Intrepid
Intrepid_HGRAD_TRI_Cn_FEM_ORTH.hpp
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43
49#ifndef INTREPID_HGRAD_TRI_Cn_FEM_ORTHHPP
50#define INTREPID_HGRAD_TRI_Cn_FEM_ORTHHPP
51
52#include "Intrepid_Basis.hpp"
53#include "Sacado.hpp"
54namespace Intrepid {
55
65template<class Scalar, class ArrayScalar>
66class Basis_HGRAD_TRI_Cn_FEM_ORTH: public Basis<Scalar, ArrayScalar> {
67private:
70 void initializeTags();
71
72public:
73
77 Basis_HGRAD_TRI_Cn_FEM_ORTH( int degree );
78
79
90 void getValues(ArrayScalar & outputValues,
91 const ArrayScalar & inputPoints,
92 const EOperator operatorType) const;
93
94
97 void getValues(ArrayScalar & outputValues,
98 const ArrayScalar & inputPoints,
99 const ArrayScalar & cellVertices,
100 const EOperator operatorType = OPERATOR_VALUE) const;
101
102};
103
117template<typename Scalar,typename ArrayScalar, unsigned derivOrder>
119{
120public:
130 static void tabulate( ArrayScalar & outputValues ,
131 const int deg ,
132 const ArrayScalar &inputPoints );
133
134
135};
136
137
138
143template<typename Scalar,typename ArrayScalar>
144class TabulatorTri<Scalar,ArrayScalar,0>
145{
146public:
155 static void tabulate( ArrayScalar & outputValues ,
156 const int deg ,
157 const ArrayScalar &inputPoints );
158
164 static int idx(int p, int q)
165 {
166 return (p+q)*(p+q+1)/2+q;
167 }
168
187 static void jrc(const Scalar &alpha , const Scalar &beta ,
188 const int &n ,
189 Scalar &an , Scalar &bn, Scalar &cn )
190 {
191 an = (2.0 * n + 1.0 + alpha + beta) * ( 2.0 * n + 2.0 + alpha + beta )
192 / ( 2.0 * ( n + 1 ) * ( n + 1 + alpha + beta ) );
193 bn = (alpha*alpha-beta*beta)*(2.0*n+1.0+alpha+beta)
194 / ( 2.0*(n+1.0)*(2.0*n+alpha+beta)*(n+1.0+alpha+beta) );
195 cn = (n+alpha)*(n+beta)*(2.0*n+2.0+alpha+beta)
196 / ( (n+1.0)*(n+1.0+alpha+beta)*(2.0*n+alpha+beta) );
197
198 return;
199 }
200
201
202
203};
204
211template<typename Scalar,typename ArrayScalar>
212class TabulatorTri<Scalar,ArrayScalar,1>
213{
214public:
224 static void tabulate( ArrayScalar & outputValues ,
225 const int deg ,
226 const ArrayScalar &inputPoints );
227
228};
229
230
231
232}// namespace Intrepid
233
235
236#endif
237
Header file for the abstract base class Intrepid::Basis.
Definition file for FEM orthogonal basis functions of arbitrary degree for H(grad) functions on TRI.
Implementation of the default H(grad)-compatible orthogonal basis (Dubiner) of arbitrary degree on tr...
void getValues(ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
Evaluation of a FEM basis on a reference Triangle cell.
void initializeTags()
Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.
An abstract base class that defines interface for concrete basis implementations for Finite Element (...
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
static int idx(int p, int q)
function for indexing from orthogonal expansion indices into linear space p+q = the degree of the pol...
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...