Tools to compute orientations for degrees-of-freedom. More...

#include <Intrepid2_OrientationTools.hpp>

Public Member Functions
template<typename VT >
KOKKOS_INLINE_FUNCTION void	getModifiedLinePoint (VT &ot, const VT pt, const ordinal_type ort)

template<typename VT >
KOKKOS_INLINE_FUNCTION void	getModifiedTrianglePoint (VT &ot0, VT &ot1, const VT pt0, const VT pt1, const ordinal_type ort)

template<typename VT >
KOKKOS_INLINE_FUNCTION void	getModifiedQuadrilateralPoint (VT &ot0, VT &ot1, const VT pt0, const VT pt1, const ordinal_type ort)

template<typename outPointViewType >
void	getJacobianOfOrientationMap (outPointViewType jacobian, const shards::CellTopology cellTopo, const ordinal_type cellOrt)

template<typename outPointViewType >
KOKKOS_INLINE_FUNCTION void	getJacobianOfOrientationMap (outPointViewType jacobian, const unsigned cellTopoKey, const ordinal_type cellOrt)

Static Public Member Functions
template<typename ValueType >
static KOKKOS_INLINE_FUNCTION void	getModifiedLinePoint (ValueType &ot, const ValueType pt, const ordinal_type ort)
	Computes modified point for line segment. More...

template<typename ValueType >
static KOKKOS_INLINE_FUNCTION void	getModifiedTrianglePoint (ValueType &ot0, ValueType &ot1, const ValueType pt0, const ValueType pt1, const ordinal_type ort)
	Computes modified point for triangle. More...

template<typename ValueType >
static KOKKOS_INLINE_FUNCTION void	getModifiedQuadrilateralPoint (ValueType &ot0, ValueType &ot1, const ValueType pt0, const ValueType pt1, const ordinal_type ort)
	Computes modified point for quadrilateral. More...

template<typename outPointViewType , typename refPointViewType >
static void	mapToModifiedReference (outPointViewType outPoints, const refPointViewType refPoints, const shards::CellTopology cellTopo, const ordinal_type cellOrt=0)
	Computes modified parameterization maps of 1- and 2-subcells with orientation. More...

template<typename outPointViewType , typename refPointViewType >
static KOKKOS_INLINE_FUNCTION void	mapToModifiedReference (outPointViewType outPoints, const refPointViewType refPoints, const unsigned cellTopoKey, const ordinal_type cellOrt=0)
	Computes modified parameterization maps of 1- and 2-subcells with orientation. More...

template<typename JacobianViewType >
static KOKKOS_INLINE_FUNCTION void	getLineJacobian (JacobianViewType jacobian, const ordinal_type ort)
	Computes Jacobian of orientation map for line segment. More...

template<typename JacobianViewType >
static KOKKOS_INLINE_FUNCTION void	getTriangleJacobian (JacobianViewType jacobian, const ordinal_type ort)
	Computes Jacobian of orientation map for triangle. More...

template<typename JacobianViewType >
static KOKKOS_INLINE_FUNCTION void	getQuadrilateralJacobian (JacobianViewType jacobian, const ordinal_type ort)
	Computes Jacobian of orientation map for quadrilateral. More...

template<typename JacobianViewType >
static void	getJacobianOfOrientationMap (JacobianViewType jacobian, const shards::CellTopology cellTopo, const ordinal_type cellOrt)
	Computes jacobian of the parameterization maps of 1- and 2-subcells with orientation. More...

template<typename JacobianViewType >
static KOKKOS_INLINE_FUNCTION void	getJacobianOfOrientationMap (JacobianViewType jacobian, const unsigned cellTopoKey, const ordinal_type cellOrt)
	Computes jacobian of the parameterization maps of 1- and 2-subcells with orientation. More...

template<typename TanViewType , typename ParamViewType >
static KOKKOS_INLINE_FUNCTION void	getRefSubcellTangents (TanViewType tangents, const ParamViewType subCellParametrization, const unsigned subcellTopoKey, const ordinal_type subCellOrd, const ordinal_type ort)
	Computes the (oriented) subCell tangents. More...

template<typename TanNormViewType , typename ParamViewType >
static KOKKOS_INLINE_FUNCTION void	getRefSideTangentsAndNormal (TanNormViewType tangentsAndNormal, const ParamViewType subCellParametrization, const unsigned subcellTopoKey, const ordinal_type subCellOrd, const ordinal_type ort)
	Computes the (oriented) tangents and normal of the side subCell The normals are only defined for sides (subCells of dimension D-1) and it requires the computation of tangents. More...

template<typename coordsViewType , typename subcellCoordsViewType , typename ParamViewType >
static KOKKOS_INLINE_FUNCTION void	mapSubcellCoordsToRefCell (coordsViewType cellCoords, const subcellCoordsViewType subCellCoords, const ParamViewType subcellParametrization, const unsigned subcellTopoKey, const ordinal_type subCellOrd, const ordinal_type ort)
	Maps points defined on the subCell manifold into the parent Cell accounting for orientation. More...

template<typename OutputViewType , typename subcellBasisHostType , typename cellBasisHostType >
static void	getCoeffMatrix_HGRAD (OutputViewType &output, const subcellBasisHostType &subcellBasis, const cellBasisHostType &cellBasis, const ordinal_type subcellId, const ordinal_type subcellOrt, const bool inverse=false)
	Compute orientation matrix for HGRAD basis for a given subcell and its reference basis. More...

template<typename OutputViewType , typename subcellBasisHostType , typename cellBasisHostType >
static void	getCoeffMatrix_HCURL (OutputViewType &output, const subcellBasisHostType &subcellBasis, const cellBasisHostType &cellBasis, const ordinal_type subcellId, const ordinal_type subcellOrt, const bool inverse=false)
	Compute orientation matrix for HCURL basis for a given subcell and its reference basis. More...

template<typename OutputViewType , typename subcellBasisHostType , typename cellBasisHostType >
static void	getCoeffMatrix_HDIV (OutputViewType &output, const subcellBasisHostType &subcellBasis, const cellBasisHostType &cellBasis, const ordinal_type subcellId, const ordinal_type subcellOrt, const bool inverse=false)
	Compute orientation matrix for HDIV basis for a given subcell and its reference basis. More...

template<typename OutputViewType , typename cellBasisHostType >
static void	getCoeffMatrix_HVOL (OutputViewType &output, const cellBasisHostType &cellBasis, const ordinal_type cellOrt, const bool inverse=false)
	Compute orientation matrix for HVOL basis for a given (2D or 1D) cell and its reference basis. This method is used only for side basis. More...

Detailed Description

Tools to compute orientations for degrees-of-freedom.

Definition at line 114 of file Intrepid2_OrientationTools.hpp.

Member Function Documentation

template<typename OutputViewType , typename subcellBasisHostType , typename cellBasisHostType >

static void Intrepid2::Impl::OrientationTools::getCoeffMatrix_HCURL	(	OutputViewType &	output,
		const subcellBasisHostType &	subcellBasis,
		const cellBasisHostType &	cellBasis,
		const ordinal_type	subcellId,
		const ordinal_type	subcellOrt,
		const bool	inverse = `false`
	)

inlinestatic

Compute orientation matrix for HCURL basis for a given subcell and its reference basis.

Parameters

output	[out] - rank 2 coefficient matrix
subcellBasis	[in] - reference subcell basis function
cellBasis	[in] - cell basis function
subcellId	[in] - subcell Id in the cell topology
subcellOrt	[in] - orientation number between 0 and 1
inverse	[in] - boolean, when true the inverse of the orintation matrix is computed

template<typename OutputViewType , typename subcellBasisHostType , typename cellBasisHostType >

void Intrepid2::Impl::OrientationTools::getCoeffMatrix_HDIV	(	OutputViewType &	output,
		const subcellBasisHostType &	subcellBasis,
		const cellBasisHostType &	cellBasis,
		const ordinal_type	subcellId,
		const ordinal_type	subcellOrt,
		const bool	inverse = `false`
	)

inlinestatic

Compute orientation matrix for HDIV basis for a given subcell and its reference basis.

Parameters

output	[out] - rank 2 orientation matrix
subcellBasis	[in] - reference subcell basis
cellBasis	[in] - cell basis function
subcellId	[in] - subcell Id in the cell topology
subcellOrt	[in] - orientation number between 0 and 1
inverse	[in] - boolean, when true the inverse of the orintation matrix is computed

Definition at line 175 of file Intrepid2_OrientationToolsDefCoeffMatrix_HDIV.hpp.

References Intrepid2::RefSubcellParametrization< DeviceType >::get(), Intrepid2::PointTools::getLattice(), Intrepid2::PointTools::getLatticeSize(), getRefSideTangentsAndNormal(), and mapSubcellCoordsToRefCell().

template<typename OutputViewType , typename subcellBasisHostType , typename cellBasisHostType >

void Intrepid2::Impl::OrientationTools::getCoeffMatrix_HGRAD	(	OutputViewType &	output,
		const subcellBasisHostType &	subcellBasis,
		const cellBasisHostType &	cellBasis,
		const ordinal_type	subcellId,
		const ordinal_type	subcellOrt,
		const bool	inverse = `false`
	)

inlinestatic

Compute orientation matrix for HGRAD basis for a given subcell and its reference basis.

Parameters

output	[out] - rank 2 coefficient matrix
subcellBasis	[in] - reference subcell basis function
cellBasis	[in] - cell basis function
subcellId	[in] - subcell Id in the cell topology
subcellOrt	[in] - orientation number between 0 and 1
inverse	[in] - boolean, when true the inverse of the orintation matrix is computed

Parameters

subcellBasis	this is device view
cellBasis	this must be host basis object
subcellId	this also must be host basis object

Definition at line 135 of file Intrepid2_OrientationToolsDefCoeffMatrix_HGRAD.hpp.

References Intrepid2::RefSubcellParametrization< DeviceType >::get(), Intrepid2::PointTools::getLattice(), Intrepid2::PointTools::getLatticeSize(), mapSubcellCoordsToRefCell(), and mapToModifiedReference().

template<typename OutputViewType , typename cellBasisHostType >

void Intrepid2::Impl::OrientationTools::getCoeffMatrix_HVOL	(	OutputViewType &	output,
		const cellBasisHostType &	cellBasis,
		const ordinal_type	cellOrt,
		const bool	inverse = `false`
	)

inlinestatic

Compute orientation matrix for HVOL basis for a given (2D or 1D) cell and its reference basis. This method is used only for side basis.

Parameters

output	[out] - rank 2 coefficient matrix
cellBasis	[in] - cell basis function
subcellOrt	[in] - orientation number between 0 and 1
inverse	[in] - boolean, when true the inverse of the orintation matrix is computed

Parameters

cellBasis	this is device view
cellOrt	this also must be host basis object

Definition at line 114 of file Intrepid2_OrientationToolsDefCoeffMatrix_HVOL.hpp.

References getJacobianOfOrientationMap(), Intrepid2::PointTools::getLattice(), and mapToModifiedReference().

template<typename JacobianViewType >

static void Intrepid2::Impl::OrientationTools::getJacobianOfOrientationMap	(	JacobianViewType	jacobian,
		const shards::CellTopology	cellTopo,
		const ordinal_type	cellOrt
	)

inlinestatic

Computes jacobian of the parameterization maps of 1- and 2-subcells with orientation.

Parameters

jacobian	[out] - rank-2 (D,D) array with jacobian of the orientation map
cellTopo	[in] - cell topology of the parameterized domain (1- and 2-subcells)
cellOrt	[in] - cell orientation number (zero is aligned with shards default configuration

Referenced by getCoeffMatrix_HVOL(), and getRefSubcellTangents().

template<typename JacobianViewType >

static KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::getJacobianOfOrientationMap	(	JacobianViewType	jacobian,
		const unsigned	cellTopoKey,
		const ordinal_type	cellOrt
	)

static

Computes jacobian of the parameterization maps of 1- and 2-subcells with orientation.

Parameters

jacobian	[out] - rank-2 (D,D) array with jacobian of the orientation map
cellTopoKey	[in] - key of the cell topology of the parameterized domain (1- and 2-subcells)
cellOrt	[in] - cell orientation number (zero is aligned with shards default configuration

template<typename JacobianViewType >

KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::getLineJacobian	(	JacobianViewType	jacobian,
		const ordinal_type	ort
	)

static

Computes Jacobian of orientation map for line segment.

Parameters

jacobian	[out] - rank-2 (D,D) array with jacobian of the orientation map
ort	[in] - orientation number between 0 and 1

Definition at line 91 of file Intrepid2_OrientationToolsDefModifyPoints.hpp.

template<typename ValueType >

static KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::getModifiedLinePoint	(	ValueType &	ot,
		const ValueType	pt,
		const ordinal_type	ort
	)

static

Computes modified point for line segment.

Parameters

ot	[out] - modified point value
pt	[in] - input point in [-1.0 , 1.0]
ort	[in] - orientation number between 0 and 1

Referenced by mapToModifiedReference().

template<typename ValueType >

static KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::getModifiedQuadrilateralPoint	(	ValueType &	ot0,
		ValueType &	ot1,
		const ValueType	pt0,
		const ValueType	pt1,
		const ordinal_type	ort
	)

static

Computes modified point for quadrilateral.

Parameters

ot0	[out] - modified coordinate 0
ot1	[out] - modified coordinate 1
pt0	[out] - input coordinate 0
pt1	[out] - input coordinate 1
ort	[in] - orientation number between 0 and 7

Referenced by mapToModifiedReference().

template<typename ValueType >

static KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::getModifiedTrianglePoint	(	ValueType &	ot0,
		ValueType &	ot1,
		const ValueType	pt0,
		const ValueType	pt1,
		const ordinal_type	ort
	)

static

Computes modified point for triangle.

Parameters

ot0	[out] - modified coordinate 0
ot1	[out] - modified coordinate 1
pt0	[out] - input coordinate 0
pt1	[out] - input coordinate 1
ort	[in] - orientation number between 0 and 5

Referenced by mapToModifiedReference().

template<typename JacobianViewType >

KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::getQuadrilateralJacobian	(	JacobianViewType	jacobian,
		const ordinal_type	ort
	)

static

Computes Jacobian of orientation map for quadrilateral.

Parameters

jacobian	[out] - rank-2 (D,D) array with jacobian of the orientation map
ort	[in] - orientation number between 0 and 7

Definition at line 220 of file Intrepid2_OrientationToolsDefModifyPoints.hpp.

template<typename TanNormViewType , typename ParamViewType >

KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::getRefSideTangentsAndNormal	(	TanNormViewType	tangentsAndNormal,
		const ParamViewType	subCellParametrization,
		const unsigned	subcellTopoKey,
		const ordinal_type	subCellOrd,
		const ordinal_type	ort
	)

static

Computes the (oriented) tangents and normal of the side subCell The normals are only defined for sides (subCells of dimension D-1) and it requires the computation of tangents.

Parameters

tangentsAndNormal	[out] - rank-2 (D,D), (D-1) tangents and 1 normal. D: parent cell dimension
subcellParam	[in] - rank-2 (N, scD+1), subCells parametrization. N:number of subcells, scD: subCell dimension
cellTopoKey	[in] - key of the cell topology of the parameterized domain (1- and 2-subcells)
subCellOrd	[in] - position of the subCell among subCells of a given dimension
ort	[in] - subCell orientation number

Definition at line 400 of file Intrepid2_OrientationToolsDefModifyPoints.hpp.

References getRefSubcellTangents().

Referenced by getCoeffMatrix_HDIV().

template<typename TanViewType , typename ParamViewType >

KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::getRefSubcellTangents	(	TanViewType	tangents,
		const ParamViewType	subCellParametrization,
		const unsigned	subcellTopoKey,
		const ordinal_type	subCellOrd,
		const ordinal_type	ort
	)

static

Computes the (oriented) subCell tangents.

Parameters

tangents	[out] - rank-2 (scD,D), tangents of the subcell. scD: subCell dimension, D: parent cell dimension
subcellParam	[in] - rank-2 (N, scD+1), subCells parametrization. N:number of subcells, scD: subCell dimension
cellTopoKey	[in] - key of the cell topology of the parameterized domain (1- and 2-subcells)
subCellOrd	[in] - position of the subCell among subCells of a given dimension
ort	[in] - subCell orientation number

Definition at line 376 of file Intrepid2_OrientationToolsDefModifyPoints.hpp.

References getJacobianOfOrientationMap().

Referenced by getRefSideTangentsAndNormal().

template<typename JacobianViewType >

KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::getTriangleJacobian	(	JacobianViewType	jacobian,
		const ordinal_type	ort
	)

static

Computes Jacobian of orientation map for triangle.

Parameters

jacobian	[out] - rank-2 (D,D) array with jacobian of the orientation map
ort	[in] - orientation number between 0 and 5

Definition at line 151 of file Intrepid2_OrientationToolsDefModifyPoints.hpp.

template<typename coordsViewType , typename subcellCoordsViewType , typename ParamViewType >

KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::mapSubcellCoordsToRefCell	(	coordsViewType	cellCoords,
		const subcellCoordsViewType	subCellCoords,
		const ParamViewType	subcellParametrization,
		const unsigned	subcellTopoKey,
		const ordinal_type	subCellOrd,
		const ordinal_type	ort
	)

static

Maps points defined on the subCell manifold into the parent Cell accounting for orientation.

Parameters

cellCoords	[out] - rank-2 (P, D), P points mapped in the parent cell manifold.
subCellCoords	[in] - rank-2 (P, scD), P points defined on the subCell manifold, scD: subCell dimension
subcellParam	[in] - rank-2 (N, scD+1), subCells parametrization. N:number of subCells, scD: subCell dimension
cellTopoKey	[in] - key of the cell topology of the parameterized domain (1- and 2-subCells)
subCellOrd	[in] - position of the subCell among subCells of a given dimension
ort	[in] - subCell orientation number

Definition at line 425 of file Intrepid2_OrientationToolsDefModifyPoints.hpp.

References mapToModifiedReference().

Referenced by getCoeffMatrix_HDIV(), and getCoeffMatrix_HGRAD().

template<typename outPointViewType , typename refPointViewType >

void Intrepid2::Impl::OrientationTools::mapToModifiedReference	(	outPointViewType	outPoints,
		const refPointViewType	refPoints,
		const shards::CellTopology	cellTopo,
		const ordinal_type	cellOrt = `0`
	)

inlinestatic

Computes modified parameterization maps of 1- and 2-subcells with orientation.

Parameters

outPoints	[out] - rank-2 (P,D2) array with points in 1D or 2D modified domain with orientation
refPoints	[in] - rank-2 (P,D2) array with points in 1D or 2D parameter domain
cellTopo	[in] - cell topology of the parameterized domain (1- and 2-subcells)
cellOrt	[in] - cell orientation number (zero is aligned with shards default configuration

Definition at line 255 of file Intrepid2_OrientationToolsDefModifyPoints.hpp.

Referenced by getCoeffMatrix_HGRAD(), getCoeffMatrix_HVOL(), and mapSubcellCoordsToRefCell().

template<typename outPointViewType , typename refPointViewType >

KOKKOS_INLINE_FUNCTION void Intrepid2::Impl::OrientationTools::mapToModifiedReference	(	outPointViewType	outPoints,
		const refPointViewType	refPoints,
		const unsigned	cellTopoKey,
		const ordinal_type	cellOrt = `0`
	)

static

Computes modified parameterization maps of 1- and 2-subcells with orientation.

Parameters

outPoints	[out] - rank-2 (P,D2) array with points in 1D or 2D modified domain with orientation
refPoints	[in] - rank-2 (P,D2) array with points in 1D or 2D parameter domain
cellTopoKey	[in] - key of the cell topology of the parameterized domain (1- and 2-subcells)
cellOrt	[in] - cell orientation number (zero is aligned with shards default configuration

Definition at line 281 of file Intrepid2_OrientationToolsDefModifyPoints.hpp.

References getModifiedLinePoint(), getModifiedQuadrilateralPoint(), and getModifiedTrianglePoint().

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

http://docs.trilinos.org/dev/packages/intrepid2/src/Orientation/Intrepid2_OrientationTools.hpp
http://docs.trilinos.org/dev/packages/intrepid2/src/Orientation/Intrepid2_OrientationToolsDefCoeffMatrix_HDIV.hpp
http://docs.trilinos.org/dev/packages/intrepid2/src/Orientation/Intrepid2_OrientationToolsDefCoeffMatrix_HGRAD.hpp
http://docs.trilinos.org/dev/packages/intrepid2/src/Orientation/Intrepid2_OrientationToolsDefCoeffMatrix_HVOL.hpp
http://docs.trilinos.org/dev/packages/intrepid2/src/Orientation/Intrepid2_OrientationToolsDefModifyPoints.hpp

Public Member Functions

Static Public Member Functions

Detailed Description

Member Function Documentation