Basis defining integrated Legendre basis on the line, a polynomial subspace of H(grad) on the line. More...

#include <Intrepid2_IntegratedLegendreBasis_HGRAD_LINE.hpp>

Inheritance diagram for Intrepid2::IntegratedLegendreBasis_HGRAD_LINE< ExecutionSpace, OutputScalar, PointScalar, defineVertexFunctions, useMinusOneToOneReferenceElement >:

Public Types
using	OrdinalTypeArray1DHost = typename Basis< ExecutionSpace, OutputScalar, PointScalar >::OrdinalTypeArray1DHost

using	OrdinalTypeArray2DHost = typename Basis< ExecutionSpace, OutputScalar, PointScalar >::OrdinalTypeArray2DHost

typedef Basis< ExecutionSpace, OutputScalar, PointScalar > ::OutputViewType	OutputViewType

typedef Basis< ExecutionSpace, OutputScalar, PointScalar > ::PointViewType	PointViewType

typedef Basis< ExecutionSpace, OutputScalar, PointScalar > ::ScalarViewType	ScalarViewType

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

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

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

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

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

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

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

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

using	OrdinalTypeArray3DHost = Kokkos::View< ordinal_type ***, typename 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 *, ExecutionSpace >
	View type for 1d device array.

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

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

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

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

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

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

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

Public Member Functions
	IntegratedLegendreBasis_HGRAD_LINE (int polyOrder)
	Constructor. More...

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

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

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

Public Member Functions inherited from Intrepid2::Basis< ExecutionSpace, OutputScalar, PointScalar >
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.

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
int	polyOrder_

bool	defineVertexFunctions_

Protected Attributes inherited from Intrepid2::Basis< ExecutionSpace, OutputScalar, PointScalar >
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, ExecutionSpace >	dofCoords_
	Coordinates of degrees-of-freedom for basis functions defined in physical space.

Kokkos::DynRankView < scalarType, 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< ExecutionSpace, OutputScalar, PointScalar >
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 ExecutionSpace = Kokkos::DefaultExecutionSpace, typename OutputScalar = double, typename PointScalar = double, bool defineVertexFunctions = true, bool useMinusOneToOneReferenceElement = true>
class Intrepid2::IntegratedLegendreBasis_HGRAD_LINE< ExecutionSpace, OutputScalar, PointScalar, defineVertexFunctions, useMinusOneToOneReferenceElement >

Basis defining integrated Legendre basis on the line, a polynomial subspace of H(grad) on the line.

This is used in the construction of hierarchical bases on higher-dimensional topologies. For mathematical details of the construction, see:

Federico Fuentes, Brendan Keith, Leszek Demkowicz, Sriram Nagaraj. "Orientation embedded high order shape functions for the exact sequence elements of all shapes." Computers & Mathematics with Applications, Volume 70, Issue 4, 2015, Pages 353-458, ISSN 0898-1221. https://doi.org/10.1016/j.camwa.2015.04.027.

Note that the template argument defineVertexFunctions controls whether this basis is defined in a strictly hierarchical way. If defineVertexFunctions is false, then the first basis function is the constant 1.0, and this basis will be suitable for discontinuous discretizations. If defineVertexFunctions is true, then the first basis function will instead be 1.0-x, and the basis will be suitable for continuous discretizations.

Definition at line 235 of file Intrepid2_IntegratedLegendreBasis_HGRAD_LINE.hpp.

Constructor & Destructor Documentation

template<typename ExecutionSpace = Kokkos::DefaultExecutionSpace, typename OutputScalar = double, typename PointScalar = double, bool defineVertexFunctions = true, bool useMinusOneToOneReferenceElement = true>

Intrepid2::IntegratedLegendreBasis_HGRAD_LINE< ExecutionSpace, OutputScalar, PointScalar, defineVertexFunctions, useMinusOneToOneReferenceElement >::IntegratedLegendreBasis_HGRAD_LINE ( int polyOrder )

inline

Constructor.

Parameters

[in] polyOrder - the polynomial order of the basis.

The basis will have polyOrder + 1 members.

If defineVertexFunctions is false, then all basis functions are identified with the interior of the line element, and the first two basis functions are 1 and x.

If defineVertexFunctions is true, then the first two basis functions are 1-x and x, and these are identified with the left and right vertices of the cell.

Definition at line 259 of file Intrepid2_IntegratedLegendreBasis_HGRAD_LINE.hpp.

Member Function Documentation

template<typename ExecutionSpace = Kokkos::DefaultExecutionSpace, typename OutputScalar = double, typename PointScalar = double, bool defineVertexFunctions = true, bool useMinusOneToOneReferenceElement = true>

const char* Intrepid2::IntegratedLegendreBasis_HGRAD_LINE< ExecutionSpace, OutputScalar, PointScalar, defineVertexFunctions, useMinusOneToOneReferenceElement >::getName ( ) const

inlineoverridevirtual

Returns basis name.

Returns: the name of the basis

Reimplemented from Intrepid2::Basis< ExecutionSpace, OutputScalar, PointScalar >.

Definition at line 345 of file Intrepid2_IntegratedLegendreBasis_HGRAD_LINE.hpp.

template<typename ExecutionSpace = Kokkos::DefaultExecutionSpace, typename OutputScalar = double, typename PointScalar = double, bool defineVertexFunctions = true, bool useMinusOneToOneReferenceElement = true>

virtual void Intrepid2::IntegratedLegendreBasis_HGRAD_LINE< ExecutionSpace, OutputScalar, PointScalar, defineVertexFunctions, useMinusOneToOneReferenceElement >::getValues	(	OutputViewType	outputValues,
		const PointViewType	inputPoints,
		const EOperator	operatorType = `OPERATOR_VALUE`
	)		const

inlineoverridevirtual

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 378 of file Intrepid2_IntegratedLegendreBasis_HGRAD_LINE.hpp.

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

http://docs.trilinos.org/r13.0/packages/intrepid2/src/Discretization/Basis/Intrepid2_IntegratedLegendreBasis_HGRAD_LINE.hpp

Public Types

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation