Intrepid::Basis_HDIV_HEX_I1_FEM< Scalar, ArrayScalar > Class Template Reference

Implementation of the default H(div)-compatible FEM basis of degree 1 on Hexahedron cell. More...

#include <Intrepid_HDIV_HEX_I1_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HDIV_HEX_I1_FEM< Scalar, ArrayScalar >:
Intrepid::Basis< Scalar, ArrayScalar >

List of all members.

Public Member Functions

 Basis_HDIV_HEX_I1_FEM ()
 Constructor.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
 Evaluation of a FEM basis on a reference Hexahedron 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_HDIV_HEX_I1_FEM< Scalar, ArrayScalar >

Implementation of the default H(div)-compatible FEM basis of degree 1 on Hexahedron cell.

Implements Raviart-Thomas basis of degree 1 on the reference Hexahedron cell. The basis has cardinality 6 and spans a INCOMPLETE tri-linear 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    |       2      |       0      |       0      |      1      |   L_0(u) = (u.n)(0,-1,0)   |
  |---------|--------------|--------------|--------------|-------------|----------------------------|
  |    1    |       2      |       1      |       0      |      1      |   L_1(u) = (u.n)(1,0,0)    |
  |---------|--------------|--------------|--------------|-------------|----------------------------|
  |    2    |       2      |       2      |       0      |      1      |   L_2(u) = (u.n)(0,1,0)    |
  |---------|--------------|--------------|--------------|-------------|----------------------------|
  |    3    |       2      |       3      |       0      |      1      |   L_3(u) = (u.n)(-1,0,0)   |
  |---------|--------------|--------------|--------------|-------------|----------------------------|
  |    4    |       2      |       4      |       0      |      1      |   L_4(u) = (u.n)(0,0,-1)   |
  |---------|--------------|--------------|--------------|-------------|----------------------------|
  |    5    |       2      |       5      |       0      |      1      |   L_5(u) = (u.n)(0,0,1)    |
  |=========|==============|==============|==============|=============|============================|
  |   MAX   |  maxScDim=2  |  maxScOrd=5  |  maxDfOrd=0  |      -      |                            |
  |=========|==============|==============|==============|=============|============================|
  
Remarks:
  • In the DoF functional ${\bf n}$ is a face normal. Direction of face normals is determined by the right-hand rule applied to faces oriented by their vertex order in the cell topology, from face vertex 0 to last face vertex, whereas their length is set equal to face area (see http://mathworld.wolfram.com/Right-HandRule.html for definition of right-hand rule). For example, face 1 of all Hexahedron cells has vertex order {1,2,6,5} and its right-hand rule normal can be computed, e.g., by the vector product of edge tangents to edges {1,2} and {2,6}. On the reference Hexahedron the coordinates of face 1 vertices are (1,-1,-1), (1,1,-1), (1,1,1) and (1,-1,1), the edge tangents are (0,2,0) and (0,0,2) and the face normal direction is (0,2,0) X (0,0,2) = (4,0,0). In this case the normal length already equals face area and no further normalization is needed.
  • The length of the face normal equals the face area. As a result, the DoF functional is the value of the normal component of a vector field at the face center times the face area. The resulting basis is equivalent to a basis defined by using the face flux as a DoF functional. Note that the faces of reference Hexahedron<> cells all have the same area equal to 4.

Definition at line 92 of file Intrepid_HDIV_HEX_I1_FEM.hpp.


Member Function Documentation

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HDIV_HEX_I1_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar &  outputValues,
const ArrayScalar &  inputPoints,
const EOperator  operatorType 
) const [inline, virtual]

Evaluation of a FEM basis on a reference Hexahedron cell.

Returns values of operatorType acting on FEM basis functions for a set of points in the reference Hexahedron cell. For rank and dimensions of I/O array arguments see Section MD array template arguments for basis methods.

Parameters:
outputValues [out] - rank-3 or 4 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 82 of file Intrepid_HDIV_HEX_I1_FEMDef.hpp.

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


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

Generated on Tue Oct 20 15:10:06 2009 for Intrepid by  doxygen 1.6.1