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

#include <Intrepid_CellTools.hpp>

Classes
struct	mapToPhysicalFrameTempSpec
	Computes F, the reference-to-physical frame map. More...

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

Public Member Functions
	CellTools ()
	Default constructor.

	~CellTools ()
	Destructor.

Static Public Member Functions
template<class ArrayJac , class ArrayPoint , class ArrayCell >
static void	setJacobian (ArrayJac &jacobian, const ArrayPoint &points, const ArrayCell &cellWorkset, const shards::CellTopology &cellTopo, const int &whichCell=-1)

template<class ArrayJac , class ArrayPoint , class ArrayCell >
static void	setJacobian (ArrayJac &jacobian, const ArrayPoint &points, const ArrayCell &cellWorkset, const Teuchos::RCP< Basis< Scalar, FieldContainer< Scalar > > > HGRAD_Basis, const int &whichCell=-1)

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

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

template<class ArrayPhysPoint , class ArrayRefPoint , class ArrayCell >
static void	mapToPhysicalFrame (ArrayPhysPoint &physPoints, const ArrayRefPoint &refPoints, const ArrayCell &cellWorkset, const shards::CellTopology &cellTopo, const int &whichCell=-1)
	Computes F, the reference-to-physical frame map. More...

template<class ArrayPhysPoint , class ArrayRefPoint , class ArrayCell >
static void	mapToPhysicalFrame (ArrayPhysPoint &physPoints, const ArrayRefPoint &refPoints, const ArrayCell &cellWorkset, const Teuchos::RCP< Basis< Scalar, FieldContainer< Scalar > > > HGRAD_Basis, const int &whichCell=-1)

template<class ArrayRefPoint , class ArrayPhysPoint , class ArrayCell >
static void	mapToReferenceFrame (ArrayRefPoint &refPoints, const ArrayPhysPoint &physPoints, const ArrayCell &cellWorkset, const shards::CellTopology &cellTopo, const int &whichCell=-1)
	Computes $F^{-1}_{c}$ , the inverse of the reference-to-physical frame map using a default initial guess. More...

template<class ArrayRefPoint , class ArrayPhysPoint , class ArrayCell >
static void	mapToReferenceFrame (ArrayRefPoint &refPoints, const ArrayPhysPoint &physPoints, const ArrayCell &cellWorkset, const Teuchos::RCP< Basis< Scalar, FieldContainer< Scalar > > > HGRAD_Basis, const int &whichCell=-1)

template<class ArrayRefPoint , class ArrayInitGuess , class ArrayPhysPoint , class ArrayCell >
static void	mapToReferenceFrameInitGuess (ArrayRefPoint &refPoints, const ArrayInitGuess &initGuess, const ArrayPhysPoint &physPoints, const ArrayCell &cellWorkset, const shards::CellTopology &cellTopo, const int &whichCell=-1)
	Computation of $F^{-1}_{c}$ , the inverse of the reference-to-physical frame map using user-supplied initial guess. More...

template<class ArrayRefPoint , class ArrayInitGuess , class ArrayPhysPoint , class ArrayCell >
static void	mapToReferenceFrameInitGuess (ArrayRefPoint &refPoints, const ArrayInitGuess &initGuess, const ArrayPhysPoint &physPoints, const ArrayCell &cellWorkset, const Teuchos::RCP< Basis< Scalar, FieldContainer< Scalar > > > HGRAD_Basis, const int &whichCell=-1)

template<class ArraySubcellPoint , class ArrayParamPoint >
static void	mapToReferenceSubcell (ArraySubcellPoint &refSubcellPoints, const ArrayParamPoint &paramPoints, const int subcellDim, const int subcellOrd, const shards::CellTopology &parentCell)
	Computes parameterization maps of 1- and 2-subcells of reference cells. More...

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

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

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

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

template<class ArrayEdgeTangent , class ArrayJac >
static void	getPhysicalEdgeTangents (ArrayEdgeTangent &edgeTangents, const ArrayJac &worksetJacobians, const int &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<class ArrayFaceTangentU , class ArrayFaceTangentV , class ArrayJac >
static void	getPhysicalFaceTangents (ArrayFaceTangentU &faceTanU, ArrayFaceTangentV &faceTanV, const ArrayJac &worksetJacobians, const int &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<class ArraySideNormal , class ArrayJac >
static void	getPhysicalSideNormals (ArraySideNormal &sideNormals, const ArrayJac &worksetJacobians, const int &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<class ArrayFaceNormal , class ArrayJac >
static void	getPhysicalFaceNormals (ArrayFaceNormal &faceNormals, const ArrayJac &worksetJacobians, const int &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...

static int	checkPointInclusion (const Scalar *point, const int pointDim, const shards::CellTopology &cellTopo, const double &threshold=INTREPID_THRESHOLD)
	Checks if a point belongs to a reference cell. More...

template<class ArrayPoint >
static int	checkPointsetInclusion (const ArrayPoint &points, const shards::CellTopology &cellTopo, const double &threshold=INTREPID_THRESHOLD)
	Checks if a set of points belongs to a reference cell. More...

template<class ArrayIncl , class ArrayPoint >
static void	checkPointwiseInclusion (ArrayIncl &inRefCell, const ArrayPoint &points, const shards::CellTopology &cellTopo, const double &threshold=INTREPID_THRESHOLD)
	Checks every point in a set for inclusion in a reference cell. More...

template<class ArrayIncl , class ArrayPoint , class ArrayCell >
static void	checkPointwiseInclusion (ArrayIncl &inCell, const ArrayPoint &points, const ArrayCell &cellWorkset, const shards::CellTopology &cell, const int &whichCell=-1, const double &threshold=INTREPID_THRESHOLD)
	Checks every point in a set or multiple sets for inclusion in physical cells from a cell workset. More...

static const double *	getReferenceVertex (const shards::CellTopology &cell, const int vertexOrd)
	Retrieves the Cartesian coordinates of a reference cell vertex. More...

template<class ArraySubcellVert >
static void	getReferenceSubcellVertices (ArraySubcellVert &subcellVertices, const int subcellDim, const int subcellOrd, const shards::CellTopology &parentCell)
	Retrieves the Cartesian coordinates of all vertices of a reference subcell. More...

static const double *	getReferenceNode (const shards::CellTopology &cell, const int nodeOrd)
	Retrieves the Cartesian coordinates of a reference cell node. More...

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

static int	hasReferenceCell (const shards::CellTopology &cellTopo)
	Checks if a cell topology has reference cell. More...

static void	printSubcellVertices (const int subcellDim, const int subcellOrd, const shards::CellTopology &parentCell)
	Prints the reference space coordinates of the vertices of the specified subcell. More...

template<class ArrayCell >
static void	printWorksetSubcell (const ArrayCell &cellWorkset, const shards::CellTopology &parentCell, const int &pCellOrd, const int &subcellDim, const int &subcellOrd, const int &fieldWidth=3)
	Prints the nodes of a subcell from a cell workset. More...

template<class ArrayCVCoord , class ArrayCellCoord >
static void	getSubCVCoords (ArrayCVCoord &subCVcoords, const ArrayCellCoord &cellCoords, const shards::CellTopology &primaryCell)
	Computes coordinates of sub-control volumes in each primary cell. More...

template<class ArrayCent , class ArrayCellCoord >
static void	getBarycenter (ArrayCent &barycenter, const ArrayCellCoord &cellCoords)
	Compute cell barycenters. More...

Static Private Member Functions
static const FieldContainer < double > &	getSubcellParametrization (const int 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...

static void	setSubcellParametrization (FieldContainer< double > &subcellParametrization, const int subcellDim, const shards::CellTopology &parentCell)
	Defines orientation-preserving parametrizations of reference edges and faces of cell topologies with reference cells. More...

template<class ArrayJac , class ArrayPoint , class ArrayCell >
static void	validateArguments_setJacobian (const ArrayJac &jacobian, const ArrayPoint &points, const ArrayCell &cellWorkset, const int &whichCell, const shards::CellTopology &cellTopo)
	Validates arguments to Intrepid::CellTools::setJacobian. More...

template<class ArrayJacInv , class ArrayJac >
static void	validateArguments_setJacobianInv (const ArrayJacInv &jacobianInv, const ArrayJac &jacobian)
	Validates arguments to Intrepid::CellTools::setJacobianInv. More...

template<class ArrayJacDet , class ArrayJac >
static void	validateArguments_setJacobianDetArgs (const ArrayJacDet &jacobianDet, const ArrayJac &jacobian)
	Validates arguments to Intrepid::CellTools::setJacobianDet. More...

template<class ArrayPhysPoint , class ArrayRefPoint , class ArrayCell >
static void	validateArguments_mapToPhysicalFrame (const ArrayPhysPoint &physPoints, const ArrayRefPoint &refPoints, const ArrayCell &cellWorkset, const shards::CellTopology &cellTopo, const int &whichCell)
	Validates arguments to Intrepid::CellTools::mapToPhysicalFrame. More...

template<class ArrayRefPoint , class ArrayPhysPoint , class ArrayCell >
static void	validateArguments_mapToReferenceFrame (const ArrayRefPoint &refPoints, const ArrayPhysPoint &physPoints, const ArrayCell &cellWorkset, const shards::CellTopology &cellTopo, const int &whichCell)
	Validates arguments to Intrepid::CellTools::mapToReferenceFrame with default initial guess. More...

template<class ArrayRefPoint , class ArrayInitGuess , class ArrayPhysPoint , class ArrayCell >
static void	validateArguments_mapToReferenceFrame (const ArrayRefPoint &refPoints, const ArrayInitGuess &initGuess, const ArrayPhysPoint &physPoints, const ArrayCell &cellWorkset, const shards::CellTopology &cellTopo, const int &whichCell)
	Validates arguments to Intrepid::CellTools::mapToReferenceFrame with user-defined initial guess. More...

template<class ArrayIncl , class ArrayPoint , class ArrayCell >
static void	validateArguments_checkPointwiseInclusion (ArrayIncl &inCell, const ArrayPoint &physPoints, const ArrayCell &cellWorkset, const int &whichCell, const shards::CellTopology &cell)
	Validates arguments to Intrepid::CellTools::checkPointwiseInclusion. More...

Detailed Description

template<class Scalar>
class Intrepid::CellTools< Scalar >

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 111 of file Intrepid_CellTools.hpp.

Member Function Documentation

template<class Scalar >

int Intrepid::CellTools< Scalar >::checkPointInclusion	(	const Scalar *	point,
		const int	pointDim,
		const shards::CellTopology &	cellTopo,
		const double &	threshold = `INTREPID_THRESHOLD`
	)

static

Checks if a point belongs to a reference cell.

    Requires cell topology with a reference cell.

Parameters

point	[in] - spatial coordinates of the point tested for inclusion
pointDim	[in] - spatial dimension of that point
cellTopo	[in] - cell topology of the cells stored in `cellWorkset`
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 2440 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayPoint >

int Intrepid::CellTools< Scalar >::checkPointsetInclusion	(	const ArrayPoint &	points,
		const shards::CellTopology &	cellTopo,
		const double &	threshold = `INTREPID_THRESHOLD`
	)

static

Checks if a set of points belongs to a reference cell.

    Requires cell topology with a reference cell. See Intrepid::CellTools::checkPointwiseInclusion 
    for admissible ranks and dimensions of the input point array.

Parameters

points	[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

Returns: 1 if all points are in the closure of the specified reference cell 0 if at least one point is outside the closure of the reference cell

Definition at line 2531 of file Intrepid_CellToolsDef.hpp.

References Intrepid::FieldContainer< Scalar, ArrayTypeId >::resize(), and Intrepid::FieldContainer< Scalar, ArrayTypeId >::size().

template<class Scalar >

template<class ArrayIncl , class ArrayPoint >

void Intrepid::CellTools< Scalar >::checkPointwiseInclusion	(	ArrayIncl &	inRefCell,
		const ArrayPoint &	points,
		const shards::CellTopology &	cellTopo,
		const double &	threshold = `INTREPID_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 2572 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayIncl , class ArrayPoint , class ArrayCell >

void Intrepid::CellTools< Scalar >::checkPointwiseInclusion	(	ArrayIncl &	inCell,
		const ArrayPoint &	points,
		const ArrayCell &	cellWorkset,
		const shards::CellTopology &	cell,
		const int &	whichCell = `-1`,
		const double &	threshold = `INTREPID_THRESHOLD`
	)

static

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

    There are two use cases:

Checks every point from a single point set, stored in a rank-2 array (P,D) for inclusion in a specified physical cell ${\mathcal C}$ from a cell workset.
Checks every point from 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 all cells in a cell workset.

For a single point set in a rank-2 array (P,D) and whichCell set to a valid cell ordinal relative to cellWorkset returns a rank-1 (P) array such that

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

For multiple point sets in a rank-3 array (C,P,D) and whichCell=-1 (default value) 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`
whichCell	[in] - ordinal of the cell used in the inclusion test
threshold	[in] - tolerance for inclusion tests on the input points

Definition at line 2670 of file Intrepid_CellToolsDef.hpp.

References Intrepid::FieldContainer< Scalar, ArrayTypeId >::resize().

template<class Scalar >

template<class ArrayCent , class ArrayCellCoord >

void Intrepid::CellTools< Scalar >::getBarycenter	(	ArrayCent &	barycenter,
		const ArrayCellCoord &	cellCoords
	)

static

Compute cell barycenters.

Parameters

barycenter	[out] - array containing cell baycenters
cellCoords	[in] - array containing cell coordinates

Definition at line 3451 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayEdgeTangent , class ArrayJac >

void Intrepid::CellTools< Scalar >::getPhysicalEdgeTangents	(	ArrayEdgeTangent &	edgeTangents,
		const ArrayJac &	worksetJacobians,
		const int &	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 CellTools<Scalar>::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 2247 of file Intrepid_CellToolsDef.hpp.

Referenced by Intrepid::FunctionSpaceTools::computeEdgeMeasure().

template<class Scalar >

template<class ArrayFaceNormal , class ArrayJac >

void Intrepid::CellTools< Scalar >::getPhysicalFaceNormals	(	ArrayFaceNormal &	faceNormals,
		const ArrayJac &	worksetJacobians,
		const int &	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 CellTools<Scalar>::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 2396 of file Intrepid_CellToolsDef.hpp.

References Intrepid::RealSpaceTools< Scalar >::vecprod().

Referenced by Intrepid::FunctionSpaceTools::computeFaceMeasure().

template<class Scalar >

template<class ArrayFaceTangentU , class ArrayFaceTangentV , class ArrayJac >

void Intrepid::CellTools< Scalar >::getPhysicalFaceTangents	(	ArrayFaceTangentU &	faceTanU,
		ArrayFaceTangentV &	faceTanV,
		const ArrayJac &	worksetJacobians,
		const int &	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 CellTools<Scalar>::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 2294 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArraySideNormal , class ArrayJac >

void Intrepid::CellTools< Scalar >::getPhysicalSideNormals	(	ArraySideNormal &	sideNormals,
		const ArrayJac &	worksetJacobians,
		const int &	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 CellTools<Scalar>::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 CellTools<Scalar>::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 CellTools<Scalar>::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 CellTools<Scalar>::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 2357 of file Intrepid_CellToolsDef.hpp.

Referenced by Intrepid::CubatureControlVolumeSide< Scalar, ArrayPoint, ArrayWeight >::getCubature().

template<class Scalar >

template<class ArrayEdgeTangent >

void Intrepid::CellTools< Scalar >::getReferenceEdgeTangent	(	ArrayEdgeTangent &	refEdgeTangent,
		const int &	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 2102 of file Intrepid_CellToolsDef.hpp.

Referenced by Intrepid::Basis_HCURL_TET_In_FEM< Scalar, ArrayScalar >::Basis_HCURL_TET_In_FEM(), and Intrepid::Basis_HCURL_TRI_In_FEM< Scalar, ArrayScalar >::Basis_HCURL_TRI_In_FEM().

template<class Scalar >

template<class ArrayFaceNormal >

void Intrepid::CellTools< Scalar >::getReferenceFaceNormal	(	ArrayFaceNormal &	refFaceNormal,
		const int &	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 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 2217 of file Intrepid_CellToolsDef.hpp.

References Intrepid::RealSpaceTools< Scalar >::vecprod().

template<class Scalar >

template<class ArrayFaceTangentU , class ArrayFaceTangentV >

void Intrepid::CellTools< Scalar >::getReferenceFaceTangents	(	ArrayFaceTangentU &	refFaceTanU,
		ArrayFaceTangentV &	refFaceTanV,
		const int &	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 2138 of file Intrepid_CellToolsDef.hpp.

Referenced by Intrepid::Basis_HCURL_TET_In_FEM< Scalar, ArrayScalar >::Basis_HCURL_TET_In_FEM().

template<class Scalar >

const double * Intrepid::CellTools< Scalar >::getReferenceNode	(	const shards::CellTopology &	cell,
		const int	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 CellTools<Scalar>::getReferenceVertex.

Parameters

cell	[in] - cell topology of the cell
vertexOrd	[in] - node ordinal

Returns: pointer to array with the (x,y,z) coordinates of the specified reference vertex

Definition at line 529 of file Intrepid_CellToolsDef.hpp.

Referenced by Intrepid::CellTools< Scalar >::getReferenceSubcellNodes().

template<class Scalar >

template<class ArraySideNormal >

void Intrepid::CellTools< Scalar >::getReferenceSideNormal	(	ArraySideNormal &	refSideNormal,
		const int &	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 CellTools<Scalar>::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 CellTools<Scalar>::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 2183 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArraySubcellNode >

void Intrepid::CellTools< Scalar >::getReferenceSubcellNodes	(	ArraySubcellNode &	subcellNodes,
		const int	subcellDim,
		const int	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 788 of file Intrepid_CellToolsDef.hpp.

References Intrepid::CellTools< Scalar >::getReferenceNode().

template<class Scalar >

template<class ArraySubcellVert >

void Intrepid::CellTools< Scalar >::getReferenceSubcellVertices	(	ArraySubcellVert &	subcellVertices,
		const int	subcellDim,
		const int	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 490 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

const double * Intrepid::CellTools< Scalar >::getReferenceVertex	(	const shards::CellTopology &	cell,
		const int	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

cell	[in] - cell topology of the cell
vertexOrd	[in] - vertex ordinal

Returns: pointer to array with the (x,y,z) coordinates of the specified reference vertex

Definition at line 471 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

const FieldContainer< double > & Intrepid::CellTools< Scalar >::getSubcellParametrization	(	const int	subcellDim,
		const shards::CellTopology &	parentCell
	)

staticprivate

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

    See CellTools<Scalar>::setSubcellParametrization and Section \ref sec_cell_topology_subcell_map 
    more information about parametrization maps.

Parameters

subcellDim	[in] - dimension of subcells whose parametrization map is returned
parentCell	[in] - topology of the reference cell owning the subcells

Returns: FieldContainer<double> with the coefficients of the parametrization map for all subcells of the specified dimension.

Definition at line 60 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayCVCoord , class ArrayCellCoord >

void Intrepid::CellTools< Scalar >::getSubCVCoords	(	ArrayCVCoord &	subCVcoords,
		const ArrayCellCoord &	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 3231 of file Intrepid_CellToolsDef.hpp.

Referenced by Intrepid::CubatureControlVolumeSide< Scalar, ArrayPoint, ArrayWeight >::getCubature(), Intrepid::CubatureControlVolume< Scalar, ArrayPoint, ArrayWeight >::getCubature(), and Intrepid::CubatureControlVolumeBoundary< Scalar, ArrayPoint, ArrayWeight >::getCubature().

template<class Scalar >

int Intrepid::CellTools< Scalar >::hasReferenceCell ( const shards::CellTopology & cellTopo )

static

Checks if a cell topology has reference cell.

Parameters

cell	[in] - cell topology

Returns: 1 if the cell topology has reference cell, 0 oterwise

Definition at line 839 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayPhysPoint , class ArrayRefPoint , class ArrayCell >

void Intrepid::CellTools< Scalar >::mapToPhysicalFrame	(	ArrayPhysPoint &	physPoints,
		const ArrayRefPoint &	refPoints,
		const ArrayCell &	cellWorkset,
		const shards::CellTopology &	cellTopo,
		const int &	whichCell = `-1`
	)

static

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

    There are 3 use cases:

Applies $F_{c}$ for a specified physical cell ${\mathcal C}$ from 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 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) and whichCell set to a valid cell ordinal relative to cellWorkset returns a rank-2 (P,D) array such that

$\mbox{physPoints}(p,d) = \Big(F_c(\mbox{refPoint}(p,*)) \Big)_d \quad \mbox{for $0\le c < C$ - fixed}$

For a single point set in a rank-2 array (P,D) and whichCell=-1 (default value) 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 and requires the default value whichCell=-1.

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>

    The default \c whichCell = -1 requires rank-3 output array and
    forces application of all reference-to-physical frame mappings corresponding to the
    cells stored in \c cellWorkset. Application of a single mapping is forced by selecting 
    a valid cell ordinal \c whichCell and requires rank-2 input/output point arrays.

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-3/2 array with dimensions (C,P,D)/(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`
whichCell	[in] - ordinal of the cell that defines the reference-to-physical map; default is -1

Todo:: Implement method for non-standard (shell, beam, etc) topologies.

Definition at line 1451 of file Intrepid_CellToolsDef.hpp.

Referenced by Intrepid::CubaturePolygon< Scalar, ArrayPoint, ArrayWeight >::CubaturePolygon().

template<class Scalar >

template<class ArrayRefPoint , class ArrayPhysPoint , class ArrayCell >

void Intrepid::CellTools< Scalar >::mapToReferenceFrame	(	ArrayRefPoint &	refPoints,
		const ArrayPhysPoint &	physPoints,
		const ArrayCell &	cellWorkset,
		const shards::CellTopology &	cellTopo,
		const int &	whichCell = `-1`
	)

static

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

    There are two use cases:

Applies $F^{-1}_{c}$ for a specified physical cell ${\mathcal C}$ from a cell workset to a single set of points stored in a rank-2 (P,D) array;
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 (default mode).

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

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

The whichCell argument selects the physical cell and is required to be a valid cell ordinal for cellWorkset array.

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

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

The default value whichCell=-1 selects this mode.

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-3/2 array with dimensions (C,P,D)/(P,D) with the images of the physical points
physPoints	[in] - rank-3/2 array with dimensions (C,P,D)/(P,D) with points in physical frame
cellWorkset	[in] - rank-3 array with dimensions (C,N,D) with the nodes of the cell workset
whichCell	[in] - ordinal of the cell that defines the reference-to-physical map; default is -1
cellTopo	[in] - cell topology of the cells stored in `cellWorkset`

Todo:: Implement method for non-standard (shell, beam, etc) topologies.

Definition at line 1670 of file Intrepid_CellToolsDef.hpp.

References Intrepid::FieldContainer< Scalar, ArrayTypeId >::resize().

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

template<class Scalar >

template<class ArrayRefPoint , class ArrayInitGuess , class ArrayPhysPoint , class ArrayCell >

void Intrepid::CellTools< Scalar >::mapToReferenceFrameInitGuess	(	ArrayRefPoint &	refPoints,
		const ArrayInitGuess &	initGuess,
		const ArrayPhysPoint &	physPoints,
		const ArrayCell &	cellWorkset,
		const shards::CellTopology &	cellTopo,
		const int &	whichCell = `-1`
	)

static

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

      There are two use cases:

Applies $F^{-1}_{c}$ for a specified physical cell ${\mathcal C}$ from a cell workset to a single set of points stored in a rank-2 (P,D) array;
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 (default mode).

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

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

The whichCell argument selects the physical cell and is required to be a valid cell ordinal for cellWorkset array.

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

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

The default value whichCell=-1 selects this mode.

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
cellWorkset	[in] - rank-3 array with dimensions (C,N,D) with the nodes of the cell workset
whichCell	[in] - ordinal of the cell that defines the reference-to-physical map; default is -1
cellTopo	[in] - cell topology of the cells stored in `cellWorkset`

Definition at line 1907 of file Intrepid_CellToolsDef.hpp.

References Intrepid::RealSpaceTools< Scalar >::add(), INTREPID_MAX_NEWTON, Intrepid::RealSpaceTools< Scalar >::matvec(), Intrepid::FieldContainer< Scalar, ArrayTypeId >::resize(), Intrepid::RealSpaceTools< Scalar >::subtract(), and Intrepid::RealSpaceTools< Scalar >::vectorNorm().

template<class Scalar >

template<class ArraySubcellPoint , class ArrayParamPoint >

void Intrepid::CellTools< Scalar >::mapToReferenceSubcell	(	ArraySubcellPoint &	refSubcellPoints,
		const ArrayParamPoint &	paramPoints,
		const int	subcellDim,
		const int	subcellOrd,
		const shards::CellTopology &	parentCell
	)

static

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

    Applies \form#49, the parametrization map of a subcell \form#27 
    from a given reference cell, to a set of points in the parametrization domain
    \e R  of \form#27. 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 CellTools<Scalar>::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 2035 of file Intrepid_CellToolsDef.hpp.

Referenced by Intrepid::Basis_HCURL_TET_In_FEM< Scalar, ArrayScalar >::Basis_HCURL_TET_In_FEM(), Intrepid::Basis_HCURL_TRI_In_FEM< Scalar, ArrayScalar >::Basis_HCURL_TRI_In_FEM(), Intrepid::Basis_HDIV_TET_In_FEM< Scalar, ArrayScalar >::Basis_HDIV_TET_In_FEM(), Intrepid::Basis_HDIV_TRI_In_FEM< Scalar, ArrayScalar >::Basis_HDIV_TRI_In_FEM(), Intrepid::CubatureControlVolumeSide< Scalar, ArrayPoint, ArrayWeight >::getCubature(), and Intrepid::CubatureControlVolumeBoundary< Scalar, ArrayPoint, ArrayWeight >::getCubature().

template<class Scalar >

void Intrepid::CellTools< Scalar >::printSubcellVertices	(	const int	subcellDim,
		const int	subcellOrd,
		const shards::CellTopology &	parentCell
	)

static

Prints the reference space coordinates of the vertices of the specified subcell.

Parameters

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 3148 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayCell >

void Intrepid::CellTools< Scalar >::printWorksetSubcell	(	const ArrayCell &	cellWorkset,
		const shards::CellTopology &	parentCell,
		const int &	pCellOrd,
		const int &	subcellDim,
		const int &	subcellOrd,
		const int &	fieldWidth = `3`
	)

static

Prints the nodes of a subcell from a cell workset.

Definition at line 3188 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayJacDet , class ArrayJac >

void Intrepid::CellTools< Scalar >::setJacobianDet	(	ArrayJacDet &	jacobianDet,
		const ArrayJac &	jacobian
	)

static

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

    Returns rank-2 or rank-1 array with dimensions (C,P)/(P) such that

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

Parameters

jacobianDet	[out] - rank-2/1 array with dimensions (C,P)/(P) with Jacobian determinants
jacobian	[in] - rank-4/3 array with dimensions (C,P,D,D)/(P,D,D) with the Jacobians

Definition at line 1314 of file Intrepid_CellToolsDef.hpp.

Referenced by Intrepid::CubaturePolygon< Scalar, ArrayPoint, ArrayWeight >::CubaturePolygon(), Intrepid::CubatureControlVolume< Scalar, ArrayPoint, ArrayWeight >::getCubature(), and Intrepid::CubatureControlVolumeBoundary< Scalar, ArrayPoint, ArrayWeight >::getCubature().

template<class Scalar >

template<class ArrayJacInv , class ArrayJac >

void Intrepid::CellTools< Scalar >::setJacobianInv	(	ArrayJacInv &	jacobianInv,
		const ArrayJac &	jacobian
	)

static

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

    Returns rank-4 or rank-3 array with dimensions (C,P,D,D) or (P,D,D) such that

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

Parameters

jacobianInv	[out] - rank-4/3 array with dimensions (C,P,D,D)/(P,D,D) with the inverse Jacobians
jacobian	[in] - rank-4/3 array with dimensions (C,P,D,D)/(P,D,D) with the Jacobians

Definition at line 1283 of file Intrepid_CellToolsDef.hpp.

References Intrepid::RealSpaceTools< Scalar >::inverse().

template<class Scalar >

void Intrepid::CellTools< Scalar >::setSubcellParametrization	(	FieldContainer< double > &	subcellParametrization,
		const int	subcellDim,
		const shards::CellTopology &	parentCell
	)

staticprivate

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 and stores
    them in static arrays owned by CellTools<Scalar>::getSubcellParametrization method. 
    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.

Parameters

subcellParametrization	[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 327 of file Intrepid_CellToolsDef.hpp.

References Intrepid::FieldContainer< Scalar, ArrayTypeId >::resize().

template<class Scalar >

template<class ArrayIncl , class ArrayPoint , class ArrayCell >

void Intrepid::CellTools< Scalar >::validateArguments_checkPointwiseInclusion	(	ArrayIncl &	inCell,
		const ArrayPoint &	physPoints,
		const ArrayCell &	cellWorkset,
		const int &	whichCell,
		const shards::CellTopology &	cell
	)

staticprivate

Validates arguments to Intrepid::CellTools::checkPointwiseInclusion.

Parameters

inCell	[out] - rank-1 (P) array required
physPoints	[in] - rank-2 (P,D) array required
cellWorkset	[in] - rank-3 (C,N,D) array required
whichCell	[in] - 0 <= whichCell < C required
cellTopo	[in] - cell topology with a reference cell required

Definition at line 3063 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayPhysPoint , class ArrayRefPoint , class ArrayCell >

void Intrepid::CellTools< Scalar >::validateArguments_mapToPhysicalFrame	(	const ArrayPhysPoint &	physPoints,
		const ArrayRefPoint &	refPoints,
		const ArrayCell &	cellWorkset,
		const shards::CellTopology &	cellTopo,
		const int &	whichCell
	)

staticprivate

Validates arguments to Intrepid::CellTools::mapToPhysicalFrame.

Parameters

physPoints	[in] - rank-3 (C,P,D) array or rank-2 (P,D) array required
refPoints	[in] - rank-3 (C,P,D) array or rank-2 (P,D) array required
cellWorkset	[in] - rank-3 (C,N,D) array required
whichCell	[in] - default = -1 or 0 <= whichCell < C required
cellTopo	[in] - cell topology with a reference cell required

Definition at line 2908 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayRefPoint , class ArrayPhysPoint , class ArrayCell >

void Intrepid::CellTools< Scalar >::validateArguments_mapToReferenceFrame	(	const ArrayRefPoint &	refPoints,
		const ArrayPhysPoint &	physPoints,
		const ArrayCell &	cellWorkset,
		const shards::CellTopology &	cellTopo,
		const int &	whichCell
	)

staticprivate

Validates arguments to Intrepid::CellTools::mapToReferenceFrame with default initial guess.

Parameters

physPoints	[in] - rank-3 (C,P,D) array or rank-2 (P,D) array required
refPoints	[in] - rank-3 (C,P,D) array or rank-2 (P,D) array required
cellWorkset	[in] - rank-3 (C,N,D) array required
whichCell	[in] - default = -1 or 0 <= whichCell < C required
cellTopo	[in] - cell topology with a reference cell required

Definition at line 2999 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayRefPoint , class ArrayInitGuess , class ArrayPhysPoint , class ArrayCell >

void Intrepid::CellTools< Scalar >::validateArguments_mapToReferenceFrame	(	const ArrayRefPoint &	refPoints,
		const ArrayInitGuess &	initGuess,
		const ArrayPhysPoint &	physPoints,
		const ArrayCell &	cellWorkset,
		const shards::CellTopology &	cellTopo,
		const int &	whichCell
	)

staticprivate

Validates arguments to Intrepid::CellTools::mapToReferenceFrame with user-defined initial guess.

Parameters

physPoints	[in] - rank-3 (C,P,D) array or rank-2 (P,D) array required
initGuess	[in] - rank and dimensions must match those of physPoints
refPoints	[in] - rank-3 (C,P,D) array or rank-2 (P,D) array required
cellWorkset	[in] - rank-3 (C,N,D) array required
whichCell	[in] - default = -1 or 0 <= whichCell < C required
cellTopo	[in] - cell topology with a reference cell required

Definition at line 3045 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayJac , class ArrayPoint , class ArrayCell >

void Intrepid::CellTools< Scalar >::validateArguments_setJacobian	(	const ArrayJac &	jacobian,
		const ArrayPoint &	points,
		const ArrayCell &	cellWorkset,
		const int &	whichCell,
		const shards::CellTopology &	cellTopo
	)

staticprivate

Validates arguments to Intrepid::CellTools::setJacobian.

Parameters

jacobian	[in] - rank-4 (C,P,D,D) array or rank-3 (P,D,D) array required
points	[in] - rank-2 (P,D) or rank-3 (C,P,D) array required
cellWorkset	[in] - rank-3 (C,N,D) array required
whichCell	[in] - default = -1 or 0 <= whichCell < C required
cellTopo	[in] - cell topology with a reference cell required

Definition at line 2723 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayJacDet , class ArrayJac >

void Intrepid::CellTools< Scalar >::validateArguments_setJacobianDetArgs	(	const ArrayJacDet &	jacobianDet,
		const ArrayJac &	jacobian
	)

staticprivate

Validates arguments to Intrepid::CellTools::setJacobianDet.

Parameters

jacobianDet	[in] - rank = (jacobian rank - 2) required
jacobian	[in] - rank-4 (C,P,D,D) array or rank-3 (P,D,D) array required

Definition at line 2865 of file Intrepid_CellToolsDef.hpp.

template<class Scalar >

template<class ArrayJacInv , class ArrayJac >

void Intrepid::CellTools< Scalar >::validateArguments_setJacobianInv	(	const ArrayJacInv &	jacobianInv,
		const ArrayJac &	jacobian
	)

staticprivate

Validates arguments to Intrepid::CellTools::setJacobianInv.

Parameters

jacobianInv	[in] - rank and dimensions must match jacobian array
jacobian	[in] - rank-4 (C,P,D,D) array or rank-3 (P,D,D) array required

Definition at line 2837 of file Intrepid_CellToolsDef.hpp.

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

http://docs.trilinos.org/r12.16/packages/intrepid/src/Cell/Intrepid_CellTools.hpp
http://docs.trilinos.org/r12.16/packages/intrepid/src/Cell/Intrepid_CellToolsDef.hpp

Classes

Public Member Functions

Static Public Member Functions

Static Private Member Functions

Detailed Description

template<class Scalar> class Intrepid::CellTools< Scalar >

Member Function Documentation

template<class Scalar>
class Intrepid::CellTools< Scalar >