Intrepid
Intrepid_HGRAD_LINE_Cn_FEM_JACOBIDef.hpp
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1#ifndef INTREPID_HGRAD_LINE_CN_FEM_JACOBIDEF_HPP
2#define INTREPID_HGRAD_LINE_CN_FEM_JACOBIDEF_HPP
3// @HEADER
4// ************************************************************************
5//
6// Intrepid Package
7// Copyright (2007) Sandia Corporation
8//
9// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
10// license for use of this work by or on behalf of the U.S. Government.
11//
12// Redistribution and use in source and binary forms, with or without
13// modification, are permitted provided that the following conditions are
14// met:
15//
16// 1. Redistributions of source code must retain the above copyright
17// notice, this list of conditions and the following disclaimer.
18//
19// 2. Redistributions in binary form must reproduce the above copyright
20// notice, this list of conditions and the following disclaimer in the
21// documentation and/or other materials provided with the distribution.
22//
23// 3. Neither the name of the Corporation nor the names of the
24// contributors may be used to endorse or promote products derived from
25// this software without specific prior written permission.
26//
27// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
28// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
29// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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31// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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38//
39// Questions? Contact Pavel Bochev (pbboche@sandia.gov)
40// Denis Ridzal (dridzal@sandia.gov), or
41// Kara Peterson (kjpeter@sandia.gov)
42//
43// ************************************************************************
44// @HEADER
45
51namespace Intrepid {
52
53
54template<class Scalar, class ArrayScalar>
56 this -> basisCardinality_ = order+1;
57 this -> basisDegree_ = order;
58 this -> jacobiAlpha_ = alpha;
59 this -> jacobiBeta_ = beta;
60 this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Line<> >() );
61 this -> basisType_ = BASIS_FEM_HIERARCHICAL;
62 this -> basisCoordinates_ = COORDINATES_CARTESIAN;
63 this -> basisTagsAreSet_ = false;
64}
65
66
67
68template<class Scalar, class ArrayScalar>
70 const ArrayScalar & inputPoints,
71 const EOperator operatorType) const {
72
73 // Verify arguments
74#ifdef HAVE_INTREPID_DEBUG
75 Intrepid::getValues_HGRAD_Args<Scalar, ArrayScalar>(outputValues,
76 inputPoints,
77 operatorType,
78 this -> getBaseCellTopology(),
79 this -> getCardinality() );
80#endif
81
82 // Number of evaluation points = dimension 0 of inputPoints
83 int numPoints = inputPoints.dimension(0);
84
85 Teuchos::Array<Scalar> tmpPoints(numPoints);
86 Teuchos::Array<Scalar> jacobiPolyAtPoints(numPoints);
87
88 // Copy inputPoints into tmpPoints, to prepare for call to jacobfd
89 for (int i=0; i<numPoints; i++) {
90 tmpPoints[i] = inputPoints(i, 0);
91 }
92
93 try {
94 switch (operatorType) {
95 case OPERATOR_VALUE: {
96 for (int ord = 0; ord < this -> basisCardinality_; ord++) {
97 IntrepidPolylib::jacobfd(numPoints, &tmpPoints[0], &jacobiPolyAtPoints[0], (Scalar*)0, ord, jacobiAlpha_, jacobiBeta_);
98 for (int pt = 0; pt < numPoints; pt++) {
99 // outputValues is a rank-2 array with dimensions (basisCardinality_, numPoints)
100 outputValues(ord, pt) = jacobiPolyAtPoints[pt];
101 }
102 }
103 }
104 break;
105
106 case OPERATOR_GRAD:
107 case OPERATOR_D1: {
108 for (int ord = 0; ord < this -> basisCardinality_; ord++) {
109 IntrepidPolylib::jacobd(numPoints, &tmpPoints[0], &jacobiPolyAtPoints[0], ord, jacobiAlpha_, jacobiBeta_);
110 for (int pt = 0; pt < numPoints; pt++) {
111 // outputValues is a rank-2 array with dimensions (basisCardinality_, numPoints)
112 outputValues(ord, pt, 0) = jacobiPolyAtPoints[pt];
113 }
114 }
115 }
116 break;
117
118 case OPERATOR_D2:
119 case OPERATOR_D3:
120 case OPERATOR_D4:
121 case OPERATOR_D5:
122 case OPERATOR_D6:
123 case OPERATOR_D7:
124 case OPERATOR_D8:
125 case OPERATOR_D9:
126 case OPERATOR_D10: {
127 int d_order = getOperatorOrder( operatorType );
128 // fill in derivatives of polynomials of degree 0 through d_order - 1 with 0
129 // e.g. D2 annhialates linears.
130 int stop_order;
131 if (d_order > this->getDegree()) {
132 stop_order = this->getDegree();
133 }
134 else {
135 stop_order = d_order;
136 }
137 for (int p_order=0;p_order<stop_order;p_order++) {
138 for (int pt=0;pt<numPoints;pt++) {
139 outputValues(p_order,pt,0) = 0.0;
141 }
142 // fill in rest of derivatives with the differentiation rule for Jacobi polynomials
143 for (int p_order=d_order;p_order<=this->getDegree();p_order++) {
144 // calculate the scaling factor with a little loop.
145 Scalar scalefactor = 1.0;
146 for (int d=1;d<=d_order;d++) {
147 scalefactor *= 0.5 * ( p_order + jacobiAlpha_ + jacobiBeta_ + d );
148 }
149
150 // put in the right call to IntrepidPolyLib
151 IntrepidPolylib::jacobfd(numPoints, &tmpPoints[0],
152 &jacobiPolyAtPoints[0],
153 (Scalar*)0, p_order-d_order,
154 jacobiAlpha_ + d_order,
155 jacobiBeta_ + d_order);
156 for (int pt = 0; pt < numPoints; pt++) {
157 // outputValues is a rank-3 array with dimensions (basisCardinality_, numPoints)
158 outputValues(p_order, pt,0) = scalefactor *jacobiPolyAtPoints[pt];
160
161 }
162
163 }
164 break;
165 case OPERATOR_DIV:
166 case OPERATOR_CURL:
167 TEUCHOS_TEST_FOR_EXCEPTION( !( Intrepid::isValidOperator(operatorType) ), std::invalid_argument,
168 ">>> ERROR (Basis_HGRAD_LINE_Cn_FEM_JACOBI): Invalid operator type.");
169 break;
170 default:
171 TEUCHOS_TEST_FOR_EXCEPTION( !( Intrepid::isValidOperator(operatorType) ), std::invalid_argument,
172 ">>> ERROR (Basis_HGRAD_LINE_Cn_FEM_JACOBI): Invalid operator type.");
173 break;
174 }
176 catch (std::invalid_argument &exception){
177 TEUCHOS_TEST_FOR_EXCEPTION( true , std::invalid_argument,
178 ">>> ERROR (Basis_HGRAD_LINE_Cn_FEM_JACOBI): Operator failed");
179 }
180}
181
182
183
184template<class Scalar, class ArrayScalar>
186 const ArrayScalar & inputPoints,
187 const ArrayScalar & cellVertices,
188 const EOperator operatorType) const {
189 TEUCHOS_TEST_FOR_EXCEPTION( (true), std::logic_error,
190 ">>> ERROR (Basis_HGRAD_LINE_Cn_FEM_JACOBI): FEM Basis calling an FVD member function");
191}
192
193
194
195template<class Scalar, class ArrayScalar>
197 this -> basisCardinality_ = n+1;
198 this -> basisDegree_ = n;
199 this -> jacobiAlpha_ = alpha;
200 this -> jacobiBeta_ = beta;
201 this -> initializeTags();
202}
203
204
205
206template<class Scalar, class ArrayScalar>
208
209 // Basis-dependent initializations
210
211 int tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
212 int posScDim = 0; // position in the tag, counting from 0, of the subcell dim
213 int posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
214 int posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
215
216 FieldContainer<int> tags(this->basisCardinality_, 4);
217
218 for (int i=0; i < this->basisCardinality_; i++) {
219 tags(i, 0) = 1; // these are all "internal" i.e. "volume" DoFs
220 tags(i, 1) = 0; // there is only one line
221 tags(i, 2) = i; // local DoF id
222 tags(i, 3) = this->basisCardinality_; // total number of DoFs
223 }
224
225 // Basis-independent function, sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
226 Intrepid::setOrdinalTagData(this -> tagToOrdinal_,
227 this -> ordinalToTag_,
228 &tags[0],
229 this -> basisCardinality_,
230 tagSize,
231 posScDim,
232 posScOrd,
233 posDfOrd);
234}
235
236}// namespace Intrepid
237#endif
void setOrdinalTagData(std::vector< std::vector< std::vector< int > > > &tagToOrdinal, std::vector< std::vector< int > > &ordinalToTag, const int *tags, const int basisCard, const int tagSize, const int posScDim, const int posScOrd, const int posDfOrd)
Fills ordinalToTag_ and tagToOrdinal_ by basis-specific tag data.
int getOperatorOrder(const EOperator operatorType)
Returns order of an operator.
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 Line cell.
void setBasisParameters(int n, Scalar alpha=0, Scalar beta=0)
Sets private data basisDegree_, basisCardinality_, jacobiAlpha_, and jacobiBeta_, to n,...
Basis_HGRAD_LINE_Cn_FEM_JACOBI(int order, Scalar alpha=0, Scalar beta=0)
Constructor.
Implementation of a templated lexicographical container for a multi-indexed scalar quantity....
static void jacobfd(const int np, const Scalar *z, Scalar *poly_in, Scalar *polyd, const int n, const Scalar alpha, const Scalar beta)
Routine to calculate Jacobi polynomials, , and their first derivative, .
static void jacobd(const int np, const Scalar *z, Scalar *polyd, const int n, const Scalar alpha, const Scalar beta)
Calculate the derivative of Jacobi polynomials.