Intrepid
Public Member Functions | Private Member Functions
Intrepid::Basis_HCURL_TRI_I1_FEM< Scalar, ArrayScalar > Class Template Reference

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

#include <Intrepid_HCURL_TRI_I1_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HCURL_TRI_I1_FEM< Scalar, ArrayScalar >:
Intrepid::Basis< Scalar, ArrayScalar >

List of all members.

Public Member Functions

 Basis_HCURL_TRI_I1_FEM ()
 Constructor.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
 Evaluation of a FEM basis on a reference Triangle 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_HCURL_TRI_I1_FEM< Scalar, ArrayScalar >

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

Implements Nedelec basis of the first kind of degree 1 on the reference Triangle cell. The basis has cardinality 3 and spans an INCOMPLETE 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    |       1      |       0      |       0      |      1      |  L_0(u) = (u.t)(0.5, 0)    |
  |---------|--------------|--------------|--------------|-------------|----------------------------|
  |    1    |       1      |       1      |       0      |      1      |  L_1(u) = (u.t)(0.5,0.5)   |
  |---------|--------------|--------------|--------------|-------------|----------------------------|
  |    2    |       1      |       2      |       0      |      1      |  L_2(u) = (u.t)( 0,0.5)    |
  |=========|==============|==============|==============|=============|============================|
  |   MAX   |  maxScDim=1  |  maxScOrd=2  |  maxDfOrd=0  |      -      |                            |
  |=========|==============|==============|==============|=============|============================|
  
Remarks:
  • In the DoF functional ${\bf t}$ is an edge tangent. Direction of edge tangents follows the vertex order of the edges in the cell topology and runs from edge vertex 0 to edge vertex 1, whereas their length is set equal to the edge length. For example, edge 1 of all Triangle reference cells has vertex order {1,2}, i.e., its tangent runs from vertex 1 of the reference Triangle to vertex 2 of that cell. On the reference Triangle the coordinates of these vertices are (1,0) and (0,1), respectively. Therefore, the tangent to edge 1 is (0,1)-(1,0) = (-1,1). Because its length already equals edge length, no further rescaling of the edge tangent is needed.
  • The length of the edge tangent equals the edge length. As a result, the DoF functional is the value of the tangent component of a vector field at the edge midpoint times the edge length. The resulting basis is equivalent to a basis defined by using the edge circulation as a DoF functional. Note that edges 0 and 2 of reference Triangle<> cells have unit lengths and edge 1 has length Sqrt(2).

Definition at line 96 of file Intrepid_HCURL_TRI_I1_FEM.hpp.


Member Function Documentation

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HCURL_TRI_I1_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar &  outputValues,
const ArrayScalar &  inputPoints,
const EOperator  operatorType 
) const [virtual]

Evaluation of a FEM basis on a reference Triangle cell.

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

Parameters:
outputValues[out] - rank-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 91 of file Intrepid_HCURL_TRI_I1_FEMDef.hpp.


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