.hpp.

References Intrepid2::RefCellNodes< DeviceType >::get().

Referenced by Intrepid2::ProjectionStruct< DeviceType, ValueType >::createHGradProjectionStruct(), and Intrepid2::ProjectionStruct< DeviceType, ValueType >::createL2ProjectionStruct().

template<typename DeviceType >

template<typename subcvCoordValueType , class... subcvCoordProperties, typename cellCoordValueType , class... cellCoordProperties>

void Intrepid2::CellTools< DeviceType >::getSubcvCoords	(	Kokkos::DynRankView< subcvCoordValueType, subcvCoordProperties...>	subcvCoords,
		const Kokkos::DynRankView< cellCoordValueType, cellCoordProperties...>	cellCoords,
		const shards::CellTopology	primaryCell
	)

static

Computes coordinates of sub-control volumes in each primary cell.

To build the system of equations for the control volume finite element method we need to compute geometric data for integration over control volumes. A control volume is polygon or polyhedron that surrounds a primary cell node and has vertices that include the surrounding primary cells' barycenter, edge midpoints, and face midpoints if in 3-d.

When using element-based assembly of the discrete equations over the primary mesh, a single element will contain a piece of each control volume surrounding each of the primary cell nodes. This piece of control volume (sub-control volume) is always a quadrilateral in 2-d and a hexahedron in 3-d.

In 2-d the sub-control volumes are defined in the following way:

   Quadrilateral primary element:

       O________M________O
       |        |        |
       |   3    |   2    |     B = cell barycenter
       |        |        |     O = primary cell nodes
       M________B________M     M = cell edge midpoints
       |        |        |
       |   0    |   1    |     sub-control volumes 0, 1, 2, 3
       |        |        |
       O________M________O


   Triangle primary element:

                O
               / \
              /   \             B = cell barycenter
             /     \            O = primary cell nodes
            M   2   M           M = cell edge midpoints
           / \     / \
          /   \ B /   \         sub-control volumes 0, 1, 2
         /      |      \
        /   0   |   1   \
       O________M________O

In 3-d the sub-control volumes are defined by the primary cell face centers and edge midpoints. The eight sub-control volumes for a hexahedron are shown below:

         O__________E__________O
        /|         /|         /|
       E_|________F_|________E |
      /| |       /| |       /| |
     O_|_|______E_|_|______O | |      O = primary cell nodes
     | | E------|-|-F------|-|-E      B = cell barycenter
     | |/|      | |/|      | |/|      F = cell face centers
     | F-|------|-B-|------|-F |      E = cell edge midpoints
     |/| |      |/| |      |/| |
     E_|_|______F_|_|______E | |
     | | O------|-|-E------|-|-O
     | |/       | |/       | |/
     | E--------|-F--------|-E
     |/         |/         |/
     O__________E__________O

Parameters

subCVCoords	[out] - array containing sub-control volume coordinates
cellCoords	[in] - array containing coordinates of primary cells
primaryCell	[in] - primary cell topology

Definition at line 340 of file Intrepid2_CellToolsDefControlVolume.hpp.

Referenced by Intrepid2::CubatureControlVolumeBoundary< DeviceType, pointValueType, weightValueType >::getCubature(), Intrepid2::CubatureControlVolume< DeviceType, pointValueType, weightValueType >::getCubature(), and Intrepid2::CubatureControlVolumeSide< DeviceType, pointValueType, weightValueType >::getCubature().

template<typename DeviceType >

static bool Intrepid2::CellTools< DeviceType >::hasReferenceCell ( const shards::CellTopology cellTopo )

inlinestatic

Checks if a cell topology has reference cell.

Parameters

cell	[in] - cell topology

Returns: true if the cell topology has reference cell, false otherwise

Definition at line 88 of file Intrepid2_CellTools.hpp.

References Intrepid2::RefSubcellParametrization< DeviceType >::isSupported().

template<typename DeviceType >

template<typename PhysPointValueType , typename RefPointValueType , typename WorksetType , typename HGradBasisPtrType >

static void Intrepid2::CellTools< DeviceType >::mapToPhysicalFrame	(	PhysPointValueType	physPoints,
		const RefPointValueType	refPoints,
		const WorksetType	worksetCell,
		const HGradBasisPtrType	basis
	)

static

Computes F, the reference-to-physical frame map.

There are 2 use cases:

Applies $F_{c}$ for all cells in a cell workset to a single point set stored in a rank-2 (P,D) array;
Applies $F_{c}$ for all cells in a cell workset to multiple point sets having the same number of points, indexed by cell ordinal, and stored in a rank-3 (C,P,D) array;

For a single point set in a rank-2 array (P,D) returns a rank-3 (C,P,D) array such that

$\mbox{physPoints}(c,p,d) = \Big(F_c(\mbox{refPoint}(p,*)) \Big)_d \quad c=0,\ldots, C$

For multiple point sets in a rank-3 (C,P,D) array returns a rank-3 (C,P,D) array such that

$\mbox{physPoints}(c,p,d) = \Big(F_c(\mbox{refPoint}(c,p,*)) \Big)_d \quad c=0,\ldots, C$

This corresponds to mapping multiple sets of reference points to a matching number of physical cells.

Requires pointer to HGrad basis that defines reference to physical cell mapping. See Section Reference-to-physical cell mapping for definition of the mapping function.

Warning: The array refPoints represents an arbitrary set of points in the reference frame that are not required to be in the reference cell corresponding to the specified cell topology. As a result, the images of these points under a given reference-to-physical map are not necessarily contained in the physical cell that is the image of the reference cell under that map. CellTools provides several inclusion tests methods to check whether or not the points are inside a reference cell.

Parameters

physPoints	[out] - rank-3 array with dimensions (C,P,D) with the images of the ref. points
refPoints	[in] - rank-3/2 array with dimensions (C,P,D)/(P,D) with points in reference frame
cellWorkset	[in] - rank-3 container with logical dimensions (C,N,D) with the nodes of the cell workset
basis	[in] - pointer to HGrad basis used in reference-to-physical cell mapping

Referenced by Intrepid2::CellTools< DeviceType >::mapToPhysicalFrame(), and Intrepid2::ProjectedGeometry< spaceDim, PointScalar, DeviceType >::projectOntoHGRADBasis().

template<typename DeviceType >

template<typename PhysPointViewType , typename RefPointViewType , typename WorksetCellViewType >

static void Intrepid2::CellTools< DeviceType >::mapToPhysicalFrame	(	PhysPointViewType	physPoints,
		const RefPointViewType	refPoints,
		const WorksetCellViewType	worksetCell,
		const shards::CellTopology	cellTopo
	)

inlinestatic

Computes F, the reference-to-physical frame map.

There are 2 use cases:

Applies $F_{c}$ for all cells in a cell workset to a single point set stored in a rank-2 (P,D) array;
Applies $F_{c}$ for all cells in a cell workset to multiple point sets having the same number of points, indexed by cell ordinal, and stored in a rank-3 (C,P,D) array;

For a single point set in a rank-2 array (P,D) returns a rank-3 (C,P,D) array such that

$\mbox{physPoints}(c,p,d) = \Big(F_c(\mbox{refPoint}(p,*)) \Big)_d \quad c=0,\ldots, C$

For multiple point sets in a rank-3 (C,P,D) array returns a rank-3 (C,P,D) array such that

$\mbox{physPoints}(c,p,d) = \Big(F_c(\mbox{refPoint}(c,p,*)) \Big)_d \quad c=0,\ldots, C$

This corresponds to mapping multiple sets of reference points to a matching number of physical cells.

Requires cell topology with a reference cell. See Section Reference-to-physical cell mapping for definition of the mapping function. Presently supported cell topologies are

1D: Line<2>
2D: Triangle<3>, Triangle<6>, Quadrilateral<4>, Quadrilateral<9>
3D: Tetrahedron<4>, Tetrahedron<10>, Hexahedron<8>, Hexahedron<27>

Warning: The array refPoints represents an arbitrary set of points in the reference frame that are not required to be in the reference cell corresponding to the specified cell topology. As a result, the images of these points under a given reference-to-physical map are not necessarily contained in the physical cell that is the image of the reference cell under that map. CellTools provides several inclusion tests methods to check whether or not the points are inside a reference cell.

Parameters

physPoints	[out] - rank-3 array with dimensions (C,P,D) with the images of the ref. points
refPoints	[in] - rank-3/2 array with dimensions (C,P,D)/(P,D) with points in reference frame
cellWorkset	[in] - rank-3 array with dimensions (C,N,D) with the nodes of the cell workset
cellTopo	[in] - cell topology of the cells stored in `cellWorkset`

Definition at line 1052 of file Intrepid2_CellTools.hpp.

References Intrepid2::CellTools< DeviceType >::mapToPhysicalFrame().

template<typename DeviceType >

template<typename refPointValueType , class... refPointProperties, typename physPointValueType , class... physPointProperties, typename worksetCellValueType , class... worksetCellProperties>

void Intrepid2::CellTools< DeviceType >::mapToReferenceFrame	(	Kokkos::DynRankView< refPointValueType, refPointProperties...>	refPoints,
		const Kokkos::DynRankView< physPointValueType, physPointProperties...>	physPoints,
		const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...>	worksetCell,
		const shards::CellTopology	cellTopo
	)

static

Computes $F^{-1}_{c}$ , the inverse of the reference-to-physical frame map using a default initial guess.

Applies $F^{-1}_{c}$ for all cells in a cell workset to multiple point sets having the same number of points, indexed by cell ordinal, and stored in a rank-3 (C,P,D) array. Returns a rank-3 (C,P,D) array such that

$\mbox{refPoints}(c,p,d) = \Big(F^{-1}_c(physPoint(c,p,*)) \Big)_d$

Requires cell topology with a reference cell. See Section Reference-to-physical cell mapping for definition of the mapping function. Presently supported cell topologies are

1D: Line<2>
2D: Triangle<3>, Triangle<6>, Quadrilateral<4>, Quadrilateral<9>
3D: Tetrahedron<4>, Tetrahedron<10>, Hexahedron<8>, Hexahedron<27>

Warning

Computation of the inverse map in this method uses default selection of the initial guess based on cell topology:

Line topologies: line center (0)
Triangle topologies: the point (1/3, 1/3)
Quadrilateral topologies: the point (0, 0)
Tetrahedron topologies: the point (1/6, 1/6, 1/6)
Hexahedron topologies: the point (0, 0, 0)
Wedge topologies: the point (1/2, 1/2, 0) For some cells with extended topologies, these initial guesses may not be good enough for Newton's method to converge in the allotted number of iterations. A version of this method with user-supplied initial guesses is also available.

The array physPoints represents an arbitrary set (or sets) of points in the physical frame that are not required to belong in the physical cell (cells) that define(s) the reference to physical mapping. As a result, the images of these points in the reference frame are not necessarily contained in the reference cell corresponding to the specified cell topology.

Parameters

refPoints	[out] - rank-3 array with dimensions (C,P,D) with the images of the physical points
physPoints	[in] - rank-3 array with dimensions (C,P,D) with points in physical frame
worksetCell	[in] - rank-3 array with dimensions (C,N,D) with the nodes of the cell workset
cellTopo	[in] - cell topology of the cells stored in `cellWorkset`

Definition at line 39 of file Intrepid2_CellToolsDefPhysToRef.hpp.

Referenced by Intrepid2::PointTools::getWarpBlendLatticeTetrahedron(), and Intrepid2::PointTools::getWarpBlendLatticeTriangle().

template<typename DeviceType >

template<typename refPointValueType , class... refPointProperties, typename initGuessValueType , class... initGuessProperties, typename physPointValueType , class... physPointProperties, typename worksetCellValueType , class... worksetCellProperties, typename HGradBasisPtrType >

void Intrepid2::CellTools< DeviceType >::mapToReferenceFrameInitGuess	(	Kokkos::DynRankView< refPointValueType, refPointProperties...>	refPoints,
		const Kokkos::DynRankView< initGuessValueType, initGuessProperties...>	initGuess,
		const Kokkos::DynRankView< physPointValueType, physPointProperties...>	physPoints,
		const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...>	worksetCell,
		const HGradBasisPtrType	basis
	)

static

Computation of $F^{-1}_{c}$ , the inverse of the reference-to-physical frame map using user-supplied initial guess.

Applies $F^{-1}_{c}$ for all cells in a cell workset to multiple point sets having the same number of points, indexed by cell ordinal, and stored in a rank-3 (C,P,D) array. Returns a rank-3 (C,P,D) array such that

$\mbox{refPoints}(c,p,d) = \Big(F^{-1}_c(physPoint(c,p,*)) \Big)_d$

Requires pointer to HGrad basis that defines reference to physical cell mapping. See Section Reference-to-physical cell mapping for definition of the mapping function.

Warning: The array physPoints represents an arbitrary set (or sets) of points in the physical frame that are not required to belong in the physical cell (cells) that define(s) the reference to physical mapping. As a result, the images of these points in the reference frame are not necessarily contained in the reference cell corresponding to the specified cell topology.

Parameters

refPoints	[out] - rank-3/2 array with dimensions (C,P,D)/(P,D) with the images of the physical points
initGuess	[in] - rank-3/2 array with dimensions (C,P,D)/(P,D) with the initial guesses for each point
physPoints	[in] - rank-3/2 array with dimensions (C,P,D)/(P,D) with points in physical frame
worksetCell	[in] - rank-3 array with dimensions (C,N,D) with the nodes of the cell workset
basis	[in] - pointer to HGrad basis used for reference to physical cell mapping

Definition at line 90 of file Intrepid2_CellToolsDefPhysToRef.hpp.

References Intrepid2::Parameters::MaxNewton.

Referenced by Intrepid2::CellTools< DeviceType >::mapToReferenceFrameInitGuess().

template<typename DeviceType >

template<typename refPointValueType , class... refPointProperties, typename initGuessValueType , class... initGuessProperties, typename physPointValueType , class... physPointProperties, typename worksetCellValueType , class... worksetCellProperties>

static void Intrepid2::CellTools< DeviceType >::mapToReferenceFrameInitGuess	(	Kokkos::DynRankView< refPointValueType, refPointProperties...>	refPoints,
		const Kokkos::DynRankView< initGuessValueType, initGuessProperties...>	initGuess,
		const Kokkos::DynRankView< physPointValueType, physPointProperties...>	physPoints,
		const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...>	worksetCell,
		const shards::CellTopology	cellTopo
	)

inlinestatic

Computation of $F^{-1}_{c}$ , the inverse of the reference-to-physical frame map using user-supplied initial guess.

Applies $F^{-1}_{c}$ for all cells in a cell workset to multiple point sets having the same number of points, indexed by cell ordinal, and stored in a rank-3 (C,P,D) array. Returns a rank-3 (C,P,D) array such that

$\mbox{refPoints}(c,p,d) = \Big(F^{-1}_c(physPoint(c,p,*)) \Big)_d$

Requires cell topology with a reference cell. See Section Reference-to-physical cell mapping for definition of the mapping function. Presently supported cell topologies are

1D: Line<2>
2D: Triangle<3>, Triangle<6>, Quadrilateral<4>, Quadrilateral<9>
3D: Tetrahedron<4>, Tetrahedron<10>, Hexahedron<8>, Hexahedron<27>

Warning: The array physPoints represents an arbitrary set (or sets) of points in the physical frame that are not required to belong in the physical cell (cells) that define(s) the reference to physical mapping. As a result, the images of these points in the reference frame are not necessarily contained in the reference cell corresponding to the specified cell topology.

Parameters

refPoints	[out] - rank-3/2 array with dimensions (C,P,D)/(P,D) with the images of the physical points
initGuess	[in] - rank-3/2 array with dimensions (C,P,D)/(P,D) with the initial guesses for each point
physPoints	[in] - rank-3/2 array with dimensions (C,P,D)/(P,D) with points in physical frame
worksetCell	[in] - rank-3 array with dimensions (C,N,D) with the nodes of the cell workset
cellTopo	[in] - cell topology of the cells stored in `cellWorkset`

Definition at line 1284 of file Intrepid2_CellTools.hpp.

References Intrepid2::CellTools< DeviceType >::mapToReferenceFrameInitGuess().

template<typename DeviceType >

template<typename refSubcellViewType , typename paramPointViewType >

static void Intrepid2::CellTools< DeviceType >::mapToReferenceSubcell	(	refSubcellViewType	refSubcellPoints,
		const paramPointViewType	paramPoints,
		const ordinal_type	subcellDim,
		const ordinal_type	subcellOrd,
		const shards::CellTopology	parentCell
	)

static

Computes parameterization maps of 1- and 2-subcells of reference cells.

Applies $\hat{\Phi}_i$ , the parametrization map of a subcell $\hat{\mathcal{S}}_i$ from a given reference cell, to a set of points in the parametrization domain R of $\hat{\mathcal{S}}_i$ . Returns a rank-2 array with dimensions (P,D) where for 1-subcells:

${subcellPoints}(p,*) = \hat{\Phi}_i(t_p) \quad\mbox{and}\quad \hat{\Phi}_i(t_p) = \left\{ \begin{array}{ll} (\hat{x}(t_p),\hat{y}(t_p),\hat{z}(t_p)) & \mbox{for 3D parent cells}\\[1.5ex] (\hat{x}(t_p),\hat{y}(t_p)) & \mbox{for 2D parent cells} \end{array} \right. \quad t_p \in R = [-1,1] \,;$

for 2-subcells:

${subcellPoints}(p,*) = \hat{\Phi}_i(u_p,v_p)\quad\mbox{and}\quad \hat{\Phi}_i(u_p,v_p) = (\hat{x}(u_p,v_p), \hat{y}(u_p,v_p), \hat{z}(u_p, v_p)) \quad (u_p,v_p)\in R$

and

$R = \left\{\begin{array}{rl} \{(0,0),(1,0),(0,1)\} & \mbox{if face is Triangle} \\[1ex] [-1,1]\times [-1,1] & \mbox{if face is Quadrilateral} \end{array}\right.$

Remarks

Parametrization of 1-subcells is defined for all 2D and 3D cell topologies with reference cells, including special 2D and 3D topologies such as shell and beams.
Parametrization of 2-subcells is defined for all 3D cell topologies with reference cells, including special 3D topologies such as shells.

To map a set of points from a parametrization domain to a physical subcell workset, apply Intrepid2::CellTools::mapToPhysicalFrame to the output of this method. This will effectively apply the parametrization map $\Phi_{c,i} = F_{c}\circ\hat{\Phi}_i$ of each subcell in the workset to paramPoints. Here c is ordinal of a parent cell, relative to subcell workset, and i is subcell ordinal, relative to a reference cell, of the subcell workset. See Section Subcell worksets for definition of subcell workset and Section Parametrization of physical 1- and 2-subcells for definition of parametrization maps.

Parameters

refSubcellPoints	[out] - rank-2 (P,D1) array with images of parameter space points
paramPoints	[in] - rank-2 (P,D2) array with points in 1D or 2D parameter domain
subcellDim	[in] - dimension of the subcell where points are mapped to
subcellOrd	[in] - subcell ordinal
parentCell	[in] - cell topology of the parent cell.

Referenced by Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::Basis_HCURL_TET_In_FEM(), Intrepid2::Basis_HCURL_TRI_In_FEM< DeviceType, outputValueType, pointValueType >::Basis_HCURL_TRI_In_FEM(), Intrepid2::Basis_HDIV_TET_In_FEM< DeviceType, outputValueType, pointValueType >::Basis_HDIV_TET_In_FEM(), Intrepid2::Basis_HDIV_TRI_In_FEM< DeviceType, outputValueType, pointValueType >::Basis_HDIV_TRI_In_FEM(), Intrepid2::Basis_HGRAD_TET_Cn_FEM< DeviceType, outputValueType, pointValueType >::Basis_HGRAD_TET_Cn_FEM(), Intrepid2::ProjectionStruct< DeviceType, ValueType >::createHCurlProjectionStruct(), Intrepid2::ProjectionStruct< DeviceType, ValueType >::createHDivProjectionStruct(), Intrepid2::ProjectionStruct< DeviceType, ValueType >::createHGradProjectionStruct(), Intrepid2::ProjectionStruct< DeviceType, ValueType >::createL2ProjectionStruct(), Intrepid2::CubatureControlVolumeBoundary< DeviceType, pointValueType, weightValueType >::CubatureControlVolumeBoundary(), and Intrepid2::CubatureControlVolumeSide< DeviceType, pointValueType, weightValueType >::CubatureControlVolumeSide().

template<typename DeviceType >

template<typename refSubcellViewType , typename paramPointViewType >

static void Intrepid2::CellTools< DeviceType >::mapToReferenceSubcell	(	refSubcellViewType	refSubcellPoints,
		const paramPointViewType	paramPoints,
		const typename RefSubcellParametrization< DeviceType >::ConstViewType	subcellParametrization,
		const ordinal_type	subcellOrd
	)

static

Computes parameterization maps of 1- and 2-subcells of reference cells.

Overload of the previous function (see explanation above) where the subcell parametrization is used instead of passing the parent cell topology.

template<typename DeviceType >

template<typename refSubcellViewType , typename paramPointViewType , typename ordViewType >

static void Intrepid2::CellTools< DeviceType >::mapToReferenceSubcell	(	refSubcellViewType	refSubcellPoints,
		const paramPointViewType	paramPoints,
		const typename RefSubcellParametrization< DeviceType >::ConstViewType	subcellParametrization,
		const ordViewType	subcellOrd
	)

static

Computes parameterization maps of 1- and 2-subcells of reference cells.

Overload of the previous function (see explanation above) where the subcellOrd is a rank-1 array (P).

template<typename DeviceType >

template<typename JacobianViewType , typename PointViewType , typename WorksetType , typename HGradBasisType >

void Intrepid2::CellTools< DeviceType >::setJacobian	(	JacobianViewType	jacobian,
		const PointViewType	points,
		const WorksetType	worksetCell,
		const Teuchos::RCP< HGradBasisType >	basis,
		const int	startCell = `0`,
		const int	endCell = `-1`
	)

static

Computes the Jacobian matrix DF of the reference-to-physical frame map F.

    There are two use cases:

Computes Jacobians $DF_{c}$ of the reference-to-physical map for all physical cells in a cell workset on a single set of reference points stored in a rank-2 (P,D) array;
Computes Jacobians $DF_{c}$ of the reference-to-physical map for all physical cells in a cell workset on multiple reference point sets having the same number of points, indexed by cell ordinal, and stored in a rank-3 (C,P,D) array;

For a single point set in a rank-2 array (P,D) returns a rank-4 (C,P,D,D) array such that

$\mbox{jacobian}(c,p,i,j) = [DF_{c}(\mbox{points}(p))]_{ij} \quad c=0,\ldots, C$

For multiple sets of reference points in a rank-3 (C,P,D) array returns rank-4 (C,P,D,D) array such that

$\mbox{jacobian}(c,p,i,j) = [DF_{c}(\mbox{points}(c,p))]_{ij} \quad c=0,\ldots, C$

   Requires pointer to HGrad basis that defines reference to physical cell mapping.  
   See Section \ref sec_cell_topology_ref_map_DF for definition of the Jacobian.

   \warning
   The points are not required to be in the reference cell associated with the specified
   cell topology. CellTools provides several inclusion tests methods to check whether
   or not the points are inside a reference cell.

Parameters

jacobian	[out] - rank-4 array with dimensions (C,P,D,D) with the Jacobians
points	[in] - rank-2/3 array with dimensions (P,D)/(C,P,D) with the evaluation points
cellWorkset	[in] - rank-3 container with logical dimensions (C,N,D) with the nodes of the cell workset
basis	[in] - HGrad basis for reference to physical cell mapping
startCell	[in] - first cell index in cellWorkset for which we should compute the Jacobian; corresponds to the 0 index in Jacobian and/or points container. Default: 0.
endCell	[in] - first cell index in cellWorkset that we do not process; endCell - startCell must equal the extent of the Jacobian container in dimension 0. Default: -1, a special value that indicates the extent of the cellWorkset should be used.

Definition at line 799 of file Intrepid2_CellToolsDefJacobian.hpp.

Referenced by Intrepid2::CubatureControlVolumeBoundary< DeviceType, pointValueType, weightValueType >::getCubature(), Intrepid2::CubatureControlVolume< DeviceType, pointValueType, weightValueType >::getCubature(), Intrepid2::CubatureControlVolumeSide< DeviceType, pointValueType, weightValueType >::getCubature(), Intrepid2::CellTools< DeviceType >::setJacobian(), and Intrepid2::CellGeometry< PointScalar, spaceDim, DeviceType >::setJacobianDataPrivate().

template<typename DeviceType >

template<typename JacobianViewType , typename BasisGradientsType , typename WorksetType >

void Intrepid2::CellTools< DeviceType >::setJacobian	(	JacobianViewType	jacobian,
		const WorksetType	worksetCell,
		const BasisGradientsType	gradients,
		const int	startCell = `0`,
		const int	endCell = `-1`
	)

static

Computes the Jacobian matrix DF of the reference-to-physical frame map F.

    There are two use cases:

Computes Jacobians $DF_{c}$ of the reference-to-physical map for all physical cells in a cell workset on a single set of reference points stored in a rank-2 (P,D) array;
Computes Jacobians $DF_{c}$ of the reference-to-physical map for all physical cells in a cell workset on multiple reference point sets having the same number of points, indexed by cell ordinal, and stored in a rank-3 (C,P,D) array;

For a single point set in a rank-2 array (P,D) returns a rank-4 (C,P,D,D) array such that

$\mbox{jacobian}(c,p,i,j) = [DF_{c}(\mbox{points}(p))]_{ij} \quad c=0,\ldots, C$

For multiple sets of reference points in a rank-3 (C,P,D) array returns rank-4 (C,P,D,D) array such that

$\mbox{jacobian}(c,p,i,j) = [DF_{c}(\mbox{points}(c,p))]_{ij} \quad c=0,\ldots, C$

   Requires pointer to HGrad basis that defines reference to physical cell mapping.
   See Section \ref sec_cell_topology_ref_map_DF for definition of the Jacobian.

   \warning
   The points are not required to be in the reference cell associated with the specified
   cell topology. CellTools provides several inclusion tests methods to check whether
   or not the points are inside a reference cell.

Parameters

jacobian	[out] - rank-4 array with dimensions (C,P,D,D) with the Jacobians
cellWorkset	[in] - rank-3 container with logical dimensions (C,N,D) with the nodes of the cell workset
gradients	[in] - rank-3/4 array with dimensions (N,P,D)/(C,N,P,D) with the gradients of the physical-to-cell mapping
startCell	[in] - first cell index in cellWorkset for which we should compute the Jacobian; corresponds to the 0 index in Jacobian and/or points container. Default: 0.
endCell	[in] - first cell index in cellWorkset that we do not process; endCell - startCell must equal the extent of the Jacobian container in dimension 0. Default: -1, a special value that indicates the extent of the cellWorkset should be used.

Definition at line 771 of file Intrepid2_CellToolsDefJacobian.hpp.

template<typename DeviceType >

template<typename JacobianViewType , typename PointViewType , typename WorksetCellViewType >

static void Intrepid2::CellTools< DeviceType >::setJacobian	(	JacobianViewType	jacobian,
		const PointViewType	points,
		const WorksetCellViewType	worksetCell,
		const shards::CellTopology	cellTopo
	)

inlinestatic

Computes the Jacobian matrix DF of the reference-to-physical frame map F.

    There are two use cases:

Computes Jacobians $DF_{c}$ of the reference-to-physical map for all physical cells in a cell workset on a single set of reference points stored in a rank-2 (P,D) array;
Computes Jacobians $DF_{c}$ of the reference-to-physical map for all physical cells in a cell workset on multiple reference point sets having the same number of points, indexed by cell ordinal, and stored in a rank-3 (C,P,D) array;

For a single point set in a rank-2 array (P,D) returns a rank-4 (C,P,D,D) array such that

$\mbox{jacobian}(c,p,i,j) = [DF_{c}(\mbox{points}(p))]_{ij} \quad c=0,\ldots, C$

For multiple sets of reference points in a rank-3 (C,P,D) array returns rank-4 (C,P,D,D) array such that

$\mbox{jacobian}(c,p,i,j) = [DF_{c}(\mbox{points}(c,p))]_{ij} \quad c=0,\ldots, C$

   Requires cell topology with a reference cell. See Section \ref sec_cell_topology_ref_map_DF
   for definition of the Jacobian.

   \warning
   The points are not required to be in the reference cell associated with the specified
   cell topology. CellTools provides several inclusion tests methods to check whether
   or not the points are inside a reference cell.

Parameters

jacobian	[out] - rank-4 array with dimensions (C,P,D,D) with the Jacobians
points	[in] - rank-2/3 array with dimensions (P,D)/(C,P,D) with the evaluation points
cellWorkset	[in] - rank-3 array with dimensions (C,N,D) with the nodes of the cell workset
cellTopo	[in] - cell topology of the cells stored in `cellWorkset`

Definition at line 284 of file Intrepid2_CellTools.hpp.

References Intrepid2::CellTools< DeviceType >::setJacobian().

template<typename DeviceType >

template<typename JacobianDetViewType , typename JacobianViewType >

void Intrepid2::CellTools< DeviceType >::setJacobianDet	(	JacobianDetViewType	jacobianDet,
		const JacobianViewType	jacobian
	)

static

Computes the determinant of the Jacobian matrix DF of the reference-to-physical frame map F.

Returns rank-2 array with dimensions (C,P) such that

$\mbox{jacobianDet}(c,p) = \mbox{det}(\mbox{jacobian}(c,p,*,*)) \quad c=0,\ldots, C$

Parameters

jacobianDet	[out] - rank-2 array with dimensions (C,P) with Jacobian determinants
jacobian	[in] - rank-4 array with dimensions (C,P,D,D) with the Jacobians

Definition at line 874 of file Intrepid2_CellToolsDefJacobian.hpp.

References Intrepid2::RealSpaceTools< DeviceType >::det().

Referenced by Intrepid2::CubatureControlVolumeBoundary< DeviceType, pointValueType, weightValueType >::getCubature(), and Intrepid2::CubatureControlVolume< DeviceType, pointValueType, weightValueType >::getCubature().

template<typename DeviceType >

template<class PointScalar >

void Intrepid2::CellTools< DeviceType >::setJacobianDet	(	Data< PointScalar, DeviceType > &	jacobianDet,
		const Data< PointScalar, DeviceType > &	jacobian
	)

static

Computes determinants corresponding to the Jacobians in the Data container provided.

Parameters

jacobianDet	[out] - data with shape (C,P), as returned by CellTools::allocateJacobianDet()
jacobian	[in] - data with shape (C,P,D,D), as returned by CellGeometry::allocateJacobianData()

Definition at line 165 of file Intrepid2_CellToolsDefJacobian.hpp.

template<typename DeviceType >

template<class PointScalar >

void Intrepid2::CellTools< DeviceType >::setJacobianDetInv	(	Data< PointScalar, DeviceType > &	jacobianDetInv,
		const Data< PointScalar, DeviceType > &	jacobian
	)

static

Computes reciprocals of determinants corresponding to the Jacobians in the Data container provided.

Parameters

jacobianDetInv	[out] - data with shape (C,P), as returned by CellTools::allocateJacobianDet()
jacobian	[in] - data with shape (C,P,D,D), as returned by CellGeometry::allocateJacobianData()

Definition at line 432 of file Intrepid2_CellToolsDefJacobian.hpp.

References Intrepid2::Data< DataScalar, DeviceType >::allocateConstantData(), and Intrepid2::Data< DataScalar, DeviceType >::storeInPlaceQuotient().

template<typename DeviceType >

template<class PointScalar >

static void Intrepid2::CellTools< DeviceType >::setJacobianDividedByDet	(	Data< PointScalar, DeviceType > &	jacobianDividedByDet,
		const Data< PointScalar, DeviceType > &	jacobian,
		const Data< PointScalar, DeviceType > &	jacobianDetInv
	)

static

Multiplies the Jacobian with shape (C,P,D,D) by the reciprocals of the determinants, with shape (C,P), entrywise.

Parameters

jacobianDividedByDet	[out] - data container with shape (C,P,D,D), as returned by CellTools::allocateJacobianInv()
jacobian	[in] - data container with shape (C,P,D,D), as returned by CellTools::allocateJacobianInv()
jacobianDetInv	[in] - data with shape (C,P,D,D), as returned by CellGeometry::allocateJacobianData()

template<typename DeviceType >

template<typename JacobianInvViewType , typename JacobianViewType >

void Intrepid2::CellTools< DeviceType >::setJacobianInv	(	JacobianInvViewType	jacobianInv,
		const JacobianViewType	jacobian
	)

static

Computes the inverse of the Jacobian matrix DF of the reference-to-physical frame map F.

Returns rank-4 array with dimensions (C,P,D,D) such that

$\mbox{jacobianInv}(c,p,*,*) = \mbox{jacobian}^{-1}(c,p,*,*) \quad c = 0,\ldots, C$

Parameters

jacobianInv	[out] - rank-4 array with dimensions (C,P,D,D) with the inverse Jacobians
jacobian	[in] - rank-4 array with dimensions (C,P,D,D) with the Jacobians

Definition at line 861 of file Intrepid2_CellToolsDefJacobian.hpp.

References Intrepid2::RealSpaceTools< DeviceType >::inverse().

template<typename DeviceType >

template<class PointScalar >

void Intrepid2::CellTools< DeviceType >::setJacobianInv	(	Data< PointScalar, DeviceType > &	jacobianInv,
		const Data< PointScalar, DeviceType > &	jacobian
	)

static

Computes determinants corresponding to the Jacobians in the Data container provided.

Parameters

jacobianInv	[out] - data container with shape (C,P,D,D), as returned by CellTools::allocateJacobianInv()
jacobian	[in] - data with shape (C,P,D,D), as returned by CellGeometry::allocateJacobianData()

Definition at line 442 of file Intrepid2_CellToolsDefJacobian.hpp.

References Intrepid2::Data< DataScalar, DeviceType >::blockPlusDiagonalLastNonDiagonal(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView1(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView2(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView3(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingView4(), Intrepid2::Data< DataScalar, DeviceType >::getUnderlyingViewRank(), Intrepid2::Data< DataScalar, DeviceType >::getVariationTypes(), INTREPID2_TEST_FOR_EXCEPTION_DEVICE_SAFE, and Intrepid2::RealSpaceTools< DeviceType >::inverse().

The documentation for this class was generated from the following files:

http://docs.trilinos.org/dev/packages/intrepid2/src/Cell/Intrepid2_CellTools.hpp
http://docs.trilinos.org/dev/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefControlVolume.hpp
http://docs.trilinos.org/dev/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefInclusion.hpp
http://docs.trilinos.org/dev/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefJacobian.hpp
http://docs.trilinos.org/dev/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefNodeInfo.hpp
http://docs.trilinos.org/dev/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefPhysToRef.hpp
http://docs.trilinos.org/dev/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefRefToPhys.hpp

Public Member Functions

Static Public Member Functions

Private Types

Static Private Member Functions

Detailed Description

template<typename DeviceType> class Intrepid2::CellTools< DeviceType >

Member Function Documentation

template<typename DeviceType>
class Intrepid2::CellTools< DeviceType >