Intrepid
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Intrepid::Basis_HGRAD_PYR_I2_FEM< Scalar, ArrayScalar > Class Template Reference

Implementation of an H(grad)-compatible FEM basis of degree 2 on a Pyramid cell. More...

#include <Intrepid_HGRAD_PYR_I2_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HGRAD_PYR_I2_FEM< Scalar, ArrayScalar >:
Intrepid::Basis< Scalar, ArrayScalar >

Public Member Functions

 Basis_HGRAD_PYR_I2_FEM ()
 Constructor.
 
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
 FEM basis evaluation on a reference Pyramid 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_HGRAD_PYR_I2_FEM< Scalar, ArrayScalar >

Implementation of an H(grad)-compatible FEM basis of degree 2 on a Pyramid cell.

      Implements Lagrangian basis of degree 2 on the reference Pyramid cell. The basis has
      cardinality 13 and spans an INCOMPLETE bi-quadratic 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    |       0      |       0      |       0      |      1      |   L_0(u) = u(-1,-1, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    1    |       0      |       1      |       0      |      1      |   L_1(u) = u( 1,-1, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    2    |       0      |       2      |       0      |      1      |   L_2(u) = u( 1, 1, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    3    |       0      |       3      |       0      |      1      |   L_3(u) = u(-1, 1, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    4    |       0      |       4      |       0      |      1      |   L_4(u) = u( 0, 0, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    5    |       1      |       0      |       0      |      1      |   L_5(u) = u( 0,-1, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    6    |       1      |       1      |       0      |      1      |   L_6(u) = u( 1, 0, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    7    |       1      |       2      |       0      |      1      |   L_7(u) = u( 0, 1, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    8    |       1      |       3      |       0      |      1      |   L_8(u) = u(-1, 0, 0)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    9    |       1      |       4      |       0      |      1      | L_9(u) = u(-1/2,-1/2,1/2) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   10    |       1      |       5      |       0      |      1      | L_10(u)= u( 1/2,-1/2,1/2) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   11    |       1      |       6      |       0      |      1      | L_11(u)= u( 1/2, 1/2,1/2) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   12    |       1      |       7      |       0      |      1      | L_12(u)= u(-1/2, 1/2,1/2) |
|=========|==============|==============|==============|=============|===========================|
|   MAX   |  maxScDim=1  |  maxScOrd=7  |  maxDfOrd=0  |      -      |                           |
|=========|==============|==============|==============|=============|===========================|
\remark   Ordering of DoFs follows the node order in Pyramid<13> topology. 

\remark  WARNING: Does not satisfy a patch test for arbitrarily deformed pyramids, but only
                  for pyramids with bottom quadrilateral nodes forming a plane.

Definition at line 105 of file Intrepid_HGRAD_PYR_I2_FEM.hpp.

Member Function Documentation

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HGRAD_PYR_I2_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar &  outputValues,
const ArrayScalar &  inputPoints,
const EOperator  operatorType 
) const
virtual

FEM basis evaluation on a reference Pyramid cell.

    Returns values of <var>operatorType</var> acting on FEM basis functions for a set of
    points in the <strong>reference Pyramid</strong> cell. For rank and dimensions of 
    I/O array arguments see Section \ref basis_md_array_sec .
Parameters
outputValues[out] - rank-2 or 3 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 104 of file Intrepid_HGRAD_PYR_I2_FEMDef.hpp.


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