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 >:
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 >
|
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 >
|
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:
- http://docs.trilinos.org/r13.0/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_HEX_I2_FEM.hpp
- http://docs.trilinos.org/r13.0/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_HEX_I2_FEMDef.hpp
