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"
54 namespace Intrepid {
55 
65 template<class Scalar, class ArrayScalar>
66 class Basis_HGRAD_TRI_Cn_FEM_ORTH: public Basis<Scalar, ArrayScalar> {
67 private:
70  void initializeTags();
71 
72 public:
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 
117 template<typename Scalar,typename ArrayScalar, unsigned derivOrder>
119 {
120 public:
130  static void tabulate( ArrayScalar & outputValues ,
131  const int deg ,
132  const ArrayScalar &inputPoints );
133 
134 
135 };
136 
137 
138 
143 template<typename Scalar,typename ArrayScalar>
144 class TabulatorTri<Scalar,ArrayScalar,0>
145 {
146 public:
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 
211 template<typename Scalar,typename ArrayScalar>
212 class TabulatorTri<Scalar,ArrayScalar,1>
213 {
214 public:
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 
238 
239 #if defined(Intrepid_SHOW_DEPRECATED_WARNINGS)
240 #ifdef __GNUC__
241 #warning "The Intrepid package is deprecated"
242 #endif
243 #endif
244 
Implementation of the default H(grad)-compatible orthogonal basis (Dubiner) of arbitrary degree on tr...
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
void getValues(ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
Evaluation of a FEM basis on a reference Triangle cell.
static int idx(int p, int q)
function for indexing from orthogonal expansion indices into linear space p+q = the degree of the pol...
void initializeTags()
Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.
Header file for the abstract base class Intrepid::Basis.
An abstract base class that defines interface for concrete basis implementations for Finite Element (...
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...
Definition file for FEM orthogonal basis functions of arbitrary degree for H(grad) functions on TRI...
This is an internal class with a static member function for tabulating derivatives of orthogonal expa...