Intrepid
Intrepid_CubatureSparseDef.hpp
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43
50namespace Intrepid {
51
52/**************************************************************************
53** Function Definitions for Class CubatureSparse
54***************************************************************************/
55
56template <class Scalar, int dimension_, class ArrayPoint, class ArrayWeight>
57CubatureSparse<Scalar,dimension_,ArrayPoint,ArrayWeight>::CubatureSparse(const int degree) :
58 degree_(degree) {
59
60 if(dimension_ == 2)
61 {
62 if(degree == 1)
63 level_ = 1;
64 else if(degree <= 3)
65 level_ = 2;
66 else if(degree <= 7)
67 level_ = 3;
68 else if(degree <= 11)
69 level_ = 4;
70 else if(degree <= 15)
71 level_ = 5;
72 else if(degree <= 19)
73 level_ = 6;
74 else if(degree <= 23)
75 level_ = 7;
76 else if(degree <= 27)
77 level_ = 8;
78 else if(degree <= 31)
79 level_ = 9;
80 else if(degree <= 35)
81 level_ = 10;
82 else if(degree <= 39)
83 level_ = 11;
84 else if(degree <= 43)
85 level_ = 12;
86 else if(degree <= 47)
87 level_ = 13;
88 else if(degree <= 51)
89 level_ = 14;
90 else if(degree <= 55)
91 level_ = 15;
92 else if(degree <= 59)
93 level_ = 16;
94 }
95 else if(dimension_ == 3)
96 {
97 if(degree == 1)
98 level_ = 1;
99 else if(degree <= 3)
100 level_ = 2;
101 else if(degree <= 5)
102 level_ = 3;
103 else if(degree <= 9)
104 level_ = 4;
105 else if(degree <= 13)
106 level_ = 5;
107 else if(degree <= 17)
108 level_ = 6;
109 else if(degree <= 21)
110 level_ = 7;
111 else if(degree <= 25)
112 level_ = 8;
113 else if(degree <= 29)
114 level_ = 9;
115 else if(degree <= 33)
116 level_ = 10;
117 else if(degree <= 37)
118 level_ = 11;
119 else if(degree <= 41)
120 level_ = 12;
121 else if(degree <= 45)
122 level_ = 13;
123 else if(degree <= 49)
124 level_ = 14;
125 else if(degree <= 53)
126 level_ = 15;
127 else if(degree <= 57)
128 level_ = 16;
129 }
130
131 numPoints_ = calculateNumPoints(dimension_,level_);
132}
133
134
135
136template <class Scalar, int dimension_, class ArrayPoint, class ArrayWeight>
138 ArrayWeight & cubWeights) const{
139 Teuchos::Array<Scalar> dummy_point(1);
140 dummy_point[0] = 0.0;
141 Scalar dummy_weight = 1.0;
142 SGNodes<Scalar, dimension_> grid;
143
144 iterateThroughDimensions(level_, dimension_, grid, dummy_point, dummy_weight);
145
146 grid.copyToArrays(cubPoints, cubWeights);
147} // end getCubature
148
149template<class Scalar, int dimension_, class ArrayPoint, class ArrayWeight>
151 ArrayWeight& cubWeights,
152 ArrayPoint& cellCoords) const
153{
154 TEUCHOS_TEST_FOR_EXCEPTION( (true), std::logic_error,
155 ">>> ERROR (CubatureSparse): Cubature defined in reference space calling method for physical space cubature.");
156}
157
158
159template <class Scalar, int dimension_, class ArrayPoint, class ArrayWeight>
161 return numPoints_;
162} // end getNumPoints
163
164
165
166template <class Scalar, int dimension_, class ArrayPoint, class ArrayWeight>
168 return dimension_;
169} // end dimension
170
171
172
173template <class Scalar, int dimension_, class ArrayPoint, class ArrayWeight>
175 accuracy.assign(1, degree_);
176} //end getAccuracy
177
178
179
180/************************************************************************
181** Function Definition for iterateThroughDimensions()
182** and its helper functions
183*************************************************************************/
184
185template< class Scalar, int DIM>
186void iterateThroughDimensions(int level,
187 int dims_left,
188 SGNodes<Scalar,DIM> & cubPointsND,
189 Teuchos::Array<Scalar> & partial_node,
190 Scalar partial_weight)
191{
192 int l = level;
193 int d = DIM;
194 int add_on = d - dims_left;
195 int start = dims_left > 1 ? 1 : (int)std::max(1, l);
196 int end = l + add_on;
197
198 for(int k_i = start; k_i <= end; k_i++)
199 {
200 /*******************
201 ** Slow-Gauss
202 ********************/
203 int order1D = 2*k_i-1;
204
205 /*******************
206 ** Fast-Gauss
207 ********************/
208 //int order1D = (int)pow(2,k_i) - 1;
209
210 int cubDegree1D = 2*order1D - 1;
211 CubatureDirectLineGauss<Scalar> Cub1D(cubDegree1D);
212 FieldContainer<Scalar> cubPoints1D(order1D, 1);
213 FieldContainer<Scalar> cubWeights1D(order1D);
214
215 Cub1D.getCubature(cubPoints1D, cubWeights1D);
216
217 for(int node1D = 0; node1D < order1D; node1D++)
218 {
219 Teuchos::Array<Scalar> node(d-dims_left+1);
220 node[d-dims_left] = cubPoints1D(node1D,0);
221 for(int m = 0; m < d-dims_left; m++)
222 node[m] = partial_node[m];
223
224 Scalar weight = cubWeights1D(node1D)*partial_weight;
225
226 if(dims_left != 1)
227 {
228 iterateThroughDimensions(l - k_i, dims_left-1, cubPointsND, node, weight);
229 }
230 else
231 {
232 weight = pow(-1.0, end - k_i)*combination(d-1, k_i - l)*weight;
233 cubPointsND.addNode(&node[0], weight);
234 }
235 }
236 }
237}
238
239} // end namespace Intrepid