Intrepid
Public Member Functions | Private Member Functions
Intrepid::Basis_HGRAD_TET_C2_FEM< Scalar, ArrayScalar > Class Template Reference

Implementation of the default H(grad)-compatible FEM basis of degree 2 on Tetrahedron cell. More...

#include <Intrepid_HGRAD_TET_C2_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HGRAD_TET_C2_FEM< Scalar, ArrayScalar >:
Intrepid::Basis< Scalar, ArrayScalar >

List of all members.

Public Member Functions

 Basis_HGRAD_TET_C2_FEM ()
 Constructor.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
 FEM basis evaluation on a reference Tetrahedron 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_TET_C2_FEM< Scalar, ArrayScalar >

Implementation of the default H(grad)-compatible FEM basis of degree 2 on Tetrahedron cell.

Implements Lagrangian basis of degree 2 on the reference Tetrahedron cell. The basis has cardinality 10 and spans a COMPLETE 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(0,0,0)       |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    1    |       0      |       1      |       0      |      1      |   L_1(u) = u(1,0,0)       |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    2    |       0      |       2      |       0      |      1      |   L_2(u) = u(0,1,0)       |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    3    |       0      |       3      |       0      |      1      |   L_3(u) = u(0,0,1)       |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    4    |       1      |       0      |       0      |      1      |   L_4(u) = u(1/2,0,0)     |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    5    |       1      |       1      |       0      |      1      |   L_5(u) = u(1/2,1/2,0)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    6    |       1      |       2      |       0      |      1      |   L_6(u) = u(0,1/2,0)     |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    7    |       1      |       3      |       0      |      1      |   L_7(u) = u(0,0,1/2)     |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    8    |       1      |       4      |       0      |      1      |   L_8(u) = u(1/2,0,1/2)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    9    |       1      |       5      |       0      |      1      |   L_9(u) = u(0,1/2,1/2)   |
  |=========|==============|==============|==============|=============|===========================|
  |   MAX   |  maxScDim=0  |  maxScOrd=3  |  maxDfOrd=0  |     -       |                           |
  |=========|==============|==============|==============|=============|===========================|
  
Remarks:
Ordering of DoFs follows the node order in Tetrahedron<10> topology. Note that node order in this topology follows the natural order of k-subcells where the nodes are located, i.e., L_0 to L_3 correspond to 0-subcells (vertices) 0 to 3 and L_4 to L_9 correspond to 1-subcells (edges) 0 to 5.

Definition at line 85 of file Intrepid_HGRAD_TET_C2_FEM.hpp.


Member Function Documentation

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HGRAD_TET_C2_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar &  outputValues,
const ArrayScalar &  inputPoints,
const EOperator  operatorType 
) const [virtual]

FEM basis evaluation on a reference Tetrahedron cell.

Returns values of operatorType acting on FEM basis functions for a set of points in the reference Tetrahedron 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

For rank and dimension specifications of ArrayScalar arguments see basis_array_specs

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 85 of file Intrepid_HGRAD_TET_C2_FEMDef.hpp.


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