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/** \file Intrepid_HGRAD_TET_Cn_FEM.hpp
\brief Header file for the Intrepid::HGRAD_TET_Cn_FEM_ORTH class.
\author Created by Robert C. Kirby
*/
#ifndef INTREPID_HGRAD_TET_Cn_FEM_ORTH_HPP
#define INTREPID_HGRAD_TET_Cn_FEM_ORTH_HPP
#include "Intrepid_Basis.hpp"
#include "Sacado.hpp"
namespace Intrepid {
/** \class Intrepid::Basis_HGRAD_TET_Cn_FEM_ORTH
\brief Implementation of the default H(grad)-compatible orthogonal basis of
arbitrary degree on tetrahedron.
\remarks
\li All degrees of freedom are considered to be internal (ie not assembled)
*/
template<class Scalar, class ArrayScalar>
class Basis_HGRAD_TET_Cn_FEM_ORTH: public Basis<Scalar, ArrayScalar> {
private:
/** \brief Initializes <var>tagToOrdinal_</var> and
<var>ordinalToTag_</var> lookup arrays. */
void initializeTags();
public:
/** \brief Constructor.
\param degree [in] - the degree of polynomials contained in the basis.
*/
Basis_HGRAD_TET_Cn_FEM_ORTH( int degree );
/** \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;
};
/** \class TabulatorTet
\brief This is an internal class with a static member function for
tabulating derivatives of orthogonal expansion functions.
It is a separate class to allow recursive templates partially specialized on
derivative order without throwing the HGRAD_TET_Cn_FEM_ORTH class into
an infinite compiler loop.
This class is intended only to be used internally by the HGRAD_TET_Cn_FEM_ORTH basis
to implement all the derivative orders in the Basis interface, hiding recursion
and calls to Sacado.
*/
template<typename Scalar,typename ArrayScalar, unsigned derivOrder>
class TabulatorTet
{
public:
/** \brief basic tabulate mathod evaluates the derivOrder^th derivatives
of the basis functions at inputPoints into outputValues.
\param [out] outputValues - rank 2 (if derivOrder == 0) or rank 3
array holding the result
\param [in] deg - the degree up to which to tabulate the bases
\param [in] inputPoints - a rank 2 array containing the
points at which to evaluate the basis functions.
*/
static void tabulate( ArrayScalar & outputValues ,
const int deg ,
const ArrayScalar &inputPoints );
};
/** \class TabulatorTet<Scalar,ArrayScalar,0>
\brief This is specialized on 0th derivatives to make the
tabulate function run through recurrence relations.
*/
template<typename Scalar,typename ArrayScalar>
class TabulatorTet<Scalar,ArrayScalar,0>
{
public:
/** \brief basic tabulate mathod evaluates the basis functions at inputPoints into outputValues.
\param [out] outputValues - rank 2 array (F,P) holding
the basis functions at points.
\param [in] deg - the degree up to which to tabulate the bases
\param [in] inputPoints - a rank 2 array containing the
points at which to evaluate the basis functions.
*/
static void tabulate( ArrayScalar & outputValues ,
const int deg ,
const ArrayScalar &inputPoints );
/** \brief function for indexing from orthogonal expansion indices into linear space
p+q+r = the degree of the polynomial.
\param p [in] - the first index
\param q [in] - the second index
\param r [in] - the third index */
static int idx(int p, int q,int r)
{
return (p+q+r)*(p+q+r+1)*(p+q+r+2)/6+(q+r)*(q+r+1)/2+r;
}
/** \brief function for computing the Jacobi recurrence coefficients so that
\param alpha [in] - the first Jacobi weight
\param beta [in] - the second Jacobi weight
\param n [n] - the polynomial degree
\param an [out] - the a weight for recurrence
\param bn [out] - the b weight for recurrence
\param cn [out] - the c weight for recurrence
The recurrence is
\f[
P^{\alpha,\beta}_{n+1} = \left( a_n + b_n x\right) P^{\alpha,\beta}_n - c_n P^{\alpha,\beta}_{n-1}
\f],
where
\f[
P^{\alpha,\beta}_0 = 1
\f]
*/
static void jrc( const Scalar &alpha , const Scalar &beta ,
const int &n ,
Scalar &an , Scalar &bn, Scalar &cn )
{
an = (2.0 * n + 1.0 + alpha + beta) * ( 2.0 * n + 2.0 + alpha + beta )
/ ( 2.0 * ( n + 1 ) * ( n + 1 + alpha + beta ) );
bn = (alpha*alpha-beta*beta)*(2.0*n+1.0+alpha+beta)
/ ( 2.0*(n+1.0)*(2.0*n+alpha+beta)*(n+1.0+alpha+beta) );
cn = (n+alpha)*(n+beta)*(2.0*n+2.0+alpha+beta)
/ ( (n+1.0)*(n+1.0+alpha+beta)*(2.0*n+alpha+beta) );
return;
}
};
/** \class TabulatorTet<Scalar,ArrayScalar,1>
\brief This is specialized on 1st derivatives
since it recursively calls the 0th derivative class
with Sacado AD types, and so the outputValues it passes
to that function needs to have a rank 2 rather than rank 3
*/
template<typename Scalar,typename ArrayScalar>
class TabulatorTet<Scalar,ArrayScalar,1>
{
public:
/** \brief basic tabulate mathod evaluates the first derivatives
of the basis functions at inputPoints into outputValues.
\param [out] outputValues - rank 3 array (F,P,D) holding
the derivatives of basis functions at points.
\param [in] deg - the degree up to which to tabulate the bases
\param [in] inputPoints - a rank 3 array containing the
points at which to evaluate the basis functions.
*/
static void tabulate( ArrayScalar & outputValues ,
const int deg ,
const ArrayScalar &inputPoints );
};
}// namespace Intrepid
#include "Intrepid_HGRAD_TET_Cn_FEM_ORTHDef.hpp"
#endif
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