Implementation of the default H(grad)-compatible Lagrange basis of arbitrary degree on Tetrahedron cell. More...

#include <Intrepid2_HGRAD_TET_Cn_FEM.hpp>

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

Public Types
typedef Basis< ExecSpaceType, outputValueType, pointValueType > ::ordinal_type_array_1d_host	ordinal_type_array_1d_host

typedef Basis< ExecSpaceType, outputValueType, pointValueType > ::ordinal_type_array_2d_host	ordinal_type_array_2d_host

typedef Basis< ExecSpaceType, outputValueType, pointValueType > ::ordinal_type_array_3d_host	ordinal_type_array_3d_host

typedef Basis< ExecSpaceType, outputValueType, pointValueType > ::outputViewType	outputViewType

typedef Basis< ExecSpaceType, outputValueType, pointValueType > ::pointViewType	pointViewType

typedef Basis< ExecSpaceType, outputValueType, pointValueType > ::scalarViewType	scalarViewType

typedef Basis< ExecSpaceType, outputValueType, pointValueType >::scalarType	scalarType

Public Types inherited from Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >
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
	Basis_HGRAD_TET_Cn_FEM (const ordinal_type order, const EPointType pointType=POINTTYPE_EQUISPACED)
	Constructor.

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

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

virtual void	getDofCoeffs (scalarViewType dofCoeffs) 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...

void	getVandermondeInverse (scalarViewType vinv) const

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

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

Kokkos::DynRankView< typename scalarViewType::const_value_type, ExecSpaceType >	getVandermondeInverse () const

ordinal_type	getWorkSizePerPoint (const EOperator operatorType) const

Public Member Functions inherited from Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >
outputValueType	getDummyOutputValue ()
	Dummy array to receive input arguments.

pointValueType	getDummyPointValue ()
	Dummy array to receive input arguments.

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

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...

Private Attributes
Kokkos::DynRankView < scalarType, ExecSpaceType >	vinv_
	inverse of Generalized Vandermonde matrix, whose columns store the expansion coefficients of the nodal basis in terms of phis_

Additional Inherited Members
Protected Member Functions inherited from Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >
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 inherited from Intrepid2::Basis< ExecSpaceType, outputValueType, 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.

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_HGRAD_TET_Cn_FEM< ExecSpaceType, outputValueType, pointValueType >

Implementation of the default H(grad)-compatible Lagrange basis of arbitrary degree on Tetrahedron cell.

Implements Lagrangian basis of degree n on the reference Tetrahedron cell. The basis has cardinality (n+1)(n+2)(n+3)/6 and spans a COMPLETE polynomial space of degree n. Nodal basis functions are dual to a unisolvent set of degrees-of-freedom (DoF) defined at a lattice of order n (see PointTools). In particular, the degrees of freedom are point evaluation at

The vertices
(n-1) points on each edge of the tetrahedron
max((n-1)(n-2)/2,0) points on each face of the tetrahedron
max((n-1)(n-2)(n-3)/6,0) points in the interior of the tetrahedron.

The distribution of these points is specified by the pointType argument to the class constructor. Currently, either equispaced lattice points or Warburton's warp-blend points are available.

The dof are enumerated according to the ordering on the lattice (see PointTools). In particular, dof number 0 is at the vertex (0,0,0). The dof increase along the lattice with points along the lines of constant x adjacent in the enumeration.

Definition at line 186 of file Intrepid2_HGRAD_TET_Cn_FEM.hpp.

Member Function Documentation

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

virtual void Intrepid2::Basis_HGRAD_TET_Cn_FEM< 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)

Reimplemented from Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >.

Definition at line 254 of file Intrepid2_HGRAD_TET_Cn_FEM.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getCardinality().

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

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

inlinevirtual

Returns basis name.

Returns: the name of the basis

Reimplemented from Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >.

Definition at line 275 of file Intrepid2_HGRAD_TET_Cn_FEM.hpp.

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

virtual void Intrepid2::Basis_HGRAD_TET_Cn_FEM< 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.

Reimplemented from Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >.

Definition at line 217 of file Intrepid2_HGRAD_TET_Cn_FEM.hpp.

References Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getBaseCellTopology(), Intrepid2::Basis< ExecSpaceType, outputValueType, pointValueType >::getCardinality(), Intrepid2::Parameters::MaxNumPtsPerBasisEval, and Intrepid2::Basis_HGRAD_TET_Cn_FEM< ExecSpaceType, outputValueType, pointValueType >::vinv_.

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

http://docs.trilinos.org/r12.16/packages/intrepid2/src/Discretization/Basis/Intrepid2_HGRAD_TET_Cn_FEM.hpp
http://docs.trilinos.org/r12.16/packages/intrepid2/src/Discretization/Basis/Intrepid2_HGRAD_TET_Cn_FEMDef.hpp

Public Types

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

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

Member Function Documentation

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