An abstract base class that defines interface for concrete basis implementations for Finite Element (FEM) and Finite Volume/Finite Difference (FVD) discrete spaces. More...

#include <Intrepid2_Basis.hpp>

Inheritance diagram for Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >:

Public Types
typedef Kokkos::View < ordinal_type, ExecSpaceType >	ordinal_view_type
	View type for ordinal.

typedef Kokkos::View< EBasis, ExecSpaceType >	ebasis_view_type
	View for basis type.

typedef Kokkos::View < ECoordinates, ExecSpaceType >	ecoordinates_view_type
	View for coordinate system type.

typedef Kokkos::View < ordinal_type *,typename ExecSpaceType::array_layout, Kokkos::HostSpace >	ordinal_type_array_1d_host
	View type for 1d host array.

typedef Kokkos::View < ordinal_type **,typename ExecSpaceType::array_layout, Kokkos::HostSpace >	ordinal_type_array_2d_host
	View type for 2d host array.

typedef Kokkos::View < ordinal_type ***, typename ExecSpaceType::array_layout, Kokkos::HostSpace >	ordinal_type_array_3d_host
	View type for 3d host array.

typedef Kokkos::View < ordinal_type *, Kokkos::LayoutStride, Kokkos::HostSpace >	ordinal_type_array_stride_1d_host
	View type for 1d host array.

typedef Kokkos::View < ordinal_type *,ExecSpaceType >	ordinal_type_array_1d
	View type for 1d device array.

typedef Kokkos::View < ordinal_type **,ExecSpaceType >	ordinal_type_array_2d
	View type for 2d device array.

typedef Kokkos::View < ordinal_type ***, ExecSpaceType >	ordinal_type_array_3d
	View type for 3d device array.

typedef Kokkos::View < ordinal_type *, Kokkos::LayoutStride, ExecSpaceType >	ordinal_type_array_stride_1d
	View type for 1d device array.

typedef ScalarTraits < pointValueType > ::scalar_type	scalarType
	Scalar type for point values.

typedef Kokkos::DynRankView < outputValueType, Kokkos::LayoutStride, ExecSpaceType >	outputViewType
	View type for basis value output.

typedef Kokkos::DynRankView < pointValueType, Kokkos::LayoutStride, ExecSpaceType >	pointViewType
	View type for input points.

typedef Kokkos::DynRankView < scalarType, Kokkos::LayoutStride, ExecSpaceType >	scalarViewType
	View type for scalars.

Public Member Functions
outputValueType	getDummyOutputValue ()
	Dummy array to receive input arguments.

pointValueType	getDummyPointValue ()
	Dummy array to receive input arguments.

virtual void	getValues (outputViewType, const pointViewType, const EOperator=OPERATOR_VALUE) const
	Evaluation of a FEM basis on a reference cell. More...

virtual void	getValues (outputViewType, const pointViewType, const pointViewType, const EOperator=OPERATOR_VALUE) const
	Evaluation of an FVD basis evaluation on a physical cell. More...

virtual void	getDofCoords (scalarViewType) const
	Returns spatial locations (coordinates) of degrees of freedom on the reference cell.

virtual void	getDofCoeffs (scalarViewType) const
	Coefficients for computing degrees of freedom for Lagrangian basis If P is an element of the space spanned by the basis, := P(dofCoords(i)) dofCoeffs(i) are the nodal coefficients associated to basis function i. More...

virtual const char *	getName () const
	Returns basis name. More...

virtual bool	requireOrientation () const
	True if orientation is required.

ordinal_type	getCardinality () const
	Returns cardinality of the basis. More...

ordinal_type	getDegree () const
	Returns the degree of the basis. More...

shards::CellTopology	getBaseCellTopology () const
	Returns the base cell topology for which the basis is defined. See Shards documentation https://trilinos.org/packages/shards for definition of base cell topology. More...

EBasis	getBasisType () const
	Returns the basis type. More...

ECoordinates	getCoordinateSystem () const
	Returns the type of coordinate system for which the basis is defined. More...

ordinal_type	getDofCount (const ordinal_type subcDim, const ordinal_type subcOrd) const
	DoF count for specified subcell. More...

ordinal_type	getDofOrdinal (const ordinal_type subcDim, const ordinal_type subcOrd, const ordinal_type subcDofOrd) const
	DoF tag to ordinal lookup. More...

const ordinal_type_array_3d_host	getAllDofOrdinal () const
	DoF tag to ordinal data structure.

const ordinal_type_array_stride_1d_host	getDofTag (const ordinal_type dofOrd) const
	DoF ordinal to DoF tag lookup. More...

const ordinal_type_array_2d_host	getAllDofTags () const
	Retrieves all DoF tags. More...

Protected Member Functions
template<typename OrdinalTypeView3D , typename OrdinalTypeView2D , typename OrdinalTypeView1D >
void	setOrdinalTagData (OrdinalTypeView3D &tagToOrdinal, OrdinalTypeView2D &ordinalToTag, const OrdinalTypeView1D tags, const ordinal_type basisCard, const ordinal_type tagSize, const ordinal_type posScDim, const ordinal_type posScOrd, const ordinal_type posDfOrd)
	Fills ordinalToTag_ and tagToOrdinal_ by basis-specific tag data. More...

Protected Attributes
ordinal_type	basisCardinality_
	Cardinality of the basis, i.e., the number of basis functions/degrees-of-freedom.

ordinal_type	basisDegree_
	Degree of the largest complete polynomial space that can be represented by the basis.

shards::CellTopology	basisCellTopology_
	Base topology of the cells for which the basis is defined. See the Shards package for definition of base cell topology.

EBasis	basisType_
	Type of the basis.

ECoordinates	basisCoordinates_
	The coordinate system for which the basis is defined.

ordinal_type_array_2d_host	ordinalToTag_
	"true" if tagToOrdinal_ and ordinalToTag_ have been initialized More...

ordinal_type_array_3d_host	tagToOrdinal_
	DoF tag to ordinal lookup table. More...

Kokkos::DynRankView < scalarType, ExecSpaceType >	dofCoords_
	Coordinates of degrees-of-freedom for basis functions defined in physical space.

Kokkos::DynRankView < scalarType, ExecSpaceType >	dofCoeffs_
	Coefficients for computing degrees of freedom for Lagrangian basis If P is an element of the space spanned by the basis, := P(dofCoords_(i)) dofCoeffs_(i) are the nodal coefficients associated to basis functions i. More...

Detailed Description

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>
class Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >

An abstract base class that defines interface for concrete basis implementations for Finite Element (FEM) and Finite Volume/Finite Difference (FVD) discrete spaces.

    A FEM basis spans a discrete space whose type can be either COMPLETE or INCOMPLETE.
    FEM basis functions are always defined on a reference cell and are dual to a unisolvent
    set of degrees-of-freedom (DoF). FEM basis requires cell topology with a reference cell.

    An FVD basis spans a discrete space whose type is typically BROKEN. The basis functions
    are defined directly on the physical cell and are dual to a set of DoFs on that cell.
    As a result, FVD bases require the vertex coordinates of the physical cell but the cell
    itself is not required to have a reference cell.

    Every DoF and its corresponding basis function from a given FEM or FVD basis set is
    assigned an ordinal number which which specifies its numerical position in the DoF set,
    and a 4-field DoF tag whose first 3 fields establish association between the DoF and a
    subcell of particular dimension, and the last field gives the total number of basis
    functions associated with that subcell; see Section \ref basis_dof_tag_ord_sec for details.

Remarks: To limit memory use by factory-type objects (basis factories will be included in future releases of Intrepid2), tag data is not initialized by basis ctors, instead, whenever a function that requires tag data is invoked for a first time, it calls initializeTags() to fill ordinalToTag_ and tagToOrdinal_. Because tag data is basis specific, every concrete basis class requires its own implementation of initializeTags().

Todo:: restore test for inclusion of reference points in their resective reference cells in getValues_HGRAD_Args, getValues_CURL_Args, getValues_DIV_Args

Definition at line 93 of file Intrepid2_Basis.hpp.

Member Function Documentation

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

const ordinal_type_array_2d_host Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getAllDofTags ( ) const

inline

Retrieves all DoF tags.

Returns

reference to a vector of vectors with dimensions (basisCardinality_, 4) such that

element [DofOrd][0] = tag field 0 for the DoF with the specified ordinal
element [DofOrd][1] = tag field 1 for the DoF with the specified ordinal
element [DofOrd][2] = tag field 2 for the DoF with the specified ordinal
element [DofOrd][3] = tag field 3 for the DoF with the specified ordinal

Definition at line 550 of file Intrepid2_Basis.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::ordinalToTag_.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

shards::CellTopology Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getBaseCellTopology ( ) const

inline

Returns the base cell topology for which the basis is defined. See Shards documentation https://trilinos.org/packages/shards for definition of base cell topology.

Returns: Base cell topology

Definition at line 432 of file Intrepid2_Basis.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::basisCellTopology_.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

EBasis Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getBasisType ( ) const

inline

Returns the basis type.

Returns: Basis type

Definition at line 442 of file Intrepid2_Basis.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::basisType_.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

ordinal_type Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getCardinality ( ) const

inline

Returns cardinality of the basis.

Returns: the number of basis functions in the basis

Definition at line 411 of file Intrepid2_Basis.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::basisCardinality_.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

ECoordinates Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getCoordinateSystem ( ) const

inline

Returns the type of coordinate system for which the basis is defined.

Returns: Type of the coordinate system (Cartesian, polar, R-Z, etc.).

Definition at line 452 of file Intrepid2_Basis.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::basisCoordinates_.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

ordinal_type Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getDegree ( ) const

inline

Returns the degree of the basis.

Returns: max. degree of the complete polynomials that can be represented by the basis.

Definition at line 421 of file Intrepid2_Basis.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::basisDegree_.

Referenced by Intrepid2::Basis_HGRAD_TET_Cn_FEM_ORTH< ExecSpaceType, outputValueType, pointValueType >::getValues(), Intrepid2::Basis_HGRAD_TRI_Cn_FEM_ORTH< ExecSpaceType, outputValueType, pointValueType >::getValues(), and Intrepid2::Basis_HGRAD_LINE_Cn_FEM_JACOBI< ExecSpaceType, outputValueType, pointValueType >::getValues().

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

virtual void Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getDofCoeffs ( scalarViewType ) const

inlinevirtual

Coefficients for computing degrees of freedom for Lagrangian basis If P is an element of the space spanned by the basis, := P(dofCoords(i)) dofCoeffs(i) are the nodal coefficients associated to basis function i.

Rank-1 array for scalar basis with dimension (cardinality) Rank-2 array for vector basis with dimensions (cardinality, cell dimension)

Definition at line 382 of file Intrepid2_Basis.hpp.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

ordinal_type Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getDofCount	(	const ordinal_type	subcDim,
		const ordinal_type	subcOrd
	)		const

inline

DoF count for specified subcell.

Parameters

subcDim	[in] - tag field 0: dimension of the subcell associated with the DoFs
subcOrd	[in] - tag field 1: ordinal of the subcell defined by cell topology

Returns: the number of DoFs associated with the specified subcell.

Definition at line 464 of file Intrepid2_Basis.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getDofTag(), and Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::tagToOrdinal_.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

ordinal_type Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getDofOrdinal	(	const ordinal_type	subcDim,
		const ordinal_type	subcOrd,
		const ordinal_type	subcDofOrd
	)		const

inline

DoF tag to ordinal lookup.

Parameters

subcDim	[in] - tag field 0: dimension of the subcell associated with the DoF
subcOrd	[in] - tag field 1: ordinal of the subcell defined by cell topology
subcDofOrd	[in] - tag field 2: ordinal of the DoF relative to the subcell.

Returns: the DoF ordinal corresponding to the specified DoF tag data.

Definition at line 490 of file Intrepid2_Basis.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::tagToOrdinal_.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

const ordinal_type_array_stride_1d_host Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getDofTag ( const ordinal_type dofOrd ) const

inline

DoF ordinal to DoF tag lookup.

Parameters

dofOrd [in] - ordinal of the DoF whose tag is being retrieved

Returns

reference to a vector with dimension (4) such that

element [0] = tag field 0 -> dim. of the subcell associated with the specified DoF
element [1] = tag field 1 -> ordinal of the subcell defined by cell topology
element [2] = tag field 2 -> ordinal of the specified DoF relative to the subcell
element [3] = tag field 3 -> total number of DoFs associated with the subcell

Definition at line 532 of file Intrepid2_Basis.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::ordinalToTag_.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

virtual const char* Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getName ( ) const

inlinevirtual

Returns basis name.

Returns: the name of the basis

Definition at line 394 of file Intrepid2_Basis.hpp.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

virtual void Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getValues	(	outputViewType	,
		const pointViewType	,
		const EOperator	= `OPERATOR_VALUE`
	)		const

inlinevirtual

Evaluation of a FEM basis on a reference cell.

Returns values of operatorType acting on FEM basis functions for a set of points in the reference cell for which the basis is defined.

Parameters

outputValues	[out] - variable rank array with the basis values
inputPoints	[in] - rank-2 array (P,D) with the evaluation points
operatorType	[in] - the operator acting on the basis functions

Remarks: For rank and dimension specifications of the output array see Section MD array template arguments for basis methods. Dimensions of ArrayScalar arguments are checked at runtime if HAVE_INTREPID2_DEBUG is defined.; A FEM basis spans a COMPLETE or INCOMPLETE polynomial space on the reference cell which is a smooth function space. Thus, all operator types that are meaningful for the approximated function space are admissible. When the order of the operator exceeds the degree of the basis, the output array is filled with the appropriate number of zeros.

Definition at line 325 of file Intrepid2_Basis.hpp.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

virtual void Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getValues	(	outputViewType	,
		const pointViewType	,
		const pointViewType	,
		const EOperator	= `OPERATOR_VALUE`
	)		const

inlinevirtual

Evaluation of an FVD basis evaluation on a physical cell.

Returns values of operatorType acting on FVD basis functions for a set of points in the physical cell for which the FVD basis is defined.

Parameters

outputValues	[out] - variable rank array with the basis values
inputPoints	[in] - rank-2 array (P,D) with the evaluation points
cellVertices	[in] - rank-2 array (V,D) with the vertices of the physical cell
operatorType	[in] - the operator acting on the basis functions

Remarks: For rank and dimension specifications of the output array see Section MD array template arguments for basis methods. Dimensions of ArrayScalar arguments are checked at runtime if HAVE_INTREPID2_DEBUG is defined.; A typical FVD basis spans a BROKEN discrete space which is only piecewise smooth. For example, it could be a piecewise constant space defined with respect to a partition of the cell into simplices. Because differential operators are not meaningful for such spaces, the default operator type in this method is set to OPERATOR_VALUE.

Definition at line 353 of file Intrepid2_Basis.hpp.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

template<typename OrdinalTypeView3D , typename OrdinalTypeView2D , typename OrdinalTypeView1D >

void Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::setOrdinalTagData	(	OrdinalTypeView3D &	tagToOrdinal,
		OrdinalTypeView2D &	ordinalToTag,
		const OrdinalTypeView1D	tags,
		const ordinal_type	basisCard,
		const ordinal_type	tagSize,
		const ordinal_type	posScDim,
		const ordinal_type	posScOrd,
		const ordinal_type	posDfOrd
	)

inlineprotected

Fills ordinalToTag_ and tagToOrdinal_ by basis-specific tag data.

Parameters

tagToOrdinal	[out] - Lookup table for the DoF's ordinal by its tag
ordinalToTag	[out] - Lookup table for the DoF's tag by its ordinal
tags	[in] - a set of basis-dependent tags in flat (rank-1) array format.
basisCard	[in] - cardinality of the basis
tagSize	[in] - number of fields in a DoF tag
posScDim	[in] - position in the tag, counting from 0, of the subcell dim
posScOrd	[in] - position in the tag, counting from 0, of the subcell ordinal
posDfOrd	[in] - position in the tag, counting from 0, of DoF ordinal relative to the subcell

Definition at line 215 of file Intrepid2_Basis.hpp.

Member Data Documentation

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

Kokkos::DynRankView<scalarType,ExecSpaceType> Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::dofCoeffs_

protected

Coefficients for computing degrees of freedom for Lagrangian basis If P is an element of the space spanned by the basis, := P(dofCoords_(i)) dofCoeffs_(i) are the nodal coefficients associated to basis functions i.

Rank-1 array for scalar basis with dimension (cardinality) Rank-2 array for vector basis with dimensions (cardinality, cell dimension)

Definition at line 277 of file Intrepid2_Basis.hpp.

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

ordinal_type_array_2d_host Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::ordinalToTag_

protected

"true" if tagToOrdinal_ and ordinalToTag_ have been initialized

DoF ordinal to tag lookup table.

Rank-2 array with dimensions (basisCardinality_, 4) containing the DoF tags. This array is left empty at instantiation and filled by initializeTags() only when tag data is requested.

ordinalToTag_[DofOrd][0] = dim. of the subcell associated with the specified DoF
ordinalToTag_[DofOrd][1] = ordinal of the subcell defined in the cell topology
ordinalToTag_[DodOrd][2] = ordinal of the specified DoF relative to the subcell
ordinalToTag_[DofOrd][3] = total number of DoFs associated with the subcell

Definition at line 186 of file Intrepid2_Basis.hpp.

Referenced by Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getAllDofTags(), and Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getDofTag().

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>

ordinal_type_array_3d_host Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::tagToOrdinal_

protected

DoF tag to ordinal lookup table.

Rank-3 array with dimensions (maxScDim + 1, maxScOrd + 1, maxDfOrd + 1), i.e., the columnwise maximums of the 1st three columns in the DoF tag table for the basis plus 1. For every triple (subscDim, subcOrd, subcDofOrd) that is valid DoF tag data this array stores the corresponding DoF ordinal. If the triple does not correspond to tag data, the array stores -1. This array is left empty at instantiation and filled by initializeTags() only when tag data is requested.

tagToOrdinal_[subcDim][subcOrd][subcDofOrd] = Degree-of-freedom ordinal

Definition at line 199 of file Intrepid2_Basis.hpp.

Referenced by Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getAllDofOrdinal(), Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getDofCount(), and Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getDofOrdinal().

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

http://docs.trilinos.org/r12.16/packages/intrepid2/src/Discretization/Basis/Intrepid2_Basis.hpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double> class Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >

Member Function Documentation

Member Data Documentation

template<typename ExecSpaceType = void, typename outputValueType = double, typename pointValueType = double>
class Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >