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/** \file Intrepid_HCURL_TET_In_FEM.hpp
\brief Header file for the Intrepid::HCURL_TET_In_FEM class.
\author Created by R. Kirby
*/
#ifndef INTREPID_HCURL_TET_In_FEM_HPP
#define INTREPID_HCURL_TET_In_FEM_HPP
#include "Intrepid_Types.hpp"
#include "Intrepid_Basis.hpp"
#include "Intrepid_PointTools.hpp"
#include "Intrepid_HGRAD_TET_Cn_FEM_ORTH.hpp"
#include "Intrepid_CubatureDirectTetDefault.hpp"
#include "Intrepid_CubatureDirectLineGauss.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_SerialDenseSolver.hpp"
namespace Intrepid {
/** \class Intrepid::Basis_HCURL_TET_In_FEM
\brief Implementation of the default H(curl)-compatible Nedelec (first kind)
basis of arbitrary degree on Tetrahedron cell. The lowest order space
is indexted with 1 rather than 0.
Implements nodal basis of degree n (n>=1) on the reference Tetrahedron cell. The basis has
cardinality n*(n+2)*(n+3)/2 and spans an INCOMPLETE
polynomial space of degree n. Basis functions are dual
to a unisolvent set of degrees-of-freedom (DoF) defined by
\li The tangential component of the vector field at n
points per edge. These are the first 6 * n dof.
\li The components in the directions of the tangents to
each face (see CellTools) on a lattice of order n+1 with
offset 1 (see PointTools) on each face. These are the
next 4 * n*(n-1) dof.
\li The x,y,z components on a lattice of order n+1 with
offset 1 on the interior of the tetrahedron, the remaining
degrees of freedom.
If the pointType argument to the constructor specifies equispaced points, then the edge points
will be equispaced on each edge and the interior points equispaced also. If
the pointType argument specifies warp-blend points, then Gauss-Lobatto points of order n
are chosen on each edge and the interior of warp-blend
lattice is chosen on each face and the interior.
\verbatim
\endverbatim
*/
template<class Scalar, class ArrayScalar>
class Basis_HCURL_TET_In_FEM: public Basis<Scalar, ArrayScalar> {
private:
/** \brief Initializes <var>tagToOrdinal_</var> and <var>ordinalToTag_</var> lookup arrays.
*/
virtual void initializeTags();
/** \brief Orthogonal basis of ofder n, in terms of which the H(curl) basis functions are expressed */
Basis_HGRAD_TET_Cn_FEM_ORTH<Scalar,FieldContainer<Scalar> > Phis_;
/** \brief Array holding the expansion coefficients of the nodal basis in terms of Phis_ */
FieldContainer<Scalar> coeffs_;
public:
/** \brief Constructor.
*/
Basis_HCURL_TET_In_FEM( const int n , const EPointType pointType );
/** \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] - variable rank array with the basis values
\param inputPoints [in] - rank-2 array (P,D) with the evaluation points
\param operatorType [in] - the operator acting on the 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;
};
}// namespace Intrepid
#include "Intrepid_HCURL_TET_In_FEMDef.hpp"
#endif
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