Implementation of the default H(grad)-compatible FEM basis of degree 2 on Wedge cell. More...

#include <Intrepid_HGRAD_WEDGE_C2_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HGRAD_WEDGE_C2_FEM< Scalar, ArrayScalar >:

Public Member Functions
	Basis_HGRAD_WEDGE_C2_FEM ()
	Constructor.
void	getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
	FEM basis evaluation on a reference Wedge cell.
void	getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const ArrayScalar &cellVertices, const EOperator operatorType=OPERATOR_VALUE) const
	FVD basis evaluation: invocation of this method throws an exception.
Public Member Functions inherited from Intrepid::Basis< Scalar, ArrayScalar >
virtual	~Basis ()
	Destructor.
virtual int	getCardinality () const
	Returns cardinality of the basis.
virtual int	getDegree () const
	Returns the degree of the basis.
virtual const shards::CellTopology	getBaseCellTopology () const
	Returns the base cell topology for which the basis is defined. See Shards documentation http://trilinos.sandia.gov/packages/shards for definition of base cell topology.
virtual EBasis	getBasisType () const
	Returns the basis type.
virtual ECoordinates	getCoordinateSystem () const
	Returns the type of coordinate system for which the basis is defined.
virtual int	getDofOrdinal (const int subcDim, const int subcOrd, const int subcDofOrd)
	DoF tag to ordinal lookup.
virtual const std::vector< std::vector< std::vector< int > > > &	getDofOrdinalData ()
	DoF tag to ordinal data structure.
virtual const std::vector< int > &	getDofTag (const int dofOrd)
	DoF ordinal to DoF tag lookup.
virtual const std::vector< std::vector< int > > &	getAllDofTags ()
	Retrieves all DoF tags.

Private Member Functions
void	initializeTags ()
	Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.

Additional Inherited Members
Protected Attributes inherited from Intrepid::Basis< Scalar, ArrayScalar >
int	basisCardinality_
	Cardinality of the basis, i.e., the number of basis functions/degrees-of-freedom.
int	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 http://trilinos.sandia.gov/packages/shards for definition of base cell topology.
EBasis	basisType_
	Type of the basis.
ECoordinates	basisCoordinates_
	The coordinate system for which the basis is defined.
bool	basisTagsAreSet_
	"true" if tagToOrdinal_ and ordinalToTag_ have been initialized
std::vector< std::vector< int > >	ordinalToTag_
	DoF ordinal to tag lookup table.
std::vector< std::vector< std::vector< int > > >	tagToOrdinal_
	DoF tag to ordinal lookup table.

Detailed Description

template<class Scalar, class ArrayScalar>
class Intrepid::Basis_HGRAD_WEDGE_C2_FEM< Scalar, ArrayScalar >

Implementation of the default H(grad)-compatible FEM basis of degree 2 on Wedge cell.

    Implements Lagrangian basis of degree 2 on the reference Wedge cell. The basis has
    cardinality 18 and spans a COMPLETE bi-quadratic polynomial space. Basis functions are dual 
    to a unisolvent set of degrees-of-freedom (DoF) defined and enumerated as follows:

=================================================================================================
|         |           degree-of-freedom-tag table                    |                           |
|   DoF   |----------------------------------------------------------|      DoF definition       |
| ordinal |  subc dim    | subc ordinal | subc DoF ord |subc num DoF |                           |
|=========|==============|==============|==============|=============|===========================|
|    0    |       0      |       0      |       0      |      1      |   L_0(u) = u( 0, 0,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    1    |       0      |       1      |       0      |      1      |   L_1(u) = u( 1, 0,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    2    |       0      |       2      |       0      |      1      |   L_2(u) = u( 0, 1,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    3    |       0      |       3      |       0      |      1      |   L_3(u) = u( 0, 0, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    4    |       0      |       4      |       0      |      1      |   L_4(u) = u( 1, 0, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    5    |       0      |       5      |       0      |      1      |   L_5(u) = u( 0, 1, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    6    |       1      |       0      |       0      |      1      |   L_6(u) = u(1/2, 0,-1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    7    |       1      |       1      |       0      |      1      |   L_7(u) = u(1/2,1/2,-1)  |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    8    |       1      |       2      |       0      |      1      |   L_8(u) = u( 0,1/2,-1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    9    |       1      |       6      |       0      |      1      |   L_9(u) = u( 0, 0, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   10    |       1      |       7      |       0      |      1      |   L_10(u)= u( 1, 0, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   11    |       1      |       8      |       0      |      1      |   L_11(u)= u( 0, 1, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   12    |       1      |       3      |       0      |      1      |   L_12(u)= u(1/2, 0, 1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   13    |       1      |       4      |       0      |      1      |   L_13(u)= u(1/2,1/2, 1)  |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   14    |       1      |       5      |       0      |      1      |   L_14(u)= u( 0,1/2, 1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   15    |       2      |       0      |       0      |      1      |   L_15(u)= u(1/2, 0, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   16    |       2      |       1      |       0      |      1      |   L_16(u)= u(1/2,1/2, 0)  |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   17    |       2      |       2      |       0      |      1      |   L_17(u)= u( 0,1/2, 0)   |
|=========|==============|==============|==============|=============|===========================|
|   MAX   |  maxScDim=2  |  maxScOrd=8  |  maxDfOrd=0  |      -      |                           |
|=========|==============|==============|==============|=============|===========================|

Remarks: Ordering of DoFs follows the node order in Wedge<18> topology. Note that node order in this topology does not follow the natural oder of k-subcells where the nodes are located, except for nodes 0 to 5 which coincide with the vertices of the base Wedge<6> topology. As a result, L_0 to L_5 are associated with nodes 0 to 5, but L_6 to L_14 are not associated with edges 0 to 9 in that order. The last three nodes are located on 2-subcells (faces) and follow their order. Thus, L_15, L_16 and L17 are associated with faces 0, 1 and 2 in that order.

Definition at line 119 of file Intrepid_HGRAD_WEDGE_C2_FEM.hpp.

Constructor & Destructor Documentation

◆ Basis_HGRAD_WEDGE_C2_FEM()

template<class Scalar, class ArrayScalar>

Intrepid::Basis_HGRAD_WEDGE_C2_FEM< Scalar, ArrayScalar >::Basis_HGRAD_WEDGE_C2_FEM ( )

Constructor.

Definition at line 54 of file Intrepid_HGRAD_WEDGE_C2_FEMDef.hpp.

References Intrepid::Basis< Scalar, ArrayScalar >::basisCardinality_, Intrepid::Basis< Scalar, ArrayScalar >::basisCellTopology_, Intrepid::Basis< Scalar, ArrayScalar >::basisCoordinates_, Intrepid::Basis< Scalar, ArrayScalar >::basisDegree_, Intrepid::Basis< Scalar, ArrayScalar >::basisTagsAreSet_, and Intrepid::Basis< Scalar, ArrayScalar >::basisType_.

Member Function Documentation

◆ getValues() [1/2]

template<class Scalar, class ArrayScalar>

void Intrepid::Basis_HGRAD_WEDGE_C2_FEM< Scalar, ArrayScalar >::getValues	(	ArrayScalar &	outputValues,
		const ArrayScalar &	inputPoints,
		const ArrayScalar &	cellVertices,
		const EOperator	operatorType = OPERATOR_VALUE ) const

virtual

FVD basis evaluation: invocation of this method throws an exception.

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 691 of file Intrepid_HGRAD_WEDGE_C2_FEMDef.hpp.

◆ getValues() [2/2]

template<class Scalar, class ArrayScalar>

void Intrepid::Basis_HGRAD_WEDGE_C2_FEM< Scalar, ArrayScalar >::getValues	(	ArrayScalar &	outputValues,
		const ArrayScalar &	inputPoints,
		const EOperator	operatorType ) const

virtual

FEM basis evaluation on a reference Wedge cell.

   Returns values of <var>operatorType</var> acting on FEM basis functions for a set of
   points in the <strong>reference Wedge</strong> cell. For rank and dimensions of 
   I/O array arguments see Section \ref basis_md_array_sec .

Parameters

outputValues	[out] - rank-2 or 3 array with the computed basis values
inputPoints	[in] - rank-2 array with dimensions (P,D) containing reference points
operatorType	[in] - operator applied to basis functions

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 109 of file Intrepid_HGRAD_WEDGE_C2_FEMDef.hpp.

References Intrepid::Basis< Scalar, ArrayScalar >::basisCardinality_, Intrepid::Basis< Scalar, ArrayScalar >::basisCellTopology_, Intrepid::Basis< Scalar, ArrayScalar >::getBaseCellTopology(), and Intrepid::Basis< Scalar, ArrayScalar >::getCardinality().

◆ initializeTags()

template<class Scalar, class ArrayScalar>

void Intrepid::Basis_HGRAD_WEDGE_C2_FEM< Scalar, ArrayScalar >::initializeTags ( )

privatevirtual

Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 66 of file Intrepid_HGRAD_WEDGE_C2_FEMDef.hpp.

References Intrepid::Basis< Scalar, ArrayScalar >::basisCardinality_, Intrepid::Basis< Scalar, ArrayScalar >::ordinalToTag_, and Intrepid::Basis< Scalar, ArrayScalar >::tagToOrdinal_.

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

/build/trilinos-oIrXZh/trilinos-16.1.0/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_WEDGE_C2_FEM.hpp
/build/trilinos-oIrXZh/trilinos-16.1.0/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_WEDGE_C2_FEMDef.hpp

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Basis_HGRAD_WEDGE_C2_FEM()

Member Function Documentation

◆ getValues() [1/2]

◆ getValues() [2/2]

◆ initializeTags()