Basis defined as the tensor product of two component bases. More...

#include <Intrepid2_TensorBasis.hpp>

Inheritance diagram for Intrepid2::Basis_TensorBasis< Basis1, Basis2 >:

Public Types
using	BasisSuper = ::Intrepid2::Basis< typename Basis1::ExecutionSpace, typename Basis1::OutputValueType, typename Basis1::PointValueType >

using	ExecutionSpace = typename BasisSuper::ExecutionSpace

using	OutputValueType = typename BasisSuper::OutputValueType

using	PointValueType = typename BasisSuper::PointValueType

using	OrdinalTypeArray1DHost = typename BasisSuper::OrdinalTypeArray1DHost

using	OrdinalTypeArray2DHost = typename BasisSuper::OrdinalTypeArray2DHost

using	OutputViewType = typename BasisSuper::OutputViewType

using	PointViewType = typename BasisSuper::PointViewType

Public Types inherited from Intrepid2::Basis< Basis1::ExecutionSpace, Basis1::OutputValueType, Basis1::PointValueType >
using	ExecutionSpace = Basis1::ExecutionSpace
	(Kokkos) Execution space for basis.

using	OutputValueType = Basis1::OutputValueType
	Output value type for basis; default is double.

using	PointValueType = Basis1::PointValueType
	Point value type for basis; default is double.

using	OrdinalViewType = Kokkos::View< ordinal_type, Basis1::ExecutionSpace >
	View type for ordinal.

using	EBasisViewType = Kokkos::View< EBasis, Basis1::ExecutionSpace >
	View for basis type.

using	ECoordinatesViewType = Kokkos::View< ECoordinates, Basis1::ExecutionSpace >
	View for coordinate system type.

using	OrdinalTypeArray1DHost = Kokkos::View< ordinal_type *, typename Basis1::ExecutionSpace::array_layout, Kokkos::HostSpace >
	View type for 1d host array.

using	OrdinalTypeArray2DHost = Kokkos::View< ordinal_type **, typename Basis1::ExecutionSpace::array_layout, Kokkos::HostSpace >
	View type for 2d host array.

using	OrdinalTypeArray3DHost = Kokkos::View< ordinal_type ***, typename Basis1::ExecutionSpace::array_layout, Kokkos::HostSpace >
	View type for 3d host array.

using	OrdinalTypeArrayStride1DHost = Kokkos::View< ordinal_type *, Kokkos::LayoutStride, Kokkos::HostSpace >
	View type for 1d host array.

using	OrdinalTypeArray1D = Kokkos::View< ordinal_type *, Basis1::ExecutionSpace >
	View type for 1d device array.

using	OrdinalTypeArray2D = Kokkos::View< ordinal_type **, Basis1::ExecutionSpace >
	View type for 2d device array.

using	OrdinalTypeArray3D = Kokkos::View< ordinal_type ***, Basis1::ExecutionSpace >
	View type for 3d device array.

using	OrdinalTypeArrayStride1D = Kokkos::View< ordinal_type *, Kokkos::LayoutStride, Basis1::ExecutionSpace >
	View type for 1d device array.

typedef ScalarTraits < Basis1::PointValueType > ::scalar_type	scalarType
	Scalar type for point values.

using	OutputViewType = Kokkos::DynRankView< OutputValueType, Kokkos::LayoutStride, Basis1::ExecutionSpace >
	View type for basis value output.

using	PointViewType = Kokkos::DynRankView< PointValueType, Kokkos::LayoutStride, Basis1::ExecutionSpace >
	View type for input points.

using	ScalarViewType = Kokkos::DynRankView< scalarType, Kokkos::LayoutStride, Basis1::ExecutionSpace >
	View type for scalars.

Public Member Functions
	Basis_TensorBasis (Basis1 basis1, Basis2 basis2)
	Constructor. More...

void	getComponentPoints (const PointViewType inputPoints, const bool attemptTensorDecomposition, PointViewType &inputPoints1, PointViewType &inputPoints2, bool &tensorDecompositionSucceeded) const
	Method to extract component points from composite points. More...

virtual void	getDofCoords (typename BasisSuper::ScalarViewType dofCoords) const override
	Fills in spatial locations (coordinates) of degrees of freedom (nodes) on the reference cell. More...

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

ordinal_type	getTensorDkEnumeration (ordinal_type dkEnum1, ordinal_type operatorOrder1, ordinal_type dkEnum2, ordinal_type operatorOrder2) const
	Given "Dk" enumeration indices for the component bases, returns a Dk enumeration index for the composite basis. More...

void	getValues (OutputViewType outputValues, const PointViewType inputPoints, const EOperator operatorType=OPERATOR_VALUE) const override
	Evaluation of a FEM basis on a reference cell. More...

virtual void	getValues (OutputViewType outputValues, const EOperator operatorType, const PointViewType inputPoints1, const PointViewType inputPoints2, bool tensorPoints) const
	Evaluation of a tensor FEM basis on a reference cell; subclasses should override this. More...

void	getValues (OutputViewType outputValues, const PointViewType inputPoints1, const EOperator operatorType1, const PointViewType inputPoints2, const EOperator operatorType2, bool tensorPoints, double weight=1.0) const
	Evaluation of a tensor FEM basis on a reference cell. More...

Public Member Functions inherited from Intrepid2::Basis< Basis1::ExecutionSpace, Basis1::OutputValueType, Basis1::PointValueType >
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...

OrdinalTypeArray1DHost	getFieldOrdinalsForDegree (OrdinalTypeArray1DHost &degrees) const
	For hierarchical bases, returns the field ordinals that have at most the specified degree in each dimension. Assuming that these are less than or equal to the polynomial orders provided at Basis construction, the corresponding polynomials will form a superset of the Basis of the same type constructed with polynomial orders corresponding to the specified degrees. More...

std::vector< int >	getFieldOrdinalsForDegree (std::vector< int > &degrees) const
	For hierarchical bases, returns the field ordinals that have at most the specified degree in each dimension. Assuming that these are less than or equal to the polynomial orders provided at Basis construction, the corresponding polynomials will form a superset of the Basis of the same type constructed with polynomial orders corresponding to the specified degrees. More...

OrdinalTypeArray1DHost	getPolynomialDegreeOfField (int fieldOrdinal) const
	For hierarchical bases, returns the polynomial degree (which may have multiple values in higher spatial dimensions) for the specified basis ordinal as a host array. More...

std::vector< int >	getPolynomialDegreeOfFieldAsVector (int fieldOrdinal) const
	For hierarchical bases, returns the polynomial degree (which may have multiple values in higher spatial dimensions) for the specified basis ordinal as a host array. More...

int	getPolynomialDegreeLength () const
	For hierarchical bases, returns the number of entries required to specify the polynomial degree of a basis function.

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...

EFunctionSpace	getFunctionSpace () const
	Returns the function space for 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 OrdinalTypeArray3DHost	getAllDofOrdinal () const
	DoF tag to ordinal data structure.

const OrdinalTypeArrayStride1DHost	getDofTag (const ordinal_type dofOrd) const
	DoF ordinal to DoF tag lookup. More...

const OrdinalTypeArray2DHost	getAllDofTags () const
	Retrieves all DoF tags. More...

Protected Attributes
Basis1	basis1_

Basis2	basis2_

std::string	name_

Protected Attributes inherited from Intrepid2::Basis< Basis1::ExecutionSpace, Basis1::OutputValueType, Basis1::PointValueType >
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.

EFunctionSpace	functionSpace_
	The function space in which the basis is defined.

OrdinalTypeArray2DHost	ordinalToTag_
	"true" if tagToOrdinal_ and ordinalToTag_ have been initialized More...

OrdinalTypeArray3DHost	tagToOrdinal_
	DoF tag to ordinal lookup table. More...

Kokkos::DynRankView < scalarType, Basis1::ExecutionSpace >	dofCoords_
	Coordinates of degrees-of-freedom for basis functions defined in physical space.

Kokkos::DynRankView < scalarType, Basis1::ExecutionSpace >	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...

OrdinalTypeArray2DHost	fieldOrdinalPolynomialDegree_
	Polynomial degree for each degree of freedom. Only defined for hierarchical bases right now. The number of entries per degree of freedom in this table depends on the basis type. For hypercubes, this will be the spatial dimension. We have not yet determined what this will be for simplices beyond 1D; there are not yet hierarchical simplicial bases beyond 1D in Intrepid2. More...

Additional Inherited Members
Protected Member Functions inherited from Intrepid2::Basis< Basis1::ExecutionSpace, Basis1::OutputValueType, Basis1::PointValueType >
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...

Detailed Description

template<typename Basis1, typename Basis2>
class Intrepid2::Basis_TensorBasis< Basis1, Basis2 >

Basis defined as the tensor product of two component bases.

The cell topology for the tensor basis is the tensor product of the cell topologies on which the component bases are defined;

See Also: Intrepid2::TensorTopologyMap.

The basis is ordered such that the Basis1 field ordinals are the fastest-moving index; the formula for the composite field ordinal is: compositeFieldOrdinal = componentFieldOrdinal2 * basis1Cardinality + componentFieldOrdinal1 This is done so that we can consider, e.g. Basis1 as the "x" dimension and Basis2 as the "y" dimension, and have the basis ordered in the same way that existing Intrepid2 bases on the quadrilateral are ordered, namely, one moves along the x dimension first, moving across the quadrilateral dofs "row-wise".

Definition at line 303 of file Intrepid2_TensorBasis.hpp.

Constructor & Destructor Documentation

template<typename Basis1, typename Basis2>

Intrepid2::Basis_TensorBasis< Basis1, Basis2 >::Basis_TensorBasis	(	Basis1	basis1,
		Basis2	basis2
	)

inline

Constructor.

Parameters

[in]	basis1	- the first component basis
[in]	basis2	- the second component basis

Definition at line 328 of file Intrepid2_TensorBasis.hpp.

Member Function Documentation

template<typename Basis1, typename Basis2>

void Intrepid2::Basis_TensorBasis< Basis1, Basis2 >::getComponentPoints	(	const PointViewType	inputPoints,
		const bool	attemptTensorDecomposition,
		PointViewType &	inputPoints1,
		PointViewType &	inputPoints2,
		bool &	tensorDecompositionSucceeded
	)		const

inline

Method to extract component points from composite points.

Parameters

[in]	inputPoints	- points defined on the composite cell topology
[in]	attemptTensorDecomposition	- if true, attempt to find a tensor decomposition.
[out]	inputPoints1	- points defined on the first component cell topology
[out]	inputPoints2	- points defined on the second component cell topology
[out]	tensorDecompositionSucceeded	- if true, the attempt to find a tensor decomposition succeeded.

At present, attemptTensorDecomposition is ignored, and tensorDecompositionSucceeded will always return false. However, we intend to support the tensor decomposition in the future, which will allow substantial optimizations in computation of tensor bases.

Definition at line 476 of file Intrepid2_TensorBasis.hpp.

Referenced by Intrepid2::Basis_TensorBasis< HVOL_LINE, HGRAD_LINE >::getValues().

template<typename Basis1, typename Basis2>

virtual void Intrepid2::Basis_TensorBasis< Basis1, Basis2 >::getDofCoords ( typename BasisSuper::ScalarViewType dofCoords ) const

inlineoverridevirtual

Fills in spatial locations (coordinates) of degrees of freedom (nodes) on the reference cell.

Parameters

[out] dofCoords - the container into which to place the degrees of freedom.

dofCoords should have shape (F,D), where the field dimension matches the cardinality of the basis, and D is the spatial dimension of the topology on which the basis is defined.

Note that getDofCoords() is not supported by all bases; in particular, hierarchical bases do not generally support this.

Definition at line 520 of file Intrepid2_TensorBasis.hpp.

template<typename Basis1, typename Basis2>

virtual const char* Intrepid2::Basis_TensorBasis< Basis1, Basis2 >::getName ( ) const

inlineoverridevirtual

Returns basis name.

Returns: the name of the basis

Reimplemented from Intrepid2::Basis< Basis1::ExecutionSpace, Basis1::OutputValueType, Basis1::PointValueType >.

Reimplemented in Intrepid2::Basis_Derived_HVOL_HEX< HVOL_LINE >, and Intrepid2::Basis_Derived_HVOL_QUAD< HVOL_LINE >.

Definition at line 562 of file Intrepid2_TensorBasis.hpp.

template<typename Basis1, typename Basis2>

ordinal_type Intrepid2::Basis_TensorBasis< Basis1, Basis2 >::getTensorDkEnumeration	(	ordinal_type	dkEnum1,
		ordinal_type	operatorOrder1,
		ordinal_type	dkEnum2,
		ordinal_type	operatorOrder2
	)		const

inline

Given "Dk" enumeration indices for the component bases, returns a Dk enumeration index for the composite basis.

Parameters

[in]	dkEnum1	- Dk enumeration index for first component basis
[in]	operatorOrder1	- operator order for the first component basis
[in]	dkEnum2	- Dk enumeration index for second component basis
[in]	operatorOrder2	- operator order for the second component basis

Returns: Dk enumeration index for the composite basis, corresponding to operator order operatorOrder1 + operatorOrder2.

Definition at line 574 of file Intrepid2_TensorBasis.hpp.

Referenced by Intrepid2::Basis_TensorBasis< HVOL_LINE, HGRAD_LINE >::getValues().

template<typename Basis1, typename Basis2>

void Intrepid2::Basis_TensorBasis< Basis1, Basis2 >::getValues	(	OutputViewType	outputValues,
		const PointViewType	inputPoints,
		const EOperator	operatorType = `OPERATOR_VALUE`
	)		const

inlineoverride

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 637 of file Intrepid2_TensorBasis.hpp.

template<typename Basis1, typename Basis2>

virtual void Intrepid2::Basis_TensorBasis< Basis1, Basis2 >::getValues	(	OutputViewType	outputValues,
		const EOperator	operatorType,
		const PointViewType	inputPoints1,
		const PointViewType	inputPoints2,
		bool	tensorPoints
	)		const

inlinevirtual

Evaluation of a tensor FEM basis on a reference cell; subclasses should override this.

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
operatorType	[in] - the operator acting on the basis functions
inputPoints1	[in] - rank-2 array (P1,D1) with the evaluation points for basis1
inputPoints2	[in] - rank-2 array (P2,D2) with the evaluation points for basis2
tensorPoints	[in] - whether the points should be interpreted as tensor components of the evaluation points, or in a one-to-one correspondence

Subclasses should override this method; this gives them an opportunity to specify how operatorType should be decomposed into operators on the component bases.

If tensorPoints is true, then the points dimension of outputValues should be (P1*P2). If tensorPoints is false, then P1 should equal P2, and these should match the points dimension of outputValues.

There are three variants of getValues:

The three-argument version defined by Intrepid2::Basis. TensorBasis provides an implementation of this, which calls the five-argument version (this one).
The five-argument version (this method), which provides separate point sets for the component bases, and must be specified by subclasses. Typical implementations call the seven-argument version.
The seven-argument version (below), implemented by TensorBasis, which provides separate point sets and operators for the component bases, as well as an optional weight.

The intent is that subclasses implement this five-argument version; in that implementation, they need to do little else than call the seven-argument version below.

Note that the three-argument implementation handles the OPERATOR_Dn operators directly; that is, subclasses can omit any consideration of OPERATOR_Dn operators in their implementation of the five-argument version.

Reimplemented in Intrepid2::Basis_TensorBasis3< HVOL_LINE, HGRAD_LINE, HGRAD_LINE >, Intrepid2::Basis_TensorBasis3< HVOL_LINE, HVOL_LINE, HGRAD_LINE >, Intrepid2::Basis_TensorBasis3< HGRAD_LINE, HVOL_LINE, HGRAD_LINE >, Intrepid2::Basis_TensorBasis3< HGRAD_LINE, HGRAD_LINE, HVOL_LINE >, Intrepid2::Basis_TensorBasis3< HVOL_LINE, HGRAD_LINE, HVOL_LINE >, and Intrepid2::Basis_TensorBasis3< HGRAD_LINE, HVOL_LINE, HVOL_LINE >.

Definition at line 766 of file Intrepid2_TensorBasis.hpp.

template<typename Basis1, typename Basis2>

void Intrepid2::Basis_TensorBasis< Basis1, Basis2 >::getValues	(	OutputViewType	outputValues,
		const PointViewType	inputPoints1,
		const EOperator	operatorType1,
		const PointViewType	inputPoints2,
		const EOperator	operatorType2,
		bool	tensorPoints,
		double	weight = `1.0`
	)		const

inline

Evaluation of a tensor 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
inputPoints1	[in] - rank-2 array (P1,D1) with the evaluation points for basis1
operatorType1	[in] - the operator acting on basis1
inputPoints2	[in] - rank-2 array (P2,D2) with the evaluation points for basis2
operatorType2	[in] - the operator acting on basis2
tensorPoints	[in] - whether the points should be interpreted as tensor components of the evaluation points, or in a one-to-one correspondence
weight	[in] - optional weight (typically 1.0 or -1.0)

If tensorPoints is true, then the points dimension of outputValues should be (P1*P2). If tensorPoints is false, then P1 should equal P2, and these should match the points dimension of outputValues.

There are three variants of getValues:

The three-argument version defined by Intrepid2::Basis. TensorBasis provides an implementation of this, which calls the five-argument version (this one).
The five-argument version (above), which provides separate point sets for the component bases, and must be specified by subclasses. Typical implementations call the seven-argument version.
The seven-argument version (this method), implemented by TensorBasis, which provides separate point sets and operators for the component bases, as well as an optional weight.

Subclasses should override the five-argument version above; in their implementation, they need to do little else than call this seven-argument version.

Definition at line 796 of file Intrepid2_TensorBasis.hpp.

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

http://docs.trilinos.org/r13.0/packages/intrepid2/src/Discretization/Basis/Intrepid2_TensorBasis.hpp

Public Types

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

template<typename Basis1, typename Basis2> class Intrepid2::Basis_TensorBasis< Basis1, Basis2 >

Constructor & Destructor Documentation

Member Function Documentation

template<typename Basis1, typename Basis2>
class Intrepid2::Basis_TensorBasis< Basis1, Basis2 >