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// Intrepid Package
// Copyright (2007) Sandia Corporation
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// Denis Ridzal (dridzal@sandia.gov), or
// Kara Peterson (kjpeter@sandia.gov)
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/** \file Intrepid_HCURL_TET_I1_FEM.hpp
\brief Header file for the Intrepid::HCURL_TET_I1_FEM class.
\author Created by P. Bochev, D. Ridzal and K. Peterson.
*/
#ifndef INTREPID_HCURL_TET_I1_FEM_HPP
#define INTREPID_HCURL_TET_I1_FEM_HPP
#include "Intrepid_Basis.hpp"
namespace Intrepid {
/** \class Intrepid::Basis_HCURL_TET_I1_FEM
\brief Implementation of the default H(curl)-compatible FEM basis of degree 1 on Tetrahedron cell
Implements Nedelec basis of degree 1 on the reference Tetrahedron cell. The basis has
cardinality 6 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:
\verbatim
===================================================================================================
| | 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)(0.5,0,0) |
|---------|--------------|--------------|--------------|-------------|----------------------------|
| 1 | 1 | 1 | 0 | 1 | L_1(u) = (u.t)(0.5,0.5,0) |
|---------|--------------|--------------|--------------|-------------|----------------------------|
| 2 | 1 | 2 | 0 | 1 | L_2(u) = (u.t)(0,0.5,0) |
|---------|--------------|--------------|--------------|-------------|----------------------------|
| 3 | 1 | 3 | 0 | 1 | L_3(u) = (u.t)(0,0,0.5) |
|---------|--------------|--------------|--------------|-------------|----------------------------|
| 4 | 1 | 4 | 0 | 1 | L_4(u) = (u.t)(0.5,0,0.5) |
|---------|--------------|--------------|--------------|-------------|----------------------------|
| 5 | 1 | 5 | 0 | 1 | L_5(u) = (u.t)(0,0.5,0.5) |
|=========|==============|==============|==============|=============|============================|
| MAX | maxScDim=1 | maxScOrd=5 | maxDfOrd=0 | - | |
|=========|==============|==============|==============|=============|============================|
\endverbatim
\remarks
\li In the DoF functional \f${\bf t}\f$ 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 4 of all Tetrahedron reference cells has vertex order {1,3}, i.e., its
tangent runs from vertex 1 of the reference Tetrahedron to vertex 3 of that cell. On the
reference Tetrahedron the coordinates of these vertices are (1,0,0) and (0,0,1), respectively.
Therefore, the tangent to edge 4 is (0,0,1) - (1,0,0) = (-1, 0, 1). Because its length
already equals edge length, no further rescaling of the edge tangent is needed.
\li 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, 2 and 3 of reference Tetrahedron<>
cells have unit lengths and edges 1, 4, and 5 have length Sqrt(2).
*/
template<class Scalar, class ArrayScalar>
class Basis_HCURL_TET_I1_FEM : public Basis<Scalar, ArrayScalar>, public DofCoordsInterface<ArrayScalar> {
private:
/** \brief Initializes <var>tagToOrdinal_</var> and <var>ordinalToTag_</var> lookup arrays.
*/
void initializeTags();
public:
/** \brief Constructor.
*/
Basis_HCURL_TET_I1_FEM();
/** \brief Evaluation of a FEM basis on a <strong>reference Tetrahedron</strong> cell.
Returns values of <var>operatorType</var> acting on FEM basis functions for a set of
points in the <strong>reference Tetrahedron</strong> cell. For rank and dimensions of
I/O array arguments see Section \ref basis_md_array_sec.
\param outputValues [out] - rank-3 array with the computed basis values
\param inputPoints [in] - rank-2 array with dimensions (P,D) containing reference points
\param operatorType [in] - operator applied to basis functions
*/
void getValues(ArrayScalar & outputValues,
const ArrayScalar & inputPoints,
const EOperator operatorType) const;
/** \brief FVD basis evaluation: invocation of this method throws an exception.
*/
void getValues(ArrayScalar & outputValues,
const ArrayScalar & inputPoints,
const ArrayScalar & cellVertices,
const EOperator operatorType = OPERATOR_VALUE) const;
/** \brief Returns spatial locations (coordinates) of degrees of freedom on a
<strong>reference Triangle</strong>.
\param DofCoords [out] - array with the coordinates of degrees of freedom,
dimensioned (F,D)
*/
void getDofCoords(ArrayScalar & DofCoords) const;
};
}// namespace Intrepid
#include "Intrepid_HCURL_TET_I1_FEMDef.hpp"
#endif
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