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/** \file Intrepid_HDIV_TRI_In_FEM.hpp
\brief Header file for the Intrepid::HDIV_TRI_In_FEM class.
\author Created by R. Kirby.
*/
#ifndef INTREPID_HDIV_TRI_In_FEM_HPP
#define INTREPID_HDIV_TRI_In_FEM_HPP
#include "Intrepid_Types.hpp"
#include "Intrepid_Basis.hpp"
#include "Intrepid_PointTools.hpp"
#include "Intrepid_HGRAD_TRI_Cn_FEM_ORTH.hpp"
#include "Intrepid_CubatureDirectTriDefault.hpp"
#include "Intrepid_CubatureDirectLineGauss.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_SerialDenseSolver.hpp"
namespace Intrepid {
/** \class Intrepid::Basis_HDIV_TRI_In_FEM
\brief Implementation of the default H(div)-compatible Raviart-Thomas basis of arbitrary degree on Triangle cell
Implements nodal basis of degree n (n>=1) on the reference Triangle cell. The basis has
cardinality n(n+2) and spans an INCOMPLETE polynomial
space of degree n. Basis functions are dual to a
unisolvent set of degrees-of-freedom (DoF) defined and
enumerated as
\li The normal component on a lattice of order n+1 and
offset 1 on each edge (see PointTools). This gives one point per edge in
the lowest-order case. These are the first
3 * n degrees of freedom
\li If n > 1, the x and y components at a lattice of
order n+1 and offset on the triangle. These are the rest
of the 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 of order n+1 is chosen for
the interior points.
*/
template<class Scalar, class ArrayScalar>
class Basis_HDIV_TRI_In_FEM: public Basis<Scalar, ArrayScalar> {
private:
/** \brief Initializes <var>tagToOrdinal_</var> and <var>ordinalToTag_</var> lookup arrays.
*/
virtual void initializeTags();
/** \brief Orthogonal basis out of which the nodal basis is
constructed */
Basis_HGRAD_TRI_Cn_FEM_ORTH<Scalar,FieldContainer<Scalar> > Phis;
/** \brief expansion coefficients of the nodal basis in terms of the
orthgonal one */
FieldContainer<Scalar> coeffs;
public:
/** \brief Constructor.
*/
Basis_HDIV_TRI_In_FEM( const int n , const EPointType pointType );
/** \brief Evaluation of a FEM basis on a <strong>reference Triangle</strong> cell.
Returns values of <var>operatorType</var> acting on FEM basis functions for a set of
points in the <strong>reference Triangle</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_HDIV_TRI_In_FEMDef.hpp"
#endif
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