Intrepid
Public Member Functions | Private Member Functions | Private Attributes | List of all members
Intrepid::Basis_HCURL_TRI_In_FEM< Scalar, ArrayScalar > Class Template Reference

Implementation of the default H(curl)-compatible Nedelec (first kind) basis of arbitrary degree on Triangle cell. The lowest order space is indexed with 1 rather than 0. 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 by. More...

#include <Intrepid_HCURL_TRI_In_FEM.hpp>

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

Public Member Functions

 Basis_HCURL_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. 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

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

Private Attributes

Basis_HGRAD_TRI_Cn_FEM_ORTH
< Scalar, FieldContainer
< Scalar > > 
Phis_
 Orthogonal basis of ofder n, in terms of which the H(curl) basis functions are expressed.
 
FieldContainer< Scalar > coeffs_
 Array holding the expansion coefficients of the nodal basis in terms of Phis_.
 

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_HCURL_TRI_In_FEM< Scalar, ArrayScalar >

Implementation of the default H(curl)-compatible Nedelec (first kind) basis of arbitrary degree on Triangle cell. The lowest order space is indexed with 1 rather than 0. 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 by.

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 83 of file Intrepid_HCURL_TRI_In_FEM.hpp.

Member Function Documentation

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HCURL_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 288 of file Intrepid_HCURL_TRI_In_FEMDef.hpp.

Referenced by main().


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