Intrepid
Intrepid_HGRAD_TET_Cn_FEM_ORTH.hpp
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49#ifndef INTREPID_HGRAD_TET_Cn_FEM_ORTH_HPP
50#define INTREPID_HGRAD_TET_Cn_FEM_ORTH_HPP
51
52#include "Intrepid_Basis.hpp"
53#include "Sacado.hpp"
54
55namespace Intrepid {
56
66template<class Scalar, class ArrayScalar>
67class Basis_HGRAD_TET_Cn_FEM_ORTH: public Basis<Scalar, ArrayScalar> {
68private:
71 void initializeTags();
72
73public:
74
78 Basis_HGRAD_TET_Cn_FEM_ORTH( int degree );
79
80
91 void getValues(ArrayScalar & outputValues,
92 const ArrayScalar & inputPoints,
93 const EOperator operatorType) const;
94
95
98 void getValues(ArrayScalar & outputValues,
99 const ArrayScalar & inputPoints,
100 const ArrayScalar & cellVertices,
101 const EOperator operatorType = OPERATOR_VALUE) const;
102
103};
104
118template<typename Scalar,typename ArrayScalar, unsigned derivOrder>
120{
121public:
131 static void tabulate( ArrayScalar & outputValues ,
132 const int deg ,
133 const ArrayScalar &inputPoints );
134};
135
136
141template<typename Scalar,typename ArrayScalar>
142class TabulatorTet<Scalar,ArrayScalar,0>
143{
144public:
153 static void tabulate( ArrayScalar & outputValues ,
154 const int deg ,
155 const ArrayScalar &inputPoints );
156
162 static int idx(int p, int q,int r)
163 {
164 return (p+q+r)*(p+q+r+1)*(p+q+r+2)/6+(q+r)*(q+r+1)/2+r;
165 }
166
184 static void jrc( const Scalar &alpha , const Scalar &beta ,
185 const int &n ,
186 Scalar &an , Scalar &bn, Scalar &cn )
187
188 {
189 an = (2.0 * n + 1.0 + alpha + beta) * ( 2.0 * n + 2.0 + alpha + beta )
190 / ( 2.0 * ( n + 1 ) * ( n + 1 + alpha + beta ) );
191 bn = (alpha*alpha-beta*beta)*(2.0*n+1.0+alpha+beta)
192 / ( 2.0*(n+1.0)*(2.0*n+alpha+beta)*(n+1.0+alpha+beta) );
193 cn = (n+alpha)*(n+beta)*(2.0*n+2.0+alpha+beta)
194 / ( (n+1.0)*(n+1.0+alpha+beta)*(2.0*n+alpha+beta) );
195
196 return;
197 }
198
199
200
201};
202
209template<typename Scalar,typename ArrayScalar>
210class TabulatorTet<Scalar,ArrayScalar,1>
211{
212public:
222 static void tabulate( ArrayScalar & outputValues ,
223 const int deg ,
224 const ArrayScalar &inputPoints );
225
226};
227
228
229
230}// namespace Intrepid
231
233
234#endif
235
Header file for the abstract base class Intrepid::Basis.
Definition file for FEM orthogonal basis functions of arbitrary degree for H(grad) functions on TET.
Implementation of the default H(grad)-compatible orthogonal basis of arbitrary degree on tetrahedron.
void initializeTags()
Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.
void getValues(ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
Evaluation of a FEM basis on a reference Tetrahedron cell.
An abstract base class that defines interface for concrete basis implementations for Finite Element (...
static int idx(int p, int q, int r)
function for indexing from orthogonal expansion indices into linear space p+q+r = the degree of the p...
static void jrc(const Scalar &alpha, const Scalar &beta, const int &n, Scalar &an, Scalar &bn, Scalar &cn)
function for computing the Jacobi recurrence coefficients so that
This is an internal class with a static member function for tabulating derivatives of orthogonal expa...
static void tabulate(ArrayScalar &outputValues, const int deg, const ArrayScalar &inputPoints)
basic tabulate mathod evaluates the derivOrder^th derivatives of the basis functions at inputPoints i...