Intrepid2::RefSubcellParametrization< DeviceType > Class Template Reference

This class defines the parametrizations of edges and faces of supported reference cells. The parametrization mappings are stored in static Kokkos views. The class is templated on the Kokkos::Device Type which is used to determine layout and memory space of the views. More...

#include <Intrepid2_CellData.hpp>

Public Types
using	ConstViewType = Kokkos::DynRankView< const double, DeviceType >

Public Member Functions
	RefSubcellParametrization ()=default
	Default constructor.
	~RefSubcellParametrization ()=default
	Destructor.

Static Public Member Functions
static bool	isSupported (const unsigned cellTopoKey)
	Checks if a cell topology has a reference parametrization. More...
static ConstViewType	get (const ordinal_type subcellDim, const unsigned parentCellKey)
	Returns a Kokkos view with the coefficients of the parametrization maps for the edges or faces of a reference cell topology. More...

Private Types
using	ViewType = Kokkos::DynRankView< double, DeviceType >
	static views containing the parametrization maps, allocated on DeviceType::memory_space

Static Private Member Functions
static void	set ()
	Computes and stores static views containing the parametrizations maps of edges and faces of all reference cells.
template<typename HostViewType >
static void	set (HostViewType subcellParam, const ordinal_type subcellDim, const shards::CellTopology parentCell)
	Sets parametrizations of reference edges and faces of cell topologies with reference cells. Used to populate Host views from array data. More...

Static Private Attributes
static ViewType	lineEdgesParam
static ViewType	triEdgesParam
static ViewType	quadEdgesParam
static ViewType	shellTriEdgesParam
static ViewType	shellQuadEdgesParam
static ViewType	tetEdgesParam
static ViewType	hexEdgesParam
static ViewType	pyrEdgesParam
static ViewType	wedgeEdgesParam
static ViewType	shellTriFacesParam
static ViewType	shellQuadFacesParam
static ViewType	tetFacesParam
static ViewType	hexFacesParam
static ViewType	pyrFacesParam
static ViewType	wedgeFacesParam
static bool	isSubcellParametrizationSet_ = false
	whether the parametrizations have been already computed using the method set()

Detailed Description

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

This class defines the parametrizations of edges and faces of supported reference cells. The parametrization mappings are stored in static Kokkos views. The class is templated on the Kokkos::Device Type which is used to determine layout and memory space of the views.

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.

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 Intrepid2 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 111 of file Intrepid2_CellData.hpp.

Member Function Documentation

template<typename DeviceType >

RefSubcellParametrization< DeviceType >::ConstViewType Intrepid2::RefSubcellParametrization< DeviceType >::get ( const ordinal_type  subcellDim, const unsigned  parentCellKey  )

inlinestatic

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

See Intrepid2::RefSubcellParametrization class description for details about parametrization maps.

Parameters

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

Returns

a rank-3 Kokkos::View containing coefficients of the parameterization map for all subcells of the specified dimension. Returned view has dimensions (# subcells, parentCellDim, subcellDim+1)

Definition at line 103 of file Intrepid2_CellDataDef.hpp.

Referenced by Intrepid2::ProjectionStruct< DeviceType, ValueType >::createHCurlProjectionStruct(), Intrepid2::ProjectionStruct< DeviceType, ValueType >::createHDivProjectionStruct(), Intrepid2::ProjectionStruct< DeviceType, ValueType >::createHGradProjectionStruct(), Intrepid2::ProjectionStruct< DeviceType, ValueType >::createL2ProjectionStruct(), Intrepid2::Impl::OrientationTools::getCoeffMatrix_HDIV(), Intrepid2::Impl::OrientationTools::getCoeffMatrix_HGRAD(), Intrepid2::ProjectionTools< DeviceType >::getHCurlBasisCoeffs(), Intrepid2::ProjectionTools< DeviceType >::getHGradBasisCoeffs(), Intrepid2::LagrangianTools< DeviceType >::getOrientedDofCoords(), Intrepid2::CellTools< DeviceType >::getPhysicalEdgeTangents(), Intrepid2::CellTools< DeviceType >::getPhysicalFaceTangents(), Intrepid2::CellTools< DeviceType >::getReferenceEdgeTangent(), and Intrepid2::CellTools< DeviceType >::getReferenceFaceTangents().

template<typename DeviceType >

bool Intrepid2::RefSubcellParametrization< DeviceType >::isSupported ( const unsigned  cellTopoKey )

inlinestatic

Checks if a cell topology has a reference parametrization.

Parameters

cellTopoKey

[in] - key of the cell topology

Returns

true if the cell topology has a cell parametrization, false otherwise

Definition at line 61 of file Intrepid2_CellDataDef.hpp.

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

template<typename DeviceType >

template<typename HostViewType >

void Intrepid2::RefSubcellParametrization< DeviceType >::set ( HostViewType  subcellParam, const ordinal_type  subcellDim, const shards::CellTopology  parentCell  )

staticprivate

Sets parametrizations of reference edges and faces of cell topologies with reference cells. Used to populate Host views from array data.

See Intrepid2::RefSubcellParametrization::set() for more info about parametrization maps.

Parameters

subcellParam	[out] - host view 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 278 of file Intrepid2_CellDataDef.hpp.

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

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

• http://docs.trilinos.org/dev/packages/intrepid2/src/Cell/Intrepid2_CellData.hpp
• http://docs.trilinos.org/dev/packages/intrepid2/src/Cell/Intrepid2_CellDataDef.hpp