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

#include <Intrepid_HDIV_TRI_I1_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HDIV_TRI_I1_FEM< Scalar, ArrayScalar >:

Public Member Functions
	Basis_HDIV_TRI_I1_FEM ()
	Constructor.

void	getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
	Evaluation of a FEM basis on a reference Triangle 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_TRI_I1_FEM< Scalar, ArrayScalar >

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

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

Remarks

In the DOF functional ${\bf n}=(t_2,-t_1)$ where ${\bf t}=(t_1,t_2)$ is the side (edge) tangent, i.e., the choice of normal direction is such that the pair $({\bf n},{\bf t})$ is positively oriented.

Direction of side tangents is determined by the vertex order of the sides in the cell topology and runs from side vertex 0 to side vertex 1, whereas their length is set equal to the side length. For example, side 1 of all Triangle reference cells has vertex order {1,2}, i.e., its tangent runs from vertex 1 of the reference Triangle to vertex 2 of that cell. On the reference Triangle the coordinates of these vertices are (1,0) and (0,1), respectively. Therefore, the tangent to side 1 is (0,1)-(1,0) = (-1,1) and the normal to that side is (1,1). Because its length already equals side length, no further rescaling of the side tangent is needed.

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

Definition at line 101 of file Intrepid_HDIV_TRI_I1_FEM.hpp.

Member Function Documentation

template<class Scalar , class ArrayScalar >

void Intrepid::Basis_HDIV_TRI_I1_FEM< Scalar, ArrayScalar >::getValues	(	ArrayScalar &	outputValues,
		const ArrayScalar &	inputPoints,
		const EOperator	operatorType
	)		const

virtual

Evaluation of a FEM basis on a reference Triangle cell.

    Returns values of <var>operatorType</var> acting on FEM basis functions for a set of
    points in the <strong>reference Triangle</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 95 of file Intrepid_HDIV_TRI_I1_FEMDef.hpp.

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

http://docs.trilinos.org/r12.18/packages/intrepid/src/Discretization/Basis/Intrepid_HDIV_TRI_I1_FEM.hpp
http://docs.trilinos.org/r12.18/packages/intrepid/src/Discretization/Basis/Intrepid_HDIV_TRI_I1_FEMDef.hpp

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

template<class Scalar, class ArrayScalar> class Intrepid::Basis_HDIV_TRI_I1_FEM< Scalar, ArrayScalar >

Member Function Documentation

template<class Scalar, class ArrayScalar>
class Intrepid::Basis_HDIV_TRI_I1_FEM< Scalar, ArrayScalar >