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

#include <Intrepid2_CellTools.hpp>

Classes
struct	ReferenceNodeData
	Reference node data for each supported topology. More...

struct	ReferenceNodeDataStatic
	Reference node containers for each supported topology. More...

struct	SubcellParamData
	Parametrization coefficients of edges and faces of reference cells. More...

Public Types
typedef Kokkos::DynRankView < double, ExecSpaceType >	subcellParamViewType

Public Member Functions
	CellTools ()=default
	Default constructor.

	~CellTools ()=default
	Destructor.

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

static void	setSubcellParametrization ()
	Defines orientation-preserving parametrizations of reference edges and faces of cell topologies with reference cells. More...

template<typename jacobianValueType , class... jacobianProperties, typename pointValueType , class... pointProperties, typename worksetCellValueType , class... worksetCellProperties, typename HGradBasisPtrType >
static void	setJacobian (Kokkos::DynRankView< jacobianValueType, jacobianProperties...> jacobian, const Kokkos::DynRankView< pointValueType, pointProperties...> points, const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...> worksetCell, const HGradBasisPtrType basis)
	Computes the Jacobian matrix DF of the reference-to-physical frame map F. More...

template<typename jacobianValueType , class... jacobianProperties, typename pointValueType , class... pointProperties, typename worksetCellValueType , class... worksetCellProperties>
static void	setJacobian (Kokkos::DynRankView< jacobianValueType, jacobianProperties...> jacobian, const Kokkos::DynRankView< pointValueType, pointProperties...> points, const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...> worksetCell, const shards::CellTopology cellTopo)
	Computes the Jacobian matrix DF of the reference-to-physical frame map F. More...

template<typename jacobianInvValueType , class... jacobianInvProperties, typename jacobianValueType , class... jacobianProperties>
static void	setJacobianInv (Kokkos::DynRankView< jacobianInvValueType, jacobianInvProperties...> jacobianInv, const Kokkos::DynRankView< jacobianValueType, jacobianProperties...> jacobian)
	Computes the inverse of the Jacobian matrix DF of the reference-to-physical frame map F. More...

template<typename jacobianDetValueType , class... jacobianDetProperties, typename jacobianValueType , class... jacobianProperties>
static void	setJacobianDet (Kokkos::DynRankView< jacobianDetValueType, jacobianDetProperties...> jacobianDet, const Kokkos::DynRankView< jacobianValueType, jacobianProperties...> jacobian)
	Computes the determinant of the Jacobian matrix DF of the reference-to-physical frame map F. More...

template<typename cellCenterValueType , class... cellCenterProperties, typename cellVertexValueType , class... cellVertexProperties>
static void	getReferenceCellCenter (Kokkos::DynRankView< cellCenterValueType, cellCenterProperties...> cellCenter, Kokkos::DynRankView< cellVertexValueType, cellVertexProperties...> cellVertex, const shards::CellTopology cell)
	Computes the Cartesian coordinates of reference cell center. 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 subcellNodeValueType , class... subcellNodeProperties>
static void	getReferenceSubcellNodes (Kokkos::DynRankView< subcellNodeValueType, subcellNodeProperties...> 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 refEdgeTangentValueType , class... refEdgeTangentProperties>
static void	getReferenceEdgeTangent (Kokkos::DynRankView< refEdgeTangentValueType, refEdgeTangentProperties...> refEdgeTangent, const ordinal_type edgeOrd, const shards::CellTopology parentCell)
	Computes constant tangent vectors to edges of 2D or 3D reference cells. More...

template<typename refFaceTanUValueType , class... refFaceTanUProperties, typename refFaceTanVValueType , class... refFaceTanVProperties>
static void	getReferenceFaceTangents (Kokkos::DynRankView< refFaceTanUValueType, refFaceTanUProperties...> refFaceTanU, Kokkos::DynRankView< refFaceTanVValueType, refFaceTanVProperties...> 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 refSideNormalValueType , class... refSideNormalProperties>
static void	getReferenceSideNormal (Kokkos::DynRankView< refSideNormalValueType, refSideNormalProperties...> refSideNormal, const ordinal_type sideOrd, const shards::CellTopology parentCell)
	Computes constant normal vectors to sides of 2D or 3D reference cells. More...

template<typename refFaceNormalValueType , class... refFaceNormalProperties>
static void	getReferenceFaceNormal (Kokkos::DynRankView< refFaceNormalValueType, refFaceNormalProperties...> 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 faceTanUValueType , class... faceTanUProperties, typename faceTanVValueType , class... faceTanVProperties, typename worksetJacobianValueType , class... worksetJacobianProperties>
static void	getPhysicalFaceTangents (Kokkos::DynRankView< faceTanUValueType, faceTanUProperties...> faceTanU, Kokkos::DynRankView< faceTanVValueType, faceTanVProperties...> 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 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 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 physPointValueType , class... physPointProperties, typename refPointValueType , class... refPointProperties, typename worksetCellValueType , class... worksetCellProperties, typename HGradBasisPtrType >
static void	mapToPhysicalFrame (Kokkos::DynRankView< physPointValueType, physPointProperties...> physPoints, const Kokkos::DynRankView< refPointValueType, refPointProperties...> refPoints, const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...> worksetCell, const HGradBasisPtrType basis)
	Computes F, the reference-to-physical frame map. More...

template<typename physPointValueType , class... physPointProperties, typename refPointValueType , class... refPointProperties, typename worksetCellValueType , class... worksetCellProperties>
static void	mapToPhysicalFrame (Kokkos::DynRankView< physPointValueType, physPointProperties...> physPoints, const Kokkos::DynRankView< refPointValueType, refPointProperties...> refPoints, const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...> worksetCell, const shards::CellTopology cellTopo)
	Computes F, the reference-to-physical frame map. More...

static void	getSubcellParametrization (subcellParamViewType &subcellParam, const ordinal_type subcellDim, const shards::CellTopology parentCell)
	Returns array with the coefficients of the parametrization maps for the edges or faces of a reference cell topology. More...

template<typename refSubcellPointValueType , class... refSubcellPointProperties, typename paramPointValueType , class... paramPointProperties>
static void	mapToReferenceSubcell (Kokkos::DynRankView< refSubcellPointValueType, refSubcellPointProperties...> refSubcellPoints, const Kokkos::DynRankView< paramPointValueType, paramPointProperties...> 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 refSubcellPointValueType , class... refSubcellPointProperties, typename paramPointValueType , class... paramPointProperties>
static void KOKKOS_INLINE_FUNCTION	mapToReferenceSubcell (Kokkos::DynRankView< refSubcellPointValueType, refSubcellPointProperties...> refSubcellPoints, const Kokkos::DynRankView< paramPointValueType, paramPointProperties...> paramPoints, const subcellParamViewType subcellMap, const ordinal_type subcellDim, const ordinal_type subcellOrd, const ordinal_type parentCellDim)
	Overload of mapToReferenceSubcell that runs on device. 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 pointValueType , class... pointProperties>
static bool	checkPointInclusion (const Kokkos::DynRankView< pointValueType, pointProperties...> point, const shards::CellTopology cellTopo, const double thres=threshold())
	Checks if a point belongs to a reference cell. More...

template<typename inCellValueType , class... inCellProperties, typename pointValueType , class... pointProperties>
static void	checkPointwiseInclusion (Kokkos::DynRankView< inCellValueType, inCellProperties...> inCell, const Kokkos::DynRankView< pointValueType, pointProperties...> points, const shards::CellTopology cellTopo, const double thres=threshold())
	Checks every point in a set for inclusion in 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 double thres=threshold())
	Checks every point in a set or multiple sets for inclusion in physical cells from a cell workset. More...

Private Types
typedef Kokkos::DynRankView < const double, Kokkos::LayoutRight, Kokkos::HostSpace >	referenceNodeDataViewHostType

typedef Kokkos::DynRankView < double, Kokkos::LayoutRight, ExecSpaceType >	referenceNodeDataViewType

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

static void	setReferenceNodeData ()
	Set reference node coordinates for supported topologies.

static void	setSubcellParametrization (subcellParamViewType &subcellParam, const ordinal_type subcellDim, const shards::CellTopology parentCell)
	Sets orientation-preserving parametrizations of reference edges and faces of cell topologies with reference cells. Used to populate Intrepid2::CellTools::SubcellParamData. More...

Static Private Attributes
static const ReferenceNodeDataStatic	refNodeDataStatic_

static ReferenceNodeData	refNodeData_

static bool	isReferenceNodeDataSet_

static SubcellParamData	subcellParamData_

static bool	isSubcellParametrizationSet_

Detailed Description

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

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 104 of file Intrepid2_CellTools.hpp.

Member Function Documentation

template<typename SpT >

template<typename pointValueType , class... pointProperties>

bool Intrepid2::CellTools< SpT >::checkPointInclusion	(	const Kokkos::DynRankView< pointValueType, pointProperties...>	point,
		const shards::CellTopology	cellTopo,
		const double	thres = `threshold()`
	)

static

Checks if a point belongs to a reference cell.

Requires cell topology with a reference cell.

Parameters

point	[in] - reference coordinates of the point tested for inclusion
cellTopo	[in] - cell topology
threshold	[in] - "tightness" of the inclusion test

Returns: 1 if the point is in the closure of the specified reference cell and 0 otherwise.

Definition at line 70 of file Intrepid2_CellToolsDefInclusion.hpp.

template<typename SpT >

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

void Intrepid2::CellTools< SpT >::checkPointwiseInclusion	(	Kokkos::DynRankView< inCellValueType, inCellProperties...>	inCell,
		const Kokkos::DynRankView< pointValueType, pointProperties...>	points,
		const shards::CellTopology	cellTopo,
		const double	thres = `threshold()`
	)

static

Checks every point in a set for inclusion in a reference cell.

    Requires cell topology with a reference cell. Admissible ranks and dimensions of the
    input point array and the corresponding rank and dimension of the output array are as follows:

        |-------------------|-------------|-------------|-------------|
        |  rank: (in)/(out) |    1/1      |     2/1     |    3/2      |
        |-------------------|-------------|-------------|-------------|
        |  points    (in)   |     (D)     |    (I, D)   |  (I, J, D)  |
        |-------------------|-------------|-------------|-------------|
        |  inRefCell (out)  |     (1)     |    (I)      |  (I, J)     |
        |------------------ |-------------|-------------|-------------|

Example: if points is rank-3 array with dimensions (I, J, D), then

$\mbox{inRefCell}(i,j) = \left\{\begin{array}{rl} 1 & \mbox{if $points(i,j,*)\in\hat{\mathcal{C}}$} \\[2ex] 0 & \mbox{if $points(i,j,*)\notin\hat{\mathcal{C}}$} \end{array}\right.$

Parameters

inRefCell	[out] - rank-1 or 2 array with results from the pointwise inclusion test
refPoints	[in] - rank-1,2 or 3 array (point, vector of points, matrix of points)
cellTopo	[in] - cell topology of the cells stored in `cellWorkset`
threshold	[in] - "tightness" of the inclusion test

Definition at line 230 of file Intrepid2_CellToolsDefInclusion.hpp.

template<typename SpT >

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

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

static

Checks every point in a set or multiple sets for inclusion in physical cells from a cell workset.

    Checks every point from \b multiple point sets indexed by a cell ordinal, and stored in a rank-3
    (C,P,D) array, for inclusion in the physical cell having the same cell ordinal, for \b all
    cells in a cell workset.

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

$\mbox{inCell}(c,p) = \left\{\begin{array}{rl} 1 & \mbox{if $points(c,p,*)\in {\mathcal{C}}$} \\ [2ex] 0 & \mbox{if $points(c,p,*)\notin {\mathcal{C}}$} \end{array}\right.$

Parameters

inCell	[out] - rank-1 array with results from the pointwise inclusion test
points	[in] - rank-2 array with dimensions (P,D) with the physical 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`
threshold	[in] - tolerance for inclusion tests on the input points

Definition at line 276 of file Intrepid2_CellToolsDefInclusion.hpp.

template<typename ExecSpaceType>

template<typename outputValueType , typename pointValueType >

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

inlinestaticprivate

Generates default HGrad basis based on cell topology.

Parameters

cellTopo [in] - cell topology

Definition at line 167 of file Intrepid2_CellTools.hpp.

template<typename SpT >

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

void Intrepid2::CellTools< SpT >::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 537 of file Intrepid2_CellToolsDefNodeInfo.hpp.

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

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

template<typename SpT >

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

void Intrepid2::CellTools< SpT >::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 691 of file Intrepid2_CellToolsDefNodeInfo.hpp.

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

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

template<typename SpT >

template<typename faceTanUValueType , class... faceTanUProperties, typename faceTanVValueType , class... faceTanVProperties, typename worksetJacobianValueType , class... worksetJacobianProperties>

void Intrepid2::CellTools< SpT >::getPhysicalFaceTangents	(	Kokkos::DynRankView< faceTanUValueType, faceTanUProperties...>	faceTanU,
		Kokkos::DynRankView< faceTanVValueType, faceTanVProperties...>	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 586 of file Intrepid2_CellToolsDefNodeInfo.hpp.

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

template<typename SpT >

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

void Intrepid2::CellTools< SpT >::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 649 of file Intrepid2_CellToolsDefNodeInfo.hpp.

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

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

template<typename SpT >

template<typename cellCenterValueType , class... cellCenterProperties, typename cellVertexValueType , class... cellVertexProperties>

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

static

Computes the Cartesian coordinates of reference cell center.

Requires cell topology with a reference cell. Center coordinates are always returned as an (x,y,z)-triple regardlesss of the actual topological cell dimension. The unused coordinates are set to zero.

Parameters

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

Definition at line 170 of file Intrepid2_CellToolsDefNodeInfo.hpp.

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

template<typename SpT >

template<typename refEdgeTangentValueType , class... refEdgeTangentProperties>

void Intrepid2::CellTools< SpT >::getReferenceEdgeTangent	(	Kokkos::DynRankView< refEdgeTangentValueType, refEdgeTangentProperties...>	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 391 of file Intrepid2_CellToolsDefNodeInfo.hpp.

Referenced by Intrepid2::Basis_HCURL_TET_In_FEM< ExecSpaceType, outputValueType, pointValueType >::Basis_HCURL_TET_In_FEM(), Intrepid2::Basis_HCURL_TRI_In_FEM< ExecSpaceType, outputValueType, pointValueType >::Basis_HCURL_TRI_In_FEM(), Intrepid2::Impl::OrientationTools::getCoeffMatrix_HCURL(), and Intrepid2::Experimental::LagrangianInterpolation< ExecSpaceType >::getDofCoordsAndCoeffs().

template<typename SpT >

template<typename refFaceNormalValueType , class... refFaceNormalProperties>

void Intrepid2::CellTools< SpT >::getReferenceFaceNormal	(	Kokkos::DynRankView< refFaceNormalValueType, refFaceNormalProperties...>	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 504 of file Intrepid2_CellToolsDefNodeInfo.hpp.

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

Referenced by Intrepid2::Experimental::LagrangianInterpolation< ExecSpaceType >::getDofCoordsAndCoeffs().

template<typename SpT >

template<typename refFaceTanUValueType , class... refFaceTanUProperties, typename refFaceTanVValueType , class... refFaceTanVProperties>

void Intrepid2::CellTools< SpT >::getReferenceFaceTangents	(	Kokkos::DynRankView< refFaceTanUValueType, refFaceTanUProperties...>	refFaceTanU,
		Kokkos::DynRankView< refFaceTanVValueType, refFaceTanVProperties...>	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 428 of file Intrepid2_CellToolsDefNodeInfo.hpp.

Referenced by Intrepid2::Basis_HCURL_TET_In_FEM< ExecSpaceType, outputValueType, pointValueType >::Basis_HCURL_TET_In_FEM(), Intrepid2::Impl::OrientationTools::getCoeffMatrix_HCURL(), and Intrepid2::Experimental::LagrangianInterpolation< ExecSpaceType >::getDofCoordsAndCoeffs().

template<typename SpT >

template<typename cellNodeValueType , class... cellNodeProperties>

void Intrepid2::CellTools< SpT >::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 269 of file Intrepid2_CellToolsDefNodeInfo.hpp.

template<typename SpT >

template<typename refSideNormalValueType , class... refSideNormalProperties>

void Intrepid2::CellTools< SpT >::getReferenceSideNormal	(	Kokkos::DynRankView< refSideNormalValueType, refSideNormalProperties...>	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 471 of file Intrepid2_CellToolsDefNodeInfo.hpp.

Referenced by Intrepid2::Basis_HDIV_TET_In_FEM< ExecSpaceType, outputValueType, pointValueType >::Basis_HDIV_TET_In_FEM(), Intrepid2::Basis_HDIV_TRI_In_FEM< ExecSpaceType, outputValueType, pointValueType >::Basis_HDIV_TRI_In_FEM(), Intrepid2::Impl::OrientationTools::getCoeffMatrix_HDIV(), and Intrepid2::Experimental::LagrangianInterpolation< ExecSpaceType >::getDofCoordsAndCoeffs().

template<typename SpT >

template<typename subcellNodeValueType , class... subcellNodeProperties>

void Intrepid2::CellTools< SpT >::getReferenceSubcellNodes	(	Kokkos::DynRankView< subcellNodeValueType, subcellNodeProperties...>	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 349 of file Intrepid2_CellToolsDefNodeInfo.hpp.

template<typename SpT >

template<typename subcellVertexValueType , class... subcellVertexProperties>

void Intrepid2::CellTools< SpT >::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 233 of file Intrepid2_CellToolsDefNodeInfo.hpp.

template<typename SpT >

template<typename cellVertexValueType , class... cellVertexProperties>

void Intrepid2::CellTools< SpT >::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. Vertex 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., vertex 0 of Line<2> is returned as {-1,0,0}.

Parameters

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

Definition at line 207 of file Intrepid2_CellToolsDefNodeInfo.hpp.

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

template<typename SpT >

void Intrepid2::CellTools< SpT >::getSubcellParametrization	(	subcellParamViewType &	subcellParam,
		const ordinal_type	subcellDim,
		const shards::CellTopology	parentCell
	)

static

Returns array with the coefficients of the parametrization maps for the edges or faces of a reference cell topology.

See Intrepid2::CellTools::setSubcellParametrization and Section Parametrization of physical 1- and 2-subcells more information about parametrization maps.

Parameters

subcellParam	[out] - coefficients of the parameterization map for all subcells of the specified dimension
subcellDim	[in] - dimension of subcells whose parametrization map is returned
parentCell	[in] - topology of the reference cell owning the subcells

Definition at line 156 of file Intrepid2_CellToolsDefParametrization.hpp.

Referenced by Intrepid2::Experimental::LagrangianInterpolation< ExecSpaceType >::getDofCoordsAndCoeffs().

template<typename SpT >

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

void Intrepid2::CellTools< SpT >::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 376 of file Intrepid2_CellToolsDefControlVolume.hpp.

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

template<typename ExecSpaceType>

static bool Intrepid2::CellTools< ExecSpaceType >::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 113 of file Intrepid2_CellTools.hpp.

template<typename SpT >

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

void Intrepid2::CellTools< SpT >::mapToPhysicalFrame	(	Kokkos::DynRankView< physPointValueType, physPointProperties...>	physPoints,
		const Kokkos::DynRankView< refPointValueType, refPointProperties...>	refPoints,
		const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...>	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 array with dimensions (C,N,D) with the nodes of the cell workset
basis	[in] - pointer to HGrad basis used in reference-to-physical cell mapping

Definition at line 136 of file Intrepid2_CellToolsDefRefToPhys.hpp.

Referenced by Intrepid2::CellTools< ExecSpaceType >::mapToPhysicalFrame().

template<typename ExecSpaceType>

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

static void Intrepid2::CellTools< ExecSpaceType >::mapToPhysicalFrame	(	Kokkos::DynRankView< physPointValueType, physPointProperties...>	physPoints,
		const Kokkos::DynRankView< refPointValueType, refPointProperties...>	refPoints,
		const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...>	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 1054 of file Intrepid2_CellTools.hpp.

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

template<typename SpT >

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

void Intrepid2::CellTools< SpT >::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 72 of file Intrepid2_CellToolsDefPhysToRef.hpp.

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

template<typename SpT >

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

void Intrepid2::CellTools< SpT >::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 113 of file Intrepid2_CellToolsDefPhysToRef.hpp.

References Intrepid2::Parameters::MaxNewton.

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

template<typename ExecSpaceType>

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

static void Intrepid2::CellTools< ExecSpaceType >::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 1301 of file Intrepid2_CellTools.hpp.

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

template<typename SpT >

template<typename refSubcellPointValueType , class... refSubcellPointProperties, typename paramPointValueType , class... paramPointProperties>

void Intrepid2::CellTools< SpT >::mapToReferenceSubcell	(	Kokkos::DynRankView< refSubcellPointValueType, refSubcellPointProperties...>	refSubcellPoints,
		const Kokkos::DynRankView< paramPointValueType, paramPointProperties...>	paramPoints,
		const ordinal_type	subcellDim,
		const ordinal_type	subcellOrd,
		const shards::CellTopology	parentCell
	)

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.

Definition at line 192 of file Intrepid2_CellToolsDefRefToPhys.hpp.

Referenced by Intrepid2::Basis_HCURL_TET_In_FEM< ExecSpaceType, outputValueType, pointValueType >::Basis_HCURL_TET_In_FEM(), Intrepid2::Basis_HCURL_TRI_In_FEM< ExecSpaceType, outputValueType, pointValueType >::Basis_HCURL_TRI_In_FEM(), Intrepid2::Basis_HDIV_TET_In_FEM< ExecSpaceType, outputValueType, pointValueType >::Basis_HDIV_TET_In_FEM(), Intrepid2::Basis_HDIV_TRI_In_FEM< ExecSpaceType, outputValueType, pointValueType >::Basis_HDIV_TRI_In_FEM(), Intrepid2::Basis_HGRAD_TET_Cn_FEM< ExecSpaceType, outputValueType, pointValueType >::Basis_HGRAD_TET_Cn_FEM(), Intrepid2::CubatureControlVolumeBoundary< ExecSpaceType, pointValueType, weightValueType >::CubatureControlVolumeBoundary(), Intrepid2::CubatureControlVolumeSide< ExecSpaceType, pointValueType, weightValueType >::CubatureControlVolumeSide(), Intrepid2::Impl::OrientationTools::getCoeffMatrix_HCURL(), Intrepid2::Impl::OrientationTools::getCoeffMatrix_HDIV(), and Intrepid2::Impl::OrientationTools::getCoeffMatrix_HGRAD().

template<typename SpT >

template<typename refSubcellPointValueType , class... refSubcellPointProperties, typename paramPointValueType , class... paramPointProperties>

void KOKKOS_INLINE_FUNCTION Intrepid2::CellTools< SpT >::mapToReferenceSubcell	(	Kokkos::DynRankView< refSubcellPointValueType, refSubcellPointProperties...>	refSubcellPoints,
		const Kokkos::DynRankView< paramPointValueType, paramPointProperties...>	paramPoints,
		const subcellParamViewType	subcellMap,
		const ordinal_type	subcellDim,
		const ordinal_type	subcellOrd,
		const ordinal_type	parentCellDim
	)

static

Overload of mapToReferenceSubcell that runs on device.

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
subcellMap	[in] - array with the coefficients of the subcell parametrization map
subcellDim	[in] - dimension of the subcell where points are mapped to
subcellOrd	[in] - subcell ordinal
parentCellDim	[in] - dimension of the parent cell.

Definition at line 251 of file Intrepid2_CellToolsDefRefToPhys.hpp.

template<typename SpT >

template<typename jacobianValueType , class... jacobianProperties, typename pointValueType , class... pointProperties, typename worksetCellValueType , class... worksetCellProperties, typename HGradBasisPtrType >

void Intrepid2::CellTools< SpT >::setJacobian	(	Kokkos::DynRankView< jacobianValueType, jacobianProperties...>	jacobian,
		const Kokkos::DynRankView< pointValueType, pointProperties...>	points,
		const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...>	worksetCell,
		const HGradBasisPtrType	basis
	)

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 array with dimensions (C,N,D) with the nodes of the cell workset
basis	[in] - HGrad basis for reference to physical cell mapping

Definition at line 114 of file Intrepid2_CellToolsDefJacobian.hpp.

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

template<typename ExecSpaceType>

template<typename jacobianValueType , class... jacobianProperties, typename pointValueType , class... pointProperties, typename worksetCellValueType , class... worksetCellProperties>

static void Intrepid2::CellTools< ExecSpaceType >::setJacobian	(	Kokkos::DynRankView< jacobianValueType, jacobianProperties...>	jacobian,
		const Kokkos::DynRankView< pointValueType, pointProperties...>	points,
		const Kokkos::DynRankView< worksetCellValueType, worksetCellProperties...>	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 418 of file Intrepid2_CellTools.hpp.

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

template<typename SpT >

template<typename jacobianDetValueType , class... jacobianDetProperties, typename jacobianValueType , class... jacobianProperties>

void Intrepid2::CellTools< SpT >::setJacobianDet	(	Kokkos::DynRankView< jacobianDetValueType, jacobianDetProperties...>	jacobianDet,
		const Kokkos::DynRankView< jacobianValueType, jacobianProperties...>	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 194 of file Intrepid2_CellToolsDefJacobian.hpp.

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

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

template<typename SpT >

template<typename jacobianInvValueType , class... jacobianInvProperties, typename jacobianValueType , class... jacobianProperties>

void Intrepid2::CellTools< SpT >::setJacobianInv	(	Kokkos::DynRankView< jacobianInvValueType, jacobianInvProperties...>	jacobianInv,
		const Kokkos::DynRankView< jacobianValueType, jacobianProperties...>	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 181 of file Intrepid2_CellToolsDefJacobian.hpp.

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

template<typename SpT >

void Intrepid2::CellTools< SpT >::setSubcellParametrization	(	subcellParamViewType &	subcellParam,
		const ordinal_type	subcellDim,
		const shards::CellTopology	parentCell
	)

staticprivate

Sets orientation-preserving parametrizations of reference edges and faces of cell topologies with reference cells. Used to populate Intrepid2::CellTools::SubcellParamData.

See Intrepid2::CellTools::setSubcellParametrization and Section Parametrization of physical 1- and 2-subcells more information about parametrization maps.

Parameters

subcellParam	[out] - array with the coefficients of the parametrization map
subcellDim	[in] - dimension of the subcells being parametrized (1 or 2)
parentCell	[in] - topology of the parent cell owning the subcells.

Definition at line 219 of file Intrepid2_CellToolsDefParametrization.hpp.

References Intrepid2::Parameters::MaxDimension.

template<typename SpT >

void Intrepid2::CellTools< SpT >::setSubcellParametrization ( )

static

Defines orientation-preserving parametrizations of reference edges and faces of cell topologies with reference cells.

Given an edge {V0, V1} of some reference cell, its parametrization is a mapping from [-1,1] onto the edge. Parametrization of a triangular face {V0,V1,V2} is mapping from the standard 2-simplex {(0,0,0), (1,0,0), (0,1,0)}, embedded in 3D onto that face. Parametrization of a quadrilateral face {V0,V1,V2,V3} is mapping from the standard 2-cube {(-1,-1,0),(1,-1,0),(1,1,0),(-1,1,0)}, embedded in 3D, onto that face.

This method computes the coefficients of edge and face parametrization maps. All mappings are affine and orientation-preserving, i.e., they preserve the tangent and normal directions implied by the vertex order of the edge or the face relative to the reference cell:

the tangent on [-1,1] from -1 in the direction of 1 is mapped to a tangent on edge {V0,V1} from V0 in the direction of V1 (the forward direction of the edge determined by its start and end vertices)

the normal in the direction of (0,0,1) to the standard 2-simplex {(0,0,0),(1,0,0),(0,1,0)} and the standard 2-cube {(-1,-1,0),(1,-1,0),(1,1,0),(-1,1,0)} is mapped to a normal on {V0,V1,V2} and {V0,V1,V2,V3}, determined according to the right-hand rule (see http://mathworld.wolfram.com/Right-HandRule.html for definition of right-hand rule and Section Section sec_cell_topology_subcell_map for further details).

Because faces of all reference cells supported in Intrepid are affine images of either the standard 2-simplex or the standard 2-cube, the coordinate functions of the respective parmetrization maps are linear polynomials in the parameter variables (u,v), i.e., they are of the form F_i(u,v)=C_0(i)+C_1(i)u+C_2(i)v; 0<=i<3 (face parametrizations are supported only for 3D cells, thus parametrization maps have 3 coordinate functions). As a result, application of these maps is independent of the face type which is convenient for cells such as Wedge or Pyramid that have both types of faces. Also, coefficients of coordinate functions for all faces can be stored together in the same array.

Definition at line 69 of file Intrepid2_CellToolsDefParametrization.hpp.

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

http://docs.trilinos.org/r13.0/packages/intrepid2/src/Cell/Intrepid2_CellTools.hpp
http://docs.trilinos.org/r13.0/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefControlVolume.hpp
http://docs.trilinos.org/r13.0/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefInclusion.hpp
http://docs.trilinos.org/r13.0/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefJacobian.hpp
http://docs.trilinos.org/r13.0/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefNodeInfo.hpp
http://docs.trilinos.org/r13.0/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefParametrization.hpp
http://docs.trilinos.org/r13.0/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefPhysToRef.hpp
http://docs.trilinos.org/r13.0/packages/intrepid2/src/Cell/Intrepid2_CellToolsDefRefToPhys.hpp

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Detailed Description

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

Member Function Documentation

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