Intrepid
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Intrepid::Basis_HDIV_TRI_In_FEM< Scalar, ArrayScalar > Class Template Reference

Implementation of the default H(div)-compatible Raviart-Thomas basis of arbitrary degree on Triangle cell. More...

#include <Intrepid_HDIV_TRI_In_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HDIV_TRI_In_FEM< Scalar, ArrayScalar >:
Intrepid::Basis< Scalar, ArrayScalar >

Public Member Functions

 Basis_HDIV_TRI_In_FEM (const int n, const EPointType pointType)
 Constructor.
 
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
 Evaluation of a FEM basis on a reference Triangle 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 void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const =0
 Evaluation of a FEM basis on a reference cell.
 
virtual void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const ArrayScalar &cellVertices, const EOperator operatorType=OPERATOR_VALUE) const =0
 Evaluation of an FVD basis evaluation on a physical cell.

 
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

virtual void initializeTags ()
 Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.
 

Private Attributes

Basis_HGRAD_TRI_Cn_FEM_ORTH< Scalar, FieldContainer< Scalar > > Phis
 Orthogonal basis out of which the nodal basis is constructed.
 
FieldContainer< Scalar > coeffs
 expansion coefficients of the nodal basis in terms of the orthgonal one
 

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_HDIV_TRI_In_FEM< Scalar, ArrayScalar >

Implementation of the default H(div)-compatible Raviart-Thomas basis of arbitrary degree on Triangle cell.

    Implements nodal basis of degree n (n>=1) on the reference Triangle cell. The basis has
    cardinality n(n+2) and spans an INCOMPLETE polynomial
    space of degree n. Basis functions are dual to a
    unisolvent set of degrees-of-freedom (DoF) defined and
    enumerated as

    \li The normal component on a lattice of order n+1 and
    offset 1 on each edge (see PointTools). This gives one point per edge in
    the lowest-order case.  These are the first
    3 * n degrees of freedom

    \li If n > 1, the x and y components at a lattice of
    order n+1 and offset on the triangle.  These are the rest
    of the degrees of freedom.


    If the pointType argument to the constructor specifies equispaced points, then the edge points
    will be equispaced on each edge and the interior points equispaced also.  If
    the pointType argument specifies warp-blend points, then Gauss-Lobatto points of order n
    are chosen on each edge and the interior of warp-blend lattice of order n+1 is chosen for
    the interior points.

Definition at line 93 of file Intrepid_HDIV_TRI_In_FEM.hpp.

Constructor & Destructor Documentation

◆ Basis_HDIV_TRI_In_FEM()

template<class Scalar , class ArrayScalar >
Intrepid::Basis_HDIV_TRI_In_FEM< Scalar, ArrayScalar >::Basis_HDIV_TRI_In_FEM ( const int  n,
const EPointType  pointType 
)

Member Function Documentation

◆ getValues() [1/2]

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HDIV_TRI_In_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 355 of file Intrepid_HDIV_TRI_In_FEMDef.hpp.

◆ getValues() [2/2]

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HDIV_TRI_In_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] - 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

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 285 of file Intrepid_HDIV_TRI_In_FEMDef.hpp.

Referenced by main().

◆ initializeTags()

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HDIV_TRI_In_FEM< Scalar, ArrayScalar >::initializeTags
privatevirtual

Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 235 of file Intrepid_HDIV_TRI_In_FEMDef.hpp.

References Intrepid::setOrdinalTagData().

Member Data Documentation

◆ coeffs

template<class Scalar , class ArrayScalar >
FieldContainer<Scalar> Intrepid::Basis_HDIV_TRI_In_FEM< Scalar, ArrayScalar >::coeffs
private

expansion coefficients of the nodal basis in terms of the orthgonal one

Definition at line 105 of file Intrepid_HDIV_TRI_In_FEM.hpp.

Referenced by Intrepid::Basis_HDIV_TRI_In_FEM< Scalar, ArrayScalar >::Basis_HDIV_TRI_In_FEM().

◆ Phis

template<class Scalar , class ArrayScalar >
Basis_HGRAD_TRI_Cn_FEM_ORTH<Scalar,FieldContainer<Scalar> > Intrepid::Basis_HDIV_TRI_In_FEM< Scalar, ArrayScalar >::Phis
private

Orthogonal basis out of which the nodal basis is constructed.

Definition at line 102 of file Intrepid_HDIV_TRI_In_FEM.hpp.

Referenced by Intrepid::Basis_HDIV_TRI_In_FEM< Scalar, ArrayScalar >::Basis_HDIV_TRI_In_FEM().


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