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 >:
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. | |
| 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. | |
Private Member Functions | |
| void | initializeTags () |
| Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays. | |
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 | - | | |=========|==============|==============|==============|=============|===========================|
- Remarks:
- Ordering of DoFs follows the node order in Pyramid<13> topology.
- 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 operatorType acting on FEM basis functions for a set of points in the reference Pyramid cell. For rank and dimensions of I/O array arguments see Section MD array template arguments for basis methods .
- 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:
- /usr/src/RPM/BUILD/trilinos-11.12.1/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_PYR_I2_FEM.hpp
- /usr/src/RPM/BUILD/trilinos-11.12.1/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_PYR_I2_FEMDef.hpp
