Intrepid
Intrepid_HGRAD_TET_Cn_FEM_ORTH.hpp
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43 
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 
55 namespace Intrepid {
56 
66 template<class Scalar, class ArrayScalar>
67 class Basis_HGRAD_TET_Cn_FEM_ORTH: public Basis<Scalar, ArrayScalar> {
68 private:
71  void initializeTags();
72 
73 public:
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 
118 template<typename Scalar,typename ArrayScalar, unsigned derivOrder>
120 {
121 public:
131  static void tabulate( ArrayScalar & outputValues ,
132  const int deg ,
133  const ArrayScalar &inputPoints );
134 };
135 
136 
141 template<typename Scalar,typename ArrayScalar>
142 class TabulatorTet<Scalar,ArrayScalar,0>
143 {
144 public:
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 
209 template<typename Scalar,typename ArrayScalar>
210 class TabulatorTet<Scalar,ArrayScalar,1>
211 {
212 public:
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 
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, int r)
function for indexing from orthogonal expansion indices into linear space p+q+r = the degree of the p...
void getValues(ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
Evaluation of a FEM basis on a reference Tetrahedron cell.
Definition file for FEM orthogonal basis functions of arbitrary degree for H(grad) functions on TET...
Header file for the abstract base class Intrepid::Basis.
An abstract base class that defines interface for concrete basis implementations for Finite Element (...
void initializeTags()
Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.
This is an internal class with a static member function for tabulating derivatives of orthogonal expa...
Implementation of the default H(grad)-compatible orthogonal basis of arbitrary degree on tetrahedron...
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...