1 |
/* $Id$ */ |
2 |
|
3 |
/**************************************************************/ |
4 |
|
5 |
/* Finley: */ |
6 |
|
7 |
/**************************************************************/ |
8 |
|
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/* Copyrights by ACcESS Australia 2003 */ |
10 |
/* Author: gross@access.edu.au */ |
11 |
/* Version: $Id$ */ |
12 |
|
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/**************************************************************/ |
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|
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#include "Common.h" |
16 |
#include "Finley.h" |
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#include "Quadrature.h" |
18 |
|
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#define QUADNODES(_K_,_I_) quadNodes[INDEX2(_K_,_I_,DIM)] |
20 |
#define QUADWEIGHTS(_I_) quadWeights[_I_] |
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|
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/**************************************************************/ |
23 |
|
24 |
/* get a quadrature scheme with numQuadNodes quadrature nodes for the tri */ |
25 |
/* as a queezed scheme on a quad [0,1]^2 */ |
26 |
|
27 |
void Finley_Quad_getNodesTri(int numQuadNodes,double* quadNodes,double* quadWeights) { |
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int i; |
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double Q1,Q2; |
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#define DIM 2 |
31 |
|
32 |
/* the easy case: */ |
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|
34 |
if (numQuadNodes==1) { |
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QUADNODES(0,0)=1./3.; |
36 |
QUADNODES(1,0)=1./3.; |
37 |
QUADWEIGHTS(0)= .5; |
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} else { |
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|
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/* get scheme on [0.1]^2 */ |
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|
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Finley_Quad_getNodesRec(numQuadNodes,quadNodes,quadWeights); |
43 |
if (Finley_ErrorCode!=NO_ERROR) return; |
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|
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/* squeeze it: */ |
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|
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for (i=0;i<numQuadNodes;i++) { |
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Q1=QUADNODES(0,i); |
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Q2=QUADNODES(1,i); |
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QUADWEIGHTS(i)=QUADWEIGHTS(i)*(1.-(1./2.)*(Q1+Q2)); |
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QUADNODES(0,i)=Q1*(1.-(1./2.)*Q2); |
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QUADNODES(1,i)=Q2*(1.-(1./2.)*Q1); |
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} |
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} |
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#undef DIM |
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} |
57 |
|
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/**************************************************************/ |
59 |
|
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/* get a quadrature scheme with numQuadNodes quadrature nodes for the tet */ |
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/* as a queezed scheme on a hex [0,1]^3 */ |
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|
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void Finley_Quad_getNodesTet(int numQuadNodes,double* quadNodes,double* quadWeights) { |
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int i; |
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double Q1,Q2,Q3,JA11,JA12,JA13,JA21,JA22,JA23,JA31,JA32,JA33,DET; |
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#define DIM 3 |
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|
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/* the easy case: */ |
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|
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if (numQuadNodes==1) { |
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QUADNODES(0,0)= .25; |
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QUADNODES(1,0)= .25; |
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QUADNODES(2,0)= .25; |
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QUADWEIGHTS(0)=1./6.; |
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} else { |
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|
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/* get scheme on [0.1]^3 */ |
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|
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Finley_Quad_getNodesHex(numQuadNodes,quadNodes,quadWeights); |
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if (Finley_ErrorCode!=NO_ERROR) return; |
81 |
|
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/* squeeze it: */ |
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|
84 |
for (i=0;i<numQuadNodes;i++) { |
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Q1=QUADNODES(0,i); |
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Q2=QUADNODES(1,i); |
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Q3=QUADNODES(2,i); |
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|
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JA11= (1./3.)*Q2*Q3-(1./2.)*(Q2+Q3) +1.; |
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JA12= (1./3.)*Q1*Q3-(1./2.)*Q1; |
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JA13= (1./3.)*Q1*Q2-(1./2.)*Q1; |
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JA21= (1./3.)*Q2*Q3-(1./2.)*Q2; |
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JA22= (1./3.)*Q1*Q3-(1./2.)*(Q1+Q3) +1.; |
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JA23= (1./3.)*Q1*Q2-(1./2.)*Q2; |
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JA31= (1./3.)*Q2*Q3-(1./2.)*Q3; |
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JA32= (1./3.)*Q1*Q3-(1./2.)*Q3; |
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JA33= (1./3.)*Q1*Q2-(1./2.)*(Q1+Q2) +1.; |
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DET=JA11*JA22*JA33+JA12*JA23*JA31+JA13*JA21*JA32-JA13*JA22*JA31-JA11*JA23*JA32-JA12*JA21*JA33; |
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quadWeights[i]=quadWeights[i]*ABS(DET); |
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QUADNODES(0,i)=Q1*((1./3.)*Q2*Q3-(1./2.)*(Q2+Q3)+1.); |
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QUADNODES(1,i)=Q2*((1./3.)*Q1*Q3-(1./2.)*(Q1+Q3)+1.); |
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QUADNODES(2,i)=Q3*((1./3.)*Q1*Q2-(1./2.)*(Q1+Q2)+1.); |
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} |
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} |
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#undef DIM |
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} |
107 |
|
108 |
/**************************************************************/ |
109 |
|
110 |
/* get a quadrature scheme with numQuadNodes quadrature nodes for the quad [0.1]^2 */ |
111 |
/* as a X-product of a 1D scheme. */ |
112 |
|
113 |
void Finley_Quad_getNodesRec(int numQuadNodes,double* quadNodes,double* quadWeights) { |
114 |
int numQuadNodes1d,i,j,l; |
115 |
double quadNodes1d[numQuadNodes],quadWeights1d[numQuadNodes]; |
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#define DIM 2 |
117 |
|
118 |
/* find numQuadNodes1d with numQuadNodes1d**2==numQuadNodes: */ |
119 |
|
120 |
for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) { |
121 |
if (numQuadNodes1d*numQuadNodes1d==numQuadNodes) { |
122 |
|
123 |
/* get 1D scheme: */ |
124 |
|
125 |
Finley_Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d); |
126 |
|
127 |
/* make 2D scheme: */ |
128 |
|
129 |
if (Finley_ErrorCode==NO_ERROR) { |
130 |
l=0; |
131 |
for (i=0;i<numQuadNodes1d;i++) { |
132 |
for (j=0;j<numQuadNodes1d;j++) { |
133 |
QUADNODES(0,l)=quadNodes1d[i]; |
134 |
QUADNODES(1,l)=quadNodes1d[j]; |
135 |
QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j]; |
136 |
l++; |
137 |
} |
138 |
} |
139 |
} |
140 |
return; |
141 |
} |
142 |
} |
143 |
Finley_ErrorCode=VALUE_ERROR; |
144 |
sprintf(Finley_ErrorMsg,"Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes); |
145 |
#undef DIM |
146 |
} |
147 |
|
148 |
/**************************************************************/ |
149 |
|
150 |
/* get a quadrature scheme with numQuadNodes quadrature nodes for the hex [0.1]^3 */ |
151 |
/* as a X-product of a 1D scheme. */ |
152 |
|
153 |
void Finley_Quad_getNodesHex(int numQuadNodes,double* quadNodes,double* quadWeights) { |
154 |
int numQuadNodes1d,i,j,k,l; |
155 |
double quadNodes1d[numQuadNodes],quadWeights1d[numQuadNodes]; |
156 |
#define DIM 3 |
157 |
|
158 |
/* find numQuadNodes1d with numQuadNodes1d**3==numQuadNodes: */ |
159 |
|
160 |
for (numQuadNodes1d=1;numQuadNodes1d<=MAX_numQuadNodesLine;numQuadNodes1d++) { |
161 |
if (numQuadNodes1d*numQuadNodes1d*numQuadNodes1d==numQuadNodes) { |
162 |
|
163 |
/* get 1D scheme: */ |
164 |
|
165 |
Finley_Quad_getNodesLine(numQuadNodes1d,quadNodes1d,quadWeights1d); |
166 |
|
167 |
/* make 3D scheme: */ |
168 |
|
169 |
if (Finley_ErrorCode==NO_ERROR) { |
170 |
l=0; |
171 |
for (i=0;i<numQuadNodes1d;i++) { |
172 |
for (j=0;j<numQuadNodes1d;j++) { |
173 |
for (k=0;k<numQuadNodes1d;k++) { |
174 |
QUADNODES(0,l)=quadNodes1d[i]; |
175 |
QUADNODES(1,l)=quadNodes1d[j]; |
176 |
QUADNODES(2,l)=quadNodes1d[k]; |
177 |
QUADWEIGHTS(l)=quadWeights1d[i]*quadWeights1d[j]*quadWeights1d[k]; |
178 |
l++; |
179 |
} |
180 |
} |
181 |
} |
182 |
} |
183 |
|
184 |
return; |
185 |
} |
186 |
} |
187 |
Finley_ErrorCode=VALUE_ERROR; |
188 |
sprintf(Finley_ErrorMsg,"Illegal number of quadrature nodes %d on hexahedron.",numQuadNodes); |
189 |
#undef DIM |
190 |
} |
191 |
|
192 |
/**************************************************************/ |
193 |
|
194 |
/* get a quadrature scheme with numQuadNodes quadrature nodes for a point. As there */ |
195 |
/* in no quadrature scheme for a point any value for numQuadNodes other than 0 throws */ |
196 |
/* an error. */ |
197 |
|
198 |
void Finley_Quad_getNodesPoint(int numQuadNodes,double* quadNodes,double* quadWeights) { |
199 |
if (numQuadNodes!=0) { |
200 |
Finley_ErrorCode=VALUE_ERROR; |
201 |
sprintf(Finley_ErrorMsg,"There is no quadrature scheme on points."); |
202 |
} |
203 |
} |
204 |
|
205 |
/**************************************************************/ |
206 |
|
207 |
/* get a quadrature scheme with numQuadNodes quadrature nodes on the line [0,1]: */ |
208 |
/* The nodes and weights are set from a table. */ |
209 |
|
210 |
void Finley_Quad_getNodesLine(int numQuadNodes,double* quadNodes,double* quadWeights) { |
211 |
switch(numQuadNodes) { |
212 |
case 1: |
213 |
quadNodes[0]=0.5; |
214 |
quadWeights[0]=1.; |
215 |
break; |
216 |
|
217 |
case 2: |
218 |
quadNodes[0]=(1.-.577350269189626)/2.; |
219 |
quadNodes[1]=(1.+.577350269189626)/2.; |
220 |
quadWeights[0]=.5; |
221 |
quadWeights[1]=.5; |
222 |
break; |
223 |
|
224 |
case 3: |
225 |
quadNodes[0]=(1.-.774596669241483)/2.; |
226 |
quadNodes[1]=.5; |
227 |
quadNodes[2]=(1.+.774596669241483)/2.; |
228 |
quadWeights[0]=5./18.; |
229 |
quadWeights[1]=4./ 9.; |
230 |
quadWeights[2]=5./18.; |
231 |
break; |
232 |
|
233 |
case 4: |
234 |
quadNodes[0]=(1.-.861136311594053)/2.; |
235 |
quadNodes[1]=(1.-.339981043584856)/2.; |
236 |
quadNodes[2]=(1.+.339981043584856)/2.; |
237 |
quadNodes[3]=(1.+.861136311594053)/2.; |
238 |
quadWeights[0]=.347854845137454/2.; |
239 |
quadWeights[1]=.652145154862546/2.; |
240 |
quadWeights[2]=.652145154862546/2.; |
241 |
quadWeights[3]=.347854845137454/2.; |
242 |
break; |
243 |
|
244 |
case 5: |
245 |
quadNodes[0]=(1.-.906179845938664)/2.; |
246 |
quadNodes[1]=(1.-.538469310105683)/2.; |
247 |
quadNodes[2]= .5; |
248 |
quadNodes[3]=(1.+.538469310105683)/2.; |
249 |
quadNodes[4]=(1.+.906179845938664)/2.; |
250 |
quadWeights[0]=.236926885056189/2.; |
251 |
quadWeights[1]=.478628670499366/2.; |
252 |
quadWeights[2]=.568888888888889/2.; |
253 |
quadWeights[3]=.478628670499366/2.; |
254 |
quadWeights[4]=.236926885056189/2.; |
255 |
break; |
256 |
|
257 |
case 6: |
258 |
quadNodes[0]=(1.-.932469514203152)/2.; |
259 |
quadNodes[1]=(1.-.661209386466265)/2.; |
260 |
quadNodes[2]=(1.-.238619186083197)/2.; |
261 |
quadNodes[3]=(1.+.238619186083197)/2.; |
262 |
quadNodes[4]=(1.+.661209386466265)/2.; |
263 |
quadNodes[5]=(1.+.932469514203152)/2.; |
264 |
quadWeights[0]=.171324492379170/2.; |
265 |
quadWeights[1]=.360761573048139/2.; |
266 |
quadWeights[2]=.467913934572691/2.; |
267 |
quadWeights[3]=.467913934572691/2.; |
268 |
quadWeights[4]=.360761573048139/2.; |
269 |
quadWeights[5]=.171324492379170/2.; |
270 |
break; |
271 |
|
272 |
case 7: |
273 |
quadNodes[0]=(1.-.949107912342759)/2.; |
274 |
quadNodes[1]=(1.-.741531185599394)/2.; |
275 |
quadNodes[2]=(1.-.405845151377397)/2.; |
276 |
quadNodes[3]=0.5; |
277 |
quadNodes[4]=(1.+.405845151377397)/2.; |
278 |
quadNodes[5]=(1.+.741531185599394)/2.; |
279 |
quadNodes[6]=(1.+.949107912342759)/2.; |
280 |
quadWeights[0]= .129484966168870/2.; |
281 |
quadWeights[1]= .279705391489277/2.; |
282 |
quadWeights[2]= .381830050505119/2.; |
283 |
quadWeights[3]= .417959183673469/2.; |
284 |
quadWeights[4]= .381830050505119/2.; |
285 |
quadWeights[5]= .279705391489277/2.; |
286 |
quadWeights[6]= .129484966168870/2.; |
287 |
break; |
288 |
|
289 |
case 8: |
290 |
quadNodes[0]=(1.-.960289856497536)/2.; |
291 |
quadNodes[1]=(1.-.796666477413627)/2.; |
292 |
quadNodes[2]=(1.-.525532409916329)/2.; |
293 |
quadNodes[3]=(1.-.183434642495650)/2.; |
294 |
quadNodes[4]=(1.+.183434642495650)/2.; |
295 |
quadNodes[5]=(1.+.525532409916329)/2.; |
296 |
quadNodes[6]=(1.+.796666477413627)/2.; |
297 |
quadNodes[7]=(1.+.960289856497536)/2.; |
298 |
quadWeights[0]= .101228536290376/2.; |
299 |
quadWeights[1]= .222381034453374/2.; |
300 |
quadWeights[2]= .313706645877887/2.; |
301 |
quadWeights[3]= .362683783378362/2.; |
302 |
quadWeights[4]= .362683783378362/2.; |
303 |
quadWeights[5]= .313706645877887/2.; |
304 |
quadWeights[6]= .222381034453374/2.; |
305 |
quadWeights[7]= .101228536290376/2.; |
306 |
break; |
307 |
|
308 |
case 9: |
309 |
quadNodes[0]=(1.-.968160239507626)/2.; |
310 |
quadNodes[1]=(1.-.836031107326636)/2.; |
311 |
quadNodes[2]=(1.-.613371432700590)/2.; |
312 |
quadNodes[3]=(1.-.324253423403809)/2.; |
313 |
quadNodes[4]= .5; |
314 |
quadNodes[5]=(1.+.324253423403809)/2.; |
315 |
quadNodes[6]=(1.+.613371432700590)/2.; |
316 |
quadNodes[7]=(1.+.836031107326636)/2.; |
317 |
quadNodes[8]=(1.+.968160239507626)/2.; |
318 |
quadWeights[0]= .081274388361574/2.; |
319 |
quadWeights[1]= .180648160694857/2.; |
320 |
quadWeights[2]= .260610696402935/2.; |
321 |
quadWeights[3]= .312347077040003/2.; |
322 |
quadWeights[4]= .330239355001260/2.; |
323 |
quadWeights[5]= .312347077040003/2.; |
324 |
quadWeights[6]= .260610696402935/2.; |
325 |
quadWeights[7]= .180648160694857/2.; |
326 |
quadWeights[8]= .081274388361574/2.; |
327 |
break; |
328 |
|
329 |
case 10: |
330 |
quadNodes[0]=(1.-.973906528517172)/2.; |
331 |
quadNodes[1]=(1.-.865063366688985)/2.; |
332 |
quadNodes[2]=(1.-.679409568299024)/2.; |
333 |
quadNodes[3]=(1.-.433395394129247)/2.; |
334 |
quadNodes[4]=(1.-.148874338981631)/2.; |
335 |
quadNodes[5]=(1.+.148874338981631)/2.; |
336 |
quadNodes[6]=(1.+.433395394129247)/2.; |
337 |
quadNodes[7]=(1.+.679409568299024)/2.; |
338 |
quadNodes[8]=(1.+.865063366688985)/2.; |
339 |
quadNodes[9]=(1.+.973906528517172)/2.; |
340 |
quadWeights[0]= .066671344308688/2.; |
341 |
quadWeights[1]= .149451349150581/2.; |
342 |
quadWeights[2]= .219086362515982/2.; |
343 |
quadWeights[3]= .269266719309996/2.; |
344 |
quadWeights[4]= .295524224714753/2.; |
345 |
quadWeights[5]= .295524224714753/2.; |
346 |
quadWeights[6]= .269266719309996/2.; |
347 |
quadWeights[7]= .219086362515982/2.; |
348 |
quadWeights[8]= .149451349150581/2.; |
349 |
quadWeights[9]= .066671344308688/2.; |
350 |
break; |
351 |
|
352 |
default: |
353 |
Finley_ErrorCode=VALUE_ERROR; |
354 |
sprintf(Finley_ErrorMsg,"Negative intergration order."); |
355 |
break; |
356 |
} |
357 |
} |
358 |
/**************************************************************/ |
359 |
/* */ |
360 |
/* the following function are used define the meshes on the surface in the xy-plane */ |
361 |
|
362 |
/* triangle surface on a tetrahedron */ |
363 |
void Finley_Quad_getNodesTriOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
364 |
Finley_Quad_makeNodesOnFace(3,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesTri); |
365 |
} |
366 |
/* rectangular surface on a hexahedron */ |
367 |
void Finley_Quad_getNodesRecOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
368 |
Finley_Quad_makeNodesOnFace(3,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesRec); |
369 |
} |
370 |
/* line surface on a triangle or rectangle */ |
371 |
void Finley_Quad_getNodesLineOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
372 |
Finley_Quad_makeNodesOnFace(2,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesLine); |
373 |
} |
374 |
/* point surface on a line */ |
375 |
void Finley_Quad_getNodesPointOnFace(int numQuadNodes,double* quadNodes,double* quadWeights) { |
376 |
Finley_Quad_makeNodesOnFace(1,numQuadNodes,quadNodes,quadWeights,Finley_Quad_getNodesPoint); |
377 |
} |
378 |
|
379 |
void Finley_Quad_makeNodesOnFace(int dim, int numQuadNodes,double* quadNodes,double* quadWeights, Finley_Quad_getNodes getFaceNodes) { |
380 |
int q,i; |
381 |
double quadNodesOnFace[numQuadNodes*(dim-1)]; |
382 |
|
383 |
#define DIM dim |
384 |
getFaceNodes(numQuadNodes,quadNodesOnFace,quadWeights); |
385 |
if (Finley_ErrorCode!=NO_ERROR) return; |
386 |
|
387 |
for (q=0;q<numQuadNodes;q++) { |
388 |
for (i=0;i<dim-1;i++) QUADNODES(i,q)=quadNodesOnFace[INDEX2(i,q,dim-1)]; |
389 |
QUADNODES(dim-1,q)=0; |
390 |
} |
391 |
#undef DIM |
392 |
} |
393 |
|
394 |
/**************************************************************/ |
395 |
|
396 |
/* The following functions Finley_Quad_getNumNodes* return the nmber of quadrature points needed to */ |
397 |
/* achieve a certain accuracy. Notice that for Tet and Tri the the order is increased */ |
398 |
/* to consider the accuracy reduction through the construction process. */ |
399 |
|
400 |
|
401 |
int Finley_Quad_getNumNodesPoint(int order) { |
402 |
if (order <0 ) { |
403 |
Finley_ErrorCode=VALUE_ERROR; |
404 |
sprintf(Finley_ErrorMsg,"Negative intergration order."); |
405 |
return -1; |
406 |
} else { |
407 |
return 0; |
408 |
} |
409 |
} |
410 |
|
411 |
int Finley_Quad_getNumNodesLine(int order) { |
412 |
if (order <0 ) { |
413 |
Finley_ErrorCode=VALUE_ERROR; |
414 |
sprintf(Finley_ErrorMsg,"Negative intergration order."); |
415 |
return -1; |
416 |
} else { |
417 |
if (order > 2*MAX_numQuadNodesLine-1) { |
418 |
Finley_ErrorCode=VALUE_ERROR; |
419 |
sprintf(Finley_ErrorMsg,"requested integration order %d on line is too large (>%d).", |
420 |
order,2*MAX_numQuadNodesLine-1); |
421 |
return -1; |
422 |
} else { |
423 |
Finley_ErrorCode=NO_ERROR; |
424 |
return order/2+1; |
425 |
} |
426 |
} |
427 |
} |
428 |
|
429 |
int Finley_Quad_getNumNodesTri(int order) { |
430 |
int numQuadNodesLine; |
431 |
if (order==1) { |
432 |
return 1; |
433 |
} else { |
434 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order+1); |
435 |
if (Finley_ErrorCode==NO_ERROR) { |
436 |
return numQuadNodesLine*numQuadNodesLine; |
437 |
} else { |
438 |
return -1; |
439 |
} |
440 |
} |
441 |
} |
442 |
|
443 |
int Finley_Quad_getNumNodesRec(int order) { |
444 |
int numQuadNodesLine; |
445 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order); |
446 |
if (Finley_ErrorCode==NO_ERROR) { |
447 |
return numQuadNodesLine*numQuadNodesLine; |
448 |
} else { |
449 |
return -1; |
450 |
} |
451 |
} |
452 |
|
453 |
int Finley_Quad_getNumNodesTet(int order) { |
454 |
int numQuadNodesLine; |
455 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order+2); |
456 |
if (Finley_ErrorCode==NO_ERROR) { |
457 |
return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine; |
458 |
} else { |
459 |
return -1; |
460 |
} |
461 |
} |
462 |
|
463 |
int Finley_Quad_getNumNodesHex(int order) { |
464 |
int numQuadNodesLine; |
465 |
numQuadNodesLine=Finley_Quad_getNumNodesLine(order); |
466 |
if (Finley_ErrorCode==NO_ERROR) { |
467 |
return numQuadNodesLine*numQuadNodesLine*numQuadNodesLine; |
468 |
} else { |
469 |
return -1; |
470 |
} |
471 |
} |
472 |
/* |
473 |
* $Log$ |
474 |
* Revision 1.1 2004/10/26 06:53:57 jgs |
475 |
* Initial revision |
476 |
* |
477 |
* Revision 1.2 2004/08/03 04:49:06 gross |
478 |
* bug in Quadrature.c fixed |
479 |
* |
480 |
* Revision 1.1.1.1 2004/06/24 04:00:40 johng |
481 |
* Initial version of eys using boost-python. |
482 |
* |
483 |
* |
484 |
*/ |