Intrepid
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Intrepid::Basis_HGRAD_HEX_I2_FEM< Scalar, ArrayScalar > Class Template Reference

Implementation of the serendipity-family H(grad)-compatible FEM basis of degree 2 on a Hexahedron cell. More...

#include <Intrepid_HGRAD_HEX_I2_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HGRAD_HEX_I2_FEM< Scalar, ArrayScalar >:
Intrepid::Basis< Scalar, ArrayScalar > Intrepid::DofCoordsInterface< ArrayScalar >

Public Member Functions

 Basis_HGRAD_HEX_I2_FEM ()
 Constructor.
 
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
 Evaluation of a FEM basis on a reference Hexahedron 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.
 
void getDofCoords (ArrayScalar &DofCoords) const
 Returns spatial locations (coordinates) of degrees of freedom on a reference Quadrilateral. More...
 
- 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...
 
- Public Member Functions inherited from Intrepid::DofCoordsInterface< ArrayScalar >
virtual ~DofCoordsInterface ()=0
 Pure virtual destructor (gives warnings if not included). Following "Effective C++: 3rd Ed." item 7 the implementation is included in the definition file.
 

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_HEX_I2_FEM< Scalar, ArrayScalar >

Implementation of the serendipity-family H(grad)-compatible FEM basis of degree 2 on a Hexahedron cell.

      Implements Lagrangian basis of degree 2 on the reference Hexahedron cell. The basis has
      cardinality 20 and spans an INCOMPLETE tri-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,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    1    |       0      |       1      |       0      |      1      |   L_1(u) = u( 1,-1,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    2    |       0      |       2      |       0      |      1      |   L_2(u) = u( 1, 1,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    3    |       0      |       3      |       0      |      1      |   L_3(u) = u(-1, 1,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    4    |       0      |       4      |       0      |      1      |   L_4(u) = u(-1,-1, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    5    |       0      |       5      |       0      |      1      |   L_5(u) = u( 1,-1, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    6    |       0      |       6      |       0      |      1      |   L_6(u) = u( 1, 1, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    7    |       0      |       7      |       0      |      1      |   L_7(u) = u(-1, 1, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    8    |       1      |       0      |       0      |      1      |   L_8(u) = u( 0,-1,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    9    |       1      |       1      |       0      |      1      |   L_9(u) = u( 1, 0,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   10    |       1      |       2      |       0      |      1      |   L_10(u) = u( 0, 1,-1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   11    |       1      |       3      |       0      |      1      |   L_11(u) = u(-1, 0,-1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   12    |       1      |       8      |       0      |      1      |   L_12(u) = u(-1,-1, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   13    |       1      |       9      |       0      |      1      |   L_13(u) = u( 1,-1, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   14    |       1      |      10      |       0      |      1      |   L_14(u) = u( 1, 1, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   15    |       1      |      11      |       0      |      1      |   L_15(u) = u(-1, 1, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   16    |       1      |       4      |       0      |      1      |   L_16(u) = u( 0,-1, 1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   17    |       1      |       5      |       0      |      1      |   L_17(u) = u( 1, 0, 1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   18    |       1      |       6      |       0      |      1      |   L_18(u) = u( 0, 1, 1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   19    |       1      |       7      |       0      |      1      |   L_19(u) = u(-1, 0, 1)   |
|=========|==============|==============|==============|=============|===========================|
|   MAX   |  maxScDim=2  |  maxScOrd=12 |  maxDfOrd=0  |      -      |                           |
|=========|==============|==============|==============|=============|===========================|
Remarks
Ordering of DoFs follows the node order in Hexahedron<20> topology. Note that node order in this topology does not follow the natural order of k-subcells where the nodes are located, except for nodes 0 to 7 which coincide with the vertices of the base Hexahedron <8> topology. As a result, L_0 to L_7 are associated with nodes 0 to 7, but L_8 to L_19 are not associated with edges 0 to 12 in that order.

Definition at line 123 of file Intrepid_HGRAD_HEX_I2_FEM.hpp.

Member Function Documentation

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HGRAD_HEX_I2_FEM< Scalar, ArrayScalar >::getDofCoords ( ArrayScalar &  DofCoords) const
virtual

Returns spatial locations (coordinates) of degrees of freedom on a reference Quadrilateral.

Parameters
DofCoords[out] - array with the coordinates of degrees of freedom, dimensioned (F,D)

Implements Intrepid::DofCoordsInterface< ArrayScalar >.

Definition at line 752 of file Intrepid_HGRAD_HEX_I2_FEMDef.hpp.

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HGRAD_HEX_I2_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar &  outputValues,
const ArrayScalar &  inputPoints,
const EOperator  operatorType 
) const
virtual

Evaluation of a FEM basis on a reference Hexahedron cell.

    Returns values of <var>operatorType</var> acting on FEM basis functions for a set of
    points in the <strong>reference Hexahedron</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 113 of file Intrepid_HGRAD_HEX_I2_FEMDef.hpp.


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