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

Implementation of the default H(grad)-compatible Lagrange basis of arbitrary degree on Triangle cell. More...

#include <Intrepid_HGRAD_TRI_Cn_FEM.hpp>

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

Public Member Functions

 Basis_HGRAD_TRI_Cn_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
 The orthogonal basis on triangles, out of which the nodal basis is constructed.
 
FieldContainer< Scalar > V
 The Vandermonde matrix with V_{ij} = phi_i(x_j), where x_j is the j_th point in the lattice.
 
FieldContainer< Scalar > Vinv
 The inverse of V. The columns of Vinv express the Lagrange basis in terms of the orthogonal basis.
 
FieldContainer< Scalar > latticePts
 stores the points at which degrees of freedom are located.
 

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_HGRAD_TRI_Cn_FEM< Scalar, ArrayScalar >

Implementation of the default H(grad)-compatible Lagrange basis of arbitrary degree on Triangle cell.

Implements Lagrangian basis of degree n on the reference Triangle cell. The basis has cardinality (n+1)(n+2)/2 and spans a COMPLETE polynomial space of degree n. Basis functions are dual to a unisolvent set of degrees-of-freedom (DoF) defined on a lattice of order n (see PointTools). In particular, the degrees of freedom are point evaluation at

The distribution of these points is specified by the pointType argument to the class constructor. Currently, either equispaced lattice points or Warburton's warp-blend points are available.

The dof are enumerated according to the ordering on the lattice (see PointTools). In particular, dof number 0 is at the bottom left vertex (0,0). The dof increase along the lattice with points along the lines of constant x adjacent in the enumeration.

Definition at line 84 of file Intrepid_HGRAD_TRI_Cn_FEM.hpp.

Member Function Documentation

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HGRAD_TRI_Cn_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 190 of file Intrepid_HGRAD_TRI_Cn_FEMDef.hpp.

Referenced by main().


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