Implementation of the default H(div)-compatible FEM basis of degree 1 on Wedge cell. More...

#include <Intrepid_HDIV_WEDGE_I1_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HDIV_WEDGE_I1_FEM< Scalar, ArrayScalar >:

Public Member Functions
	Basis_HDIV_WEDGE_I1_FEM ()
	Constructor.

void	getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
	Evaluation of a FEM basis on a reference Wedge cell. More...

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. More...

virtual int	getDegree () const
	Returns the degree of the basis. More...

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. More...

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

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

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

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. More...

virtual const std::vector < std::vector< int > > &	getAllDofTags ()
	Retrieves all DoF tags. More...

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. More...

std::vector< std::vector < std::vector< int > > >	tagToOrdinal_
	DoF tag to ordinal lookup table. More...

Detailed Description

template<class Scalar, class ArrayScalar>
class Intrepid::Basis_HDIV_WEDGE_I1_FEM< Scalar, ArrayScalar >

Implementation of the default H(div)-compatible FEM basis of degree 1 on Wedge cell.

      Implements Raviart-Thomas basis of degree 1 on the reference Wedge cell. The basis has
      cardinality 5 and spans an INCOMPLETE bi-linear 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    |       2      |       0      |       0      |      1      |  L_0(u) = (u.n)(1/2,0,0)   |
|---------|--------------|--------------|--------------|-------------|----------------------------|
|    1    |       2      |       1      |       0      |      1      |  L_1(u) = (u.n)(1/2,1/2,0) |
|---------|--------------|--------------|--------------|-------------|----------------------------|
|    2    |       2      |       2      |       0      |      1      |  L_2(u) = (u.n)(0,1/2,0)   |
|---------|--------------|--------------|--------------|-------------|----------------------------|
|    3    |       2      |       3      |       0      |      1      |  L_3(u) = (u.n)(1/3,1/3,-1)|
|---------|--------------|--------------|--------------|-------------|----------------------------|
|    4    |       2      |       4      |       0      |      1      |  L_4(u) = (u.n)(1/3,1/3,1) |
|=========|==============|==============|==============|=============|============================|
|   MAX   |  maxScDim=2  |  maxScOrd=4  |  maxDfOrd=0  |      -      |                            |
|=========|==============|==============|==============|=============|============================|

Remarks

In the DoF functional ${\bf n}$ is a face normal. Direction of face normals is determined by the right-hand rule applied to faces oriented by their vertex order in the cell topology, from face vertex 0 to last face vertex, whereas their length is set equal to face area (see http://mathworld.wolfram.com/Right-HandRule.html for definition of right-hand rule). For example, face 1 of all Wedge cells has vertex order {1,2,5,4} and its right-hand rule normal can be computed, e.g., by the vector product of edge tangents to edges {1,2} and {2,5}. On the reference Wedge the coordinates of face 1 vertices are (1,0,-1), (0,1,-1), (0,1,1), and (1,0,1), the edge tangents are (-1,1,0) and (0,0,2) and the face normal direction is (-1,1,0) X (0,0,2) = (2,2,0). In this case the normal length already equals face area and no further normalization is needed.

The length of the face normal equals the face area. As a result, the DoF functional is the value of the normal component of a vector field at the face center times the face area. The resulting basis is equivalent to a basis defined by using the face flux as a DoF functional. Note that faces 0 and 2 of reference Wedge<> cells have area 2, face 1 has area 2*Sqrt(2), and faces 3 and 4 have area 1/2.

Definition at line 103 of file Intrepid_HDIV_WEDGE_I1_FEM.hpp.

Member Function Documentation

template<class Scalar , class ArrayScalar >

void Intrepid::Basis_HDIV_WEDGE_I1_FEM< Scalar, ArrayScalar >::getValues	(	ArrayScalar &	outputValues,
		const ArrayScalar &	inputPoints,
		const EOperator	operatorType
	)		const

virtual

Evaluation of a FEM basis 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-3 or 4 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 94 of file Intrepid_HDIV_WEDGE_I1_FEMDef.hpp.

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

http://docs.trilinos.org/dev/packages/intrepid/src/Discretization/Basis/Intrepid_HDIV_WEDGE_I1_FEM.hpp
http://docs.trilinos.org/dev/packages/intrepid/src/Discretization/Basis/Intrepid_HDIV_WEDGE_I1_FEMDef.hpp

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

template<class Scalar, class ArrayScalar> class Intrepid::Basis_HDIV_WEDGE_I1_FEM< Scalar, ArrayScalar >

Member Function Documentation

template<class Scalar, class ArrayScalar>
class Intrepid::Basis_HDIV_WEDGE_I1_FEM< Scalar, ArrayScalar >