Intrepid::Basis_HGRAD_WEDGE_C2_FEM< Scalar, ArrayScalar > Class Template Reference

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

#include <Intrepid_HGRAD_WEDGE_C2_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HGRAD_WEDGE_C2_FEM< Scalar, ArrayScalar >:
Intrepid::Basis< Scalar, ArrayScalar >

List of all members.

Public Member Functions

 Basis_HGRAD_WEDGE_C2_FEM ()
 Constructor.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
 FEM basis evaluation on a reference Wedge 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_WEDGE_C2_FEM< Scalar, ArrayScalar >

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

Implements Lagrangian basis of degree 2 on the reference Wedge cell. The basis has cardinality 18 and spans a COMPLETE 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( 0, 0,-1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    1    |       0      |       1      |       0      |      1      |   L_1(u) = u( 1, 0,-1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    2    |       0      |       2      |       0      |      1      |   L_2(u) = u( 0, 1,-1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    3    |       0      |       3      |       0      |      1      |   L_3(u) = u( 0, 0, 1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    4    |       0      |       4      |       0      |      1      |   L_4(u) = u( 1, 0, 1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    5    |       0      |       5      |       0      |      1      |   L_5(u) = u( 0, 1, 1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    6    |       1      |       0      |       0      |      1      |   L_6(u) = u(1/2, 0,-1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    7    |       1      |       1      |       0      |      1      |   L_7(u) = u(1/2,1/2,-1)  |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    8    |       1      |       2      |       0      |      1      |   L_8(u) = u( 0,1/2,-1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    9    |       1      |       6      |       0      |      1      |   L_9(u) = u( 0, 0, 0)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   10    |       1      |       7      |       0      |      1      |   L_10(u)= u( 1, 0, 0)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   11    |       1      |       8      |       0      |      1      |   L_11(u)= u( 0, 1, 0)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   12    |       1      |       3      |       0      |      1      |   L_12(u)= u(1/2, 0, 1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   13    |       1      |       4      |       0      |      1      |   L_13(u)= u(1/2,1/2, 1)  |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   14    |       1      |       5      |       0      |      1      |   L_14(u)= u( 0,1/2, 1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   15    |       2      |       0      |       0      |      1      |   L_15(u)= u(1/2, 0, 0)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   16    |       2      |       1      |       0      |      1      |   L_16(u)= u(1/2,1/2, 0)  |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   17    |       2      |       2      |       0      |      1      |   L_17(u)= u( 0,1/2, 0)   |
  |=========|==============|==============|==============|=============|===========================|
  |   MAX   |  maxScDim=2  |  maxScOrd=8  |  maxDfOrd=0  |      -      |                           |
  |=========|==============|==============|==============|=============|===========================|
  
Remarks:
Ordering of DoFs follows the node order in Wedge<18> topology. Note that node order in this topology does not follow the natural oder of k-subcells where the nodes are located, except for nodes 0 to 5 which coincide with the vertices of the base Wedge<6> topology. As a result, L_0 to L_5 are associated with nodes 0 to 5, but L_6 to L_14 are not associated with edges 0 to 9 in that order. The last three nodes are located on 2-subcells (faces) and follow their order. Thus, L_15, L_16 and L17 are associated with faces 0, 1 and 2 in that order.

Definition at line 105 of file Intrepid_HGRAD_WEDGE_C2_FEM.hpp.


Member Function Documentation

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HGRAD_WEDGE_C2_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar &  outputValues,
const ArrayScalar &  inputPoints,
const EOperator  operatorType 
) const [inline, virtual]

FEM basis evaluation on a reference Wedge cell.

Returns values of operatorType acting on FEM basis functions for a set of points in the reference Wedge 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 93 of file Intrepid_HGRAD_WEDGE_C2_FEMDef.hpp.

References Intrepid::Basis< Scalar, ArrayScalar >::basisCardinality_, Intrepid::Basis< Scalar, ArrayScalar >::basisCellTopology_, Intrepid::Basis< Scalar, ArrayScalar >::getBaseCellTopology(), and Intrepid::Basis< Scalar, ArrayScalar >::getCardinality().


The documentation for this class was generated from the following files:
Generated on Wed Mar 31 15:02:21 2010 for Intrepid by  doxygen 1.6.3