/[escript]/trunk/finley/src/Mesh_hex8.c
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Contents of /trunk/finley/src/Mesh_hex8.c

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Revision 1981 - (show annotations)
Thu Nov 6 05:27:33 2008 UTC (10 years, 11 months ago) by jfenwick
File MIME type: text/plain
File size: 21106 byte(s)
More warning removal.

1
2 /*******************************************************
3 *
4 * Copyright (c) 2003-2008 by University of Queensland
5 * Earth Systems Science Computational Center (ESSCC)
6 * http://www.uq.edu.au/esscc
7 *
8 * Primary Business: Queensland, Australia
9 * Licensed under the Open Software License version 3.0
10 * http://www.opensource.org/licenses/osl-3.0.php
11 *
12 *******************************************************/
13
14
15 /**************************************************************/
16
17 /* Finley: generates rectangular meshes */
18
19 /* Generates a numElements[0] x numElements[1] x numElements[2] mesh with first order elements (Hex8) in the brick */
20 /* [0,Length[0]] x [0,Length[1]] x [0,Length[2]]. order is the desired accuracy of the */
21 /* integration scheme. */
22
23 /**************************************************************/
24
25 #include "RectangularMesh.h"
26
27 Finley_Mesh* Finley_RectangularMesh_Hex8(dim_t* numElements,
28 double* Length,
29 bool_t* periodic,
30 index_t order,
31 index_t reduced_order,
32 bool_t useElementsOnFace,
33 bool_t useFullElementOrder,
34 bool_t optimize)
35 {
36 #define N_PER_E 1
37 #define DIM 3
38 dim_t N0,N1,N2,NE0,NE1,NE2,i0,i1,i2,k,Nstride0,Nstride1,Nstride2, local_NE0, local_NE1, local_NE2, local_N0, local_N1, local_N2;
39 dim_t totalNECount,faceNECount,NDOF0,NDOF1,NDOF2,NFaceElements, NN;
40 index_t node0, myRank, e_offset2, e_offset1, e_offset0, offset1, offset2, offset0, global_i0, global_i1, global_i2;
41 Finley_Mesh* out;
42 Paso_MPIInfo *mpi_info = NULL;
43 char name[50];
44 #ifdef Finley_TRACE
45 double time0=Finley_timer();
46 #endif
47
48 /* get MPI information */
49 mpi_info = Paso_MPIInfo_alloc( MPI_COMM_WORLD );
50 if (! Finley_noError()) {
51 return NULL;
52 }
53 myRank=mpi_info->rank;
54
55 /* set up the global dimensions of the mesh */
56
57 NE0=MAX(1,numElements[0]);
58 NE1=MAX(1,numElements[1]);
59 NE2=MAX(1,numElements[2]);
60 N0=N_PER_E*NE0+1;
61 N1=N_PER_E*NE1+1;
62 N2=N_PER_E*NE2+1;
63
64 /* allocate mesh: */
65 sprintf(name,"Rectangular %d x %d x %d mesh",N0,N1,N2);
66 out=Finley_Mesh_alloc(name,DIM,order, reduced_order, mpi_info);
67 if (! Finley_noError()) {
68 Paso_MPIInfo_free( mpi_info );
69 return NULL;
70 }
71
72 Finley_Mesh_setElements(out,Finley_ElementFile_alloc(Hex8,out->order,out->reduced_order,mpi_info));
73 if (useElementsOnFace) {
74 Finley_Mesh_setFaceElements(out,Finley_ElementFile_alloc(Hex8Face,
75 out->order,
76 out->reduced_order,
77 mpi_info));
78 Finley_Mesh_setContactElements(out,Finley_ElementFile_alloc(Hex8Face_Contact,
79 out->order,
80 out->reduced_order,
81 mpi_info));
82 } else {
83 Finley_Mesh_setFaceElements(out,Finley_ElementFile_alloc(Rec4,
84 out->order,
85 out->reduced_order,
86 mpi_info));
87 Finley_Mesh_setContactElements(out,Finley_ElementFile_alloc(Rec4_Contact,
88 out->order,
89 out->reduced_order,
90 mpi_info));
91 }
92 Finley_Mesh_setPoints(out,Finley_ElementFile_alloc(Point1,
93 out->order,
94 out->reduced_order,
95 mpi_info));
96 if (! Finley_noError()) {
97 Paso_MPIInfo_free( mpi_info );
98 Finley_Mesh_free(out);
99 return NULL;
100 }
101
102 /* work out the largest dimension */
103 if (N2==MAX3(N0,N1,N2)) {
104 Nstride0=1;
105 Nstride1=N0;
106 Nstride2=N0*N1;
107 local_NE0=NE0;
108 e_offset0=0;
109 local_NE1=NE1;
110 e_offset1=0;
111 Paso_MPIInfo_Split(mpi_info,NE2,&local_NE2,&e_offset2);
112 } else if (N1==MAX3(N0,N1,N2)) {
113 Nstride0=N2;
114 Nstride1=N0*N2;
115 Nstride2=1;
116 local_NE0=NE0;
117 e_offset0=0;
118 Paso_MPIInfo_Split(mpi_info,NE1,&local_NE1,&e_offset1);
119 local_NE2=NE2;
120 e_offset2=0;
121 } else {
122 Nstride0=N1*N2;
123 Nstride1=1;
124 Nstride2=N1;
125 Paso_MPIInfo_Split(mpi_info,NE0,&local_NE0,&e_offset0);
126 local_NE1=NE1;
127 e_offset1=0;
128 local_NE2=NE2;
129 e_offset2=0;
130 }
131 offset0=e_offset0*N_PER_E;
132 offset1=e_offset1*N_PER_E;
133 offset2=e_offset2*N_PER_E;
134 local_N0=local_NE0>0 ? local_NE0*N_PER_E+1 : 0;
135 local_N1=local_NE1>0 ? local_NE1*N_PER_E+1 : 0;
136 local_N2=local_NE2>0 ? local_NE2*N_PER_E+1 : 0;
137
138 /* get the number of surface elements */
139
140 NFaceElements=0;
141 if (!periodic[2] && (local_NE2>0)) {
142 NDOF2=N2;
143 if (offset2==0) NFaceElements+=local_NE1*local_NE0;
144 if (local_NE2+e_offset2 == NE2) NFaceElements+=local_NE1*local_NE0;
145 } else {
146 NDOF2=N2-1;
147 }
148
149 if (!periodic[0] && (local_NE0>0)) {
150 NDOF0=N0;
151 if (e_offset0 == 0) NFaceElements+=local_NE1*local_NE2;
152 if (local_NE0+e_offset0 == NE0) NFaceElements+=local_NE1*local_NE2;
153 } else {
154 NDOF0=N0-1;
155 }
156 if (!periodic[1] && (local_NE1>0)) {
157 NDOF1=N1;
158 if (e_offset1 == 0) NFaceElements+=local_NE0*local_NE2;
159 if (local_NE1+e_offset1 == NE1) NFaceElements+=local_NE0*local_NE2;
160 } else {
161 NDOF1=N1-1;
162 }
163
164 /* allocate tables: */
165
166 Finley_NodeFile_allocTable(out->Nodes,local_N0*local_N1*local_N2);
167 Finley_ElementFile_allocTable(out->Elements,local_NE0*local_NE1*local_NE2);
168 Finley_ElementFile_allocTable(out->FaceElements,NFaceElements);
169
170 if (Finley_noError()) {
171 /* create nodes */
172
173 #pragma omp parallel for private(i0,i1,i2,k,global_i0,global_i1,global_i2)
174 for (i2=0;i2<local_N2;i2++) {
175 for (i1=0;i1<local_N1;i1++) {
176 for (i0=0;i0<local_N0;i0++) {
177 k=i0+local_N0*i1+local_N0*local_N1*i2;
178 global_i0=i0+offset0;
179 global_i1=i1+offset1;
180 global_i2=i2+offset2;
181 out->Nodes->Coordinates[INDEX2(0,k,DIM)]=DBLE(global_i0)/DBLE(N0-1)*Length[0];
182 out->Nodes->Coordinates[INDEX2(1,k,DIM)]=DBLE(global_i1)/DBLE(N1-1)*Length[1];
183 out->Nodes->Coordinates[INDEX2(2,k,DIM)]=DBLE(global_i2)/DBLE(N2-1)*Length[2];
184 out->Nodes->Id[k]=Nstride0*global_i0+Nstride1*global_i1+Nstride2*global_i2;
185 out->Nodes->Tag[k]=0;
186 out->Nodes->globalDegreesOfFreedom[k]=Nstride0*(global_i0%NDOF0)
187 +Nstride1*(global_i1%NDOF1)
188 +Nstride2*(global_i2%NDOF2);
189 }
190 }
191 }
192 /* set the elements: */
193 NN=out->Elements->numNodes;
194 #pragma omp parallel for private(i0,i1,i2,k,node0)
195 for (i2=0;i2<local_NE2;i2++) {
196 for (i1=0;i1<local_NE1;i1++) {
197 for (i0=0;i0<local_NE0;i0++) {
198
199 k=i0+local_NE0*i1+local_NE0*local_NE1*i2;
200 node0=Nstride0*N_PER_E*(i0+e_offset0)+Nstride1*N_PER_E*(i1+e_offset1)+Nstride2*N_PER_E*(i2+e_offset2);
201
202 out->Elements->Id[k]=(i0+e_offset0)+NE0*(i1+e_offset1)+NE0*NE1*(i2+e_offset2);
203 out->Elements->Tag[k]=0;
204 out->Elements->Owner[k]=myRank;
205
206 out->Elements->Nodes[INDEX2(0,k,NN)] =node0 ;
207 out->Elements->Nodes[INDEX2(1,k,NN)] =node0+ Nstride0;
208 out->Elements->Nodes[INDEX2(2,k,NN)] =node0+ Nstride1+Nstride0;
209 out->Elements->Nodes[INDEX2(3,k,NN)] =node0+ Nstride1;
210 out->Elements->Nodes[INDEX2(4,k,NN)] =node0+Nstride2 ;
211 out->Elements->Nodes[INDEX2(5,k,NN)] =node0+Nstride2 +Nstride0;
212 out->Elements->Nodes[INDEX2(6,k,NN)] =node0+Nstride2+Nstride1+Nstride0;
213 out->Elements->Nodes[INDEX2(7,k,NN)] =node0+Nstride2+Nstride1 ;
214 }
215 }
216 }
217 /* face elements */
218 NN=out->FaceElements->numNodes;
219 totalNECount=NE0*NE1*NE2;
220 faceNECount=0;
221 /* these are the quadrilateral elements on boundary 1 (x3=0): */
222 if (!periodic[2] && (local_NE2>0)) {
223 /* ** elements on boundary 100 (x3=0): */
224 if (e_offset2==0) {
225 #pragma omp parallel for private(i0,i1,k,node0)
226 for (i1=0;i1<local_NE1;i1++) {
227 for (i0=0;i0<local_NE0;i0++) {
228
229 k=i0+local_NE0*i1+faceNECount;
230 node0=Nstride0*N_PER_E*(i0+e_offset0)+Nstride1*N_PER_E*(i1+e_offset1);
231
232 out->FaceElements->Id[k]=(i0+e_offset0)+NE0*(i1+e_offset1)+totalNECount;
233 out->FaceElements->Tag[k]=100;
234 out->FaceElements->Owner[k]=myRank;
235
236 if (useElementsOnFace) {
237 out->FaceElements->Nodes[INDEX2(0,k,NN)] =node0 ;
238 out->FaceElements->Nodes[INDEX2(1,k,NN)] =node0 +Nstride1 ;
239 out->FaceElements->Nodes[INDEX2(2,k,NN)] =node0 +Nstride1+Nstride0;
240 out->FaceElements->Nodes[INDEX2(3,k,NN)] =node0+ Nstride0 ;
241 out->FaceElements->Nodes[INDEX2(4,k,NN)] =node0+Nstride2 ;
242 out->FaceElements->Nodes[INDEX2(5,k,NN)] =node0+Nstride2+Nstride1 ;
243 out->FaceElements->Nodes[INDEX2(6,k,NN)] =node0+Nstride2+Nstride1+Nstride0;
244 out->FaceElements->Nodes[INDEX2(7,k,NN)] =node0+Nstride2 +Nstride0;
245 } else {
246 out->FaceElements->Nodes[INDEX2(0,k,NN)] =node0 ;
247 out->FaceElements->Nodes[INDEX2(1,k,NN)] =node0+ Nstride1 ;
248 out->FaceElements->Nodes[INDEX2(2,k,NN)] =node0+ Nstride1+Nstride0;
249 out->FaceElements->Nodes[INDEX2(3,k,NN)] =node0+ Nstride0;
250 }
251 }
252 }
253 faceNECount+=local_NE1*local_NE0;
254 }
255 totalNECount+=NE1*NE0;
256 /* ** elements on boundary 200 (x3=1) */
257 if (local_NE2+e_offset2 == NE2) {
258 #pragma omp parallel for private(i0,i1,k,node0)
259 for (i1=0;i1<local_NE1;i1++) {
260 for (i0=0;i0<local_NE0;i0++) {
261
262 k=i0+local_NE0*i1+faceNECount;
263 node0=Nstride0*N_PER_E*(i0+e_offset0)+Nstride1*N_PER_E*(i1+e_offset1)+Nstride2*N_PER_E*(NE2-1);
264
265 out->FaceElements->Id[k]=(i0+e_offset0)+NE0*(i1+e_offset1)+totalNECount;
266 out->FaceElements->Tag[k]=200;
267 out->FaceElements->Owner[k]=myRank;
268 if (useElementsOnFace) {
269 out->FaceElements->Nodes[INDEX2(0,k,NN)] =node0+Nstride2 ;
270 out->FaceElements->Nodes[INDEX2(1,k,NN)] =node0+Nstride2+ Nstride0;
271 out->FaceElements->Nodes[INDEX2(2,k,NN)] =node0+Nstride2+Nstride1+Nstride0;
272 out->FaceElements->Nodes[INDEX2(3,k,NN)] =node0+Nstride2+Nstride1 ;
273
274 out->FaceElements->Nodes[INDEX2(4,k,NN)] =node0 ;
275 out->FaceElements->Nodes[INDEX2(5,k,NN)] =node0+Nstride0 ;
276 out->FaceElements->Nodes[INDEX2(6,k,NN)] =node0+ Nstride1+Nstride0;
277 out->FaceElements->Nodes[INDEX2(7,k,NN)] =node0+ Nstride1;
278 } else {
279 out->FaceElements->Nodes[INDEX2(0,k,NN)] =node0+Nstride2 ;
280 out->FaceElements->Nodes[INDEX2(1,k,NN)] =node0+Nstride2 +Nstride0;
281 out->FaceElements->Nodes[INDEX2(2,k,NN)] =node0+Nstride2+Nstride1+Nstride0;
282 out->FaceElements->Nodes[INDEX2(3,k,NN)] =node0+Nstride2+Nstride1 ;
283 }
284 }
285 }
286 faceNECount+=local_NE1*local_NE0;
287 }
288 totalNECount+=NE1*NE0;
289 }
290 if (!periodic[0] && (local_NE0>0)) {
291 /* ** elements on boundary 001 (x1=0): */
292
293 if (e_offset0 == 0) {
294 #pragma omp parallel for private(i1,i2,k,node0)
295 for (i2=0;i2<local_NE2;i2++) {
296 for (i1=0;i1<local_NE1;i1++) {
297
298 k=i1+local_NE1*i2+faceNECount;
299 node0=Nstride1*N_PER_E*(i1+e_offset1)+Nstride2*N_PER_E*(i2+e_offset2);
300 out->FaceElements->Id[k]=(i1+e_offset1)+NE1*(i2+e_offset2)+totalNECount;
301 out->FaceElements->Tag[k]=1;
302 out->FaceElements->Owner[k]=myRank;
303
304 if (useElementsOnFace) {
305 out->FaceElements->Nodes[INDEX2(0,k,NN)] =node0 ;
306 out->FaceElements->Nodes[INDEX2(1,k,NN)] =node0+Nstride2 ;
307 out->FaceElements->Nodes[INDEX2(2,k,NN)] =node0+Nstride2+Nstride1 ;
308 out->FaceElements->Nodes[INDEX2(3,k,NN)] =node0+Nstride1 ;
309 out->FaceElements->Nodes[INDEX2(4,k,NN)] =node0+Nstride0 ;
310 out->FaceElements->Nodes[INDEX2(5,k,NN)] =node0+Nstride2+Nstride0 ;
311 out->FaceElements->Nodes[INDEX2(6,k,NN)] =node0+Nstride2+Nstride1+Nstride0;
312 out->FaceElements->Nodes[INDEX2(7,k,NN)] =node0+Nstride1+Nstride0 ;
313 } else {
314 out->FaceElements->Nodes[INDEX2(0,k,NN)] =node0 ;
315 out->FaceElements->Nodes[INDEX2(1,k,NN)] =node0+Nstride2 ;
316 out->FaceElements->Nodes[INDEX2(2,k,NN)] =node0+Nstride2+Nstride1 ;
317 out->FaceElements->Nodes[INDEX2(3,k,NN)] =node0+ Nstride1 ;
318 }
319 }
320 }
321 faceNECount+=local_NE1*local_NE2;
322 }
323 totalNECount+=NE1*NE2;
324 /* ** elements on boundary 002 (x1=1): */
325 if (local_NE0+e_offset0 == NE0) {
326 #pragma omp parallel for private(i1,i2,k,node0)
327 for (i2=0;i2<local_NE2;i2++) {
328 for (i1=0;i1<local_NE1;i1++) {
329 k=i1+local_NE1*i2+faceNECount;
330 node0=Nstride0*N_PER_E*(NE0-1)+Nstride1*N_PER_E*(i1+e_offset1)+Nstride2*N_PER_E*(i2+e_offset2);
331 out->FaceElements->Id[k]=(i1+e_offset1)+NE1*(i2+e_offset2)+totalNECount;
332 out->FaceElements->Tag[k]=2;
333 out->FaceElements->Owner[k]=myRank;
334
335 if (useElementsOnFace) {
336 out->FaceElements->Nodes[INDEX2(0,k,NN)]=node0+ Nstride0;
337 out->FaceElements->Nodes[INDEX2(1,k,NN)]=node0+ Nstride1+Nstride0;
338 out->FaceElements->Nodes[INDEX2(2,k,NN)]=node0+Nstride2+Nstride1+Nstride0;
339 out->FaceElements->Nodes[INDEX2(3,k,NN)]=node0+Nstride2+ Nstride0;
340
341 out->FaceElements->Nodes[INDEX2(4,k,NN)]=node0 ;
342 out->FaceElements->Nodes[INDEX2(5,k,NN)]=node0+ Nstride1 ;
343 out->FaceElements->Nodes[INDEX2(6,k,NN)]=node0+Nstride2+Nstride1 ;
344 out->FaceElements->Nodes[INDEX2(7,k,NN)]=node0+Nstride2 ;
345
346 } else {
347 out->FaceElements->Nodes[INDEX2(0,k,NN)]=node0 +Nstride0;
348 out->FaceElements->Nodes[INDEX2(1,k,NN)]=node0+ Nstride1+Nstride0;
349 out->FaceElements->Nodes[INDEX2(2,k,NN)]=node0+Nstride2+Nstride1+Nstride0;
350 out->FaceElements->Nodes[INDEX2(3,k,NN)]=node0+Nstride2+ Nstride0;
351 }
352
353 }
354 }
355 faceNECount+=local_NE1*local_NE2;
356 }
357 totalNECount+=NE1*NE2;
358 }
359 if (!periodic[1] && (local_NE1>0)) {
360 /* ** elements on boundary 010 (x2=0): */
361 if (e_offset1 == 0) {
362 #pragma omp parallel for private(i0,i2,k,node0)
363 for (i2=0;i2<local_NE2;i2++) {
364 for (i0=0;i0<local_NE0;i0++) {
365 k=i0+local_NE0*i2+faceNECount;
366 node0=Nstride0*N_PER_E*(i0+e_offset0)+Nstride2*N_PER_E*(i2+e_offset2);
367
368 out->FaceElements->Id[k]=(i2+e_offset2)+NE2*(e_offset0+i0)+totalNECount;
369 out->FaceElements->Tag[k]=10;
370 out->FaceElements->Owner[k]=myRank;
371 if (useElementsOnFace) {
372 out->FaceElements->Nodes[INDEX2(0,k,NN)]=node0 ;
373 out->FaceElements->Nodes[INDEX2(1,k,NN)]=node0+ Nstride0;
374 out->FaceElements->Nodes[INDEX2(2,k,NN)]=node0+Nstride2 +Nstride0;
375 out->FaceElements->Nodes[INDEX2(3,k,NN)]=node0+Nstride2 ;
376
377 out->FaceElements->Nodes[INDEX2(4,k,NN)]=node0+ Nstride1 ;
378 out->FaceElements->Nodes[INDEX2(5,k,NN)]=node0+Nstride1+ Nstride0;
379 out->FaceElements->Nodes[INDEX2(6,k,NN)]=node0+Nstride2+Nstride1+Nstride0;
380 out->FaceElements->Nodes[INDEX2(7,k,NN)]=node0+Nstride2+Nstride1 ;
381 } else {
382 out->FaceElements->Nodes[INDEX2(0,k,NN)]=node0 ;
383 out->FaceElements->Nodes[INDEX2(1,k,NN)]=node0+ Nstride0;
384 out->FaceElements->Nodes[INDEX2(2,k,NN)]=node0+Nstride2+ Nstride0;
385 out->FaceElements->Nodes[INDEX2(3,k,NN)]=node0+Nstride2 ;
386 }
387 }
388 }
389 faceNECount+=local_NE0*local_NE2;
390 }
391 totalNECount+=NE0*NE2;
392 /* ** elements on boundary 020 (x2=1): */
393 if (local_NE1+e_offset1 == NE1) {
394 #pragma omp parallel for private(i0,i2,k,node0)
395 for (i2=0;i2<local_NE2;i2++) {
396 for (i0=0;i0<local_NE0;i0++) {
397 k=i0+local_NE0*i2+faceNECount;
398 node0=Nstride0*N_PER_E*(i0+e_offset0)+Nstride1*N_PER_E*(NE1-1)+Nstride2*N_PER_E*(i2+e_offset2);
399
400 out->FaceElements->Id[k]=(i2+e_offset2)+NE2*(i0+e_offset0)+totalNECount;
401 out->FaceElements->Tag[k]=20;
402 out->FaceElements->Owner[k]=myRank;
403
404 if (useElementsOnFace) {
405 out->FaceElements->Nodes[INDEX2(0,k,NN)]=node0+ Nstride1 ;
406 out->FaceElements->Nodes[INDEX2(1,k,NN)]=node0+Nstride2+Nstride1 ;
407 out->FaceElements->Nodes[INDEX2(2,k,NN)]=node0+Nstride2+Nstride1+Nstride0;
408 out->FaceElements->Nodes[INDEX2(3,k,NN)]=node0+Nstride1+Nstride0 ;
409
410 out->FaceElements->Nodes[INDEX2(4,k,NN)]=node0 ;
411 out->FaceElements->Nodes[INDEX2(5,k,NN)]=node0+Nstride2 ;
412 out->FaceElements->Nodes[INDEX2(6,k,NN)]=node0+Nstride2+ Nstride0;
413 out->FaceElements->Nodes[INDEX2(7,k,NN)]=node0+ Nstride0;
414 } else {
415 out->FaceElements->Nodes[INDEX2(0,k,NN)]=node0+ Nstride1 ;
416 out->FaceElements->Nodes[INDEX2(1,k,NN)]=node0+Nstride2+Nstride1 ;
417 out->FaceElements->Nodes[INDEX2(2,k,NN)]=node0+Nstride2+Nstride1+Nstride0;
418 out->FaceElements->Nodes[INDEX2(3,k,NN)]=node0+ Nstride1+Nstride0;
419 }
420 }
421 }
422 faceNECount+=local_NE0*local_NE2;
423 }
424 totalNECount+=NE0*NE2;
425 }
426 /* add tag names */
427 Finley_Mesh_addTagMap(out,"top", 200);
428 Finley_Mesh_addTagMap(out,"bottom", 100);
429 Finley_Mesh_addTagMap(out,"left", 1);
430 Finley_Mesh_addTagMap(out,"right", 2);
431 Finley_Mesh_addTagMap(out,"front", 10);
432 Finley_Mesh_addTagMap(out,"back", 20);
433
434 /* prepare mesh for further calculatuions:*/
435 if (Finley_noError()) {
436 Finley_Mesh_resolveNodeIds(out);
437 }
438 if (Finley_noError()) {
439 Finley_Mesh_prepare(out, optimize);
440 }
441 }
442
443 if (!Finley_noError()) {
444 Finley_Mesh_free(out);
445 }
446 /* free up memory */
447 Paso_MPIInfo_free( mpi_info );
448 #ifdef Finley_TRACE
449 printf("timing: mesh generation: %.4e sec\n",Finley_timer()-time0);
450 #endif
451
452 return out;
453 }

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