Actual source code: ex4.c
1: /*$Id: ex4.c,v 1.11 2001/04/10 19:37:11 bsmith Exp $*/
2: /*
3: The Problem:
4: Solve the convection-diffusion equation:
5:
6: u_t+a*(u_x+u_y)=epsilon*(u_xx+u_yy)
7: u=0 at x=0, y=0
8: u_x=0 at x=1
9: u_y=0 at y=1
10:
11: This program tests the routine of computing the Jacobian by the
12: finite difference method as well as PETSc with PVODE.
14: */
16: static char help[] = "Solve the convection-diffusion equation. nn";
18: #include petscsys.h
19: #include petscts.h
21: extern int Monitor(TS,int,double,Vec,void *);
22: extern int Initial(Vec,void *);
24: typedef struct
25: {
26: int m; /* the number of mesh points in x-direction */
27: int n; /* the number of mesh points in y-direction */
28: double dx; /* the grid space in x-direction */
29: double dy; /* the grid space in y-direction */
30: double a; /* the convection coefficient */
31: double epsilon; /* the diffusion coefficient */
32: } Data;
34: /* two temporal functions */
35: extern int FormJacobian(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
36: extern int FormFunction(SNES,Vec,Vec,void*);
37: extern int RHSFunction(TS,double,Vec,Vec,void*);
38: extern int RHSJacobian(TS,double,Vec,Mat*,Mat*,MatStructure *,void*);
40: /* the initial function */
41: double f_ini(double x,double y)
42: {
43: double f;
44: f=exp(-20.0*(pow(x-0.5,2.0)+pow(y-0.5,2.0)));
45: return f;
46: }
49: #define linear_no_matrix 0
50: #define linear_no_time 1
51: #define linear 2
52: #define nonlinear_no_jacobian 3
53: #define nonlinear 4
55: int main(int argc,char **argv)
56: {
57: int ierr,time_steps = 100,steps,size;
58: Vec global;
59: double dt,ftime;
60: TS ts;
61: PetscViewer viewfile;
62: MatStructure A_structure;
63: Mat A = 0;
64: TSProblemType tsproblem = TS_NONLINEAR; /* Need to be TS_NONLINEAR */
65: SNES snes;
66: Vec x;
67: Data data;
68: int mn;
69: #if defined(PETSC_HAVE_PVODE) && !defined(__cplusplus)
70: PC pc;
71: PetscViewer viewer;
72: char pcinfo[120],tsinfo[120];
73: #endif
75: PetscInitialize(&argc,&argv,(char*)0,help);
76: MPI_Comm_size(PETSC_COMM_WORLD,&size);
77:
78: /* set Data */
79: data.m = 9;
80: data.n = 9;
81: data.a = 1.0;
82: data.epsilon = 0.1;
83: data.dx = 1.0/(data.m+1.0);
84: data.dy = 1.0/(data.n+1.0);
85: mn = (data.m)*(data.n);
87: PetscOptionsGetInt(PETSC_NULL,"-time",&time_steps,PETSC_NULL);
88:
89: /* set initial conditions */
90: VecCreate(PETSC_COMM_WORLD,PETSC_DECIDE,mn,&global);
91: VecSetFromOptions(global);
92: Initial(global,&data);
93: VecDuplicate(global,&x);
94:
95: /* make timestep context */
96: TSCreate(PETSC_COMM_WORLD,tsproblem,&ts);
97: TSSetMonitor(ts,Monitor,PETSC_NULL,PETSC_NULL);
99: dt = 0.1;
101: /*
102: The user provides the RHS and Jacobian
103: */
104: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,mn,mn,&A);
105: MatSetFromOptions(A);
107: /* Create SNES context */
108: SNESCreate(PETSC_COMM_WORLD,SNES_NONLINEAR_EQUATIONS,&snes);
109:
111: /* setting the RHS function and the Jacobian's non-zero structutre */
112: SNESSetFunction(snes,global,FormFunction,&data);
113: SNESSetJacobian(snes,A,A,FormJacobian,&data);
115: /* set TSPVodeRHSFunction and TSPVodeRHSJacobian, so PETSc will pick up the
116: RHS function from SNES and compute the Jacobian by FD */
117: /*
118: TSSetRHSFunction(ts,TSPVodeSetRHSFunction,snes);
119: TSPVodeSetRHSJacobian(ts,0.0,global,&A,&A,&A_structure,snes);
120: TSSetRHSJacobian(ts,A,A,TSPVodeSetRHSJacobian,snes);
121: */
122:
123: TSSetRHSFunction(ts,RHSFunction,&data);
124: RHSJacobian(ts,0.0,global,&A,&A,&A_structure,&data);
125: TSSetRHSJacobian(ts,A,A,RHSJacobian,&data);
127: /* Use PVODE */
128: TSSetType(ts,TS_PVODE);
130: TSSetFromOptions(ts);
132: TSSetInitialTimeStep(ts,0.0,dt);
133: TSSetDuration(ts,time_steps,1);
134: TSSetSolution(ts,global);
137: /* Pick up a Petsc preconditioner */
138: /* one can always set method or preconditioner during the run time */
139: #if defined(PETSC_HAVE_PVODE) && !defined(__cplusplus)
140: TSPVodeGetPC(ts,&pc);
141: PCSetType(pc,PCJACOBI);
142: TSPVodeSetType(ts,PVODE_BDF);
143: /* TSPVodeSetMethodFromOptions(ts); */
144: #endif
146: TSSetUp(ts);
147: TSStep(ts,&steps,&ftime);
149: TSGetSolution(ts,&global);
150: PetscViewerASCIIOpen(PETSC_COMM_SELF,"out.m",&viewfile);
151: PetscViewerSetFormat(viewfile,PETSC_VIEWER_ASCII_MATLAB);
152: VecView(global,viewfile);
154: #if defined(PETSC_HAVE_PVODE) && !defined(__cplusplus)
155: /* extracts the PC from ts */
156: TSPVodeGetPC(ts,&pc);
157: PetscViewerStringOpen(PETSC_COMM_WORLD,tsinfo,120,&viewer);
158: TSView(ts,viewer);
159: PetscViewerStringOpen(PETSC_COMM_WORLD,pcinfo,120,&viewer);
160: PCView(pc,viewer);
161: PetscPrintf(PETSC_COMM_WORLD,"%d Procs,%s Preconditioner,%sn",
162: size,tsinfo,pcinfo);
163: PCDestroy(pc);
164: #endif
166: /* free the memories */
167: TSDestroy(ts);
168: VecDestroy(global);
169: if (A) {ierr= MatDestroy(A);}
170: PetscFinalize();
171: return 0;
172: }
174: /* -------------------------------------------------------------------*/
175: int Initial(Vec global,void *ctx)
176: {
177: Data *data = (Data*)ctx;
178: int m;
179: int row,col;
180: double x,y,dx,dy;
181: Scalar *localptr;
182: int i,mybase,myend,ierr,locsize;
184: /* make the local copies of parameters */
185: m = data->m;
186: dx = data->dx;
187: dy = data->dy;
189: /* determine starting point of each processor */
190: VecGetOwnershipRange(global,&mybase,&myend);
191: VecGetLocalSize(global,&locsize);
193: /* Initialize the array */
194: VecGetArray(global,&localptr);
196: for (i=0; i<locsize; i++) {
197: row = 1+(mybase+i)-((mybase+i)/m)*m;
198: col = (mybase+i)/m+1;
199: x = dx*row;
200: y = dy*col;
201: localptr[i] = f_ini(x,y);
202: }
203:
204: VecRestoreArray(global,&localptr);
205: return 0;
206: }
208: int Monitor(TS ts,int step,double time,Vec global,void *ctx)
209: {
210: VecScatter scatter;
211: IS from,to;
212: int i,n,*idx;
213: Vec tmp_vec;
214: int ierr;
215: Scalar *tmp;
217: /* Get the size of the vector */
218: VecGetSize(global,&n);
220: /* Set the index sets */
221: PetscMalloc(n*sizeof(int),&idx);
222: for(i=0; i<n; i++) idx[i]=i;
223:
224: /* Create local sequential vectors */
225: VecCreateSeq(PETSC_COMM_SELF,n,&tmp_vec);
227: /* Create scatter context */
228: ISCreateGeneral(PETSC_COMM_SELF,n,idx,&from);
229: ISCreateGeneral(PETSC_COMM_SELF,n,idx,&to);
230: VecScatterCreate(global,from,tmp_vec,to,&scatter);
231: VecScatterBegin(global,tmp_vec,INSERT_VALUES,SCATTER_FORWARD,scatter);
232: VecScatterEnd(global,tmp_vec,INSERT_VALUES,SCATTER_FORWARD,scatter);
234: VecGetArray(tmp_vec,&tmp);
235: PetscPrintf(PETSC_COMM_WORLD,"At t =%14.6e u= %14.6e at the center n",time,PetscRealPart(tmp[n/2]));
236: VecRestoreArray(tmp_vec,&tmp);
238: PetscFree(idx);
239: return 0;
240: }
243: int FormFunction(SNES snes,Vec globalin,Vec globalout,void *ptr)
244: {
245: Data *data = (Data*)ptr;
246: int m,n,mn;
247: double dx,dy;
248: double xc,xl,xr,yl,yr;
249: double a,epsilon;
250: Scalar *inptr,*outptr;
251: int i,j,len,ierr;
253: IS from,to;
254: int *idx;
255: VecScatter scatter;
256: Vec tmp_in,tmp_out;
258: m = data->m;
259: n = data->n;
260: mn = m*n;
261: dx = data->dx;
262: dy = data->dy;
263: a = data->a;
264: epsilon = data->epsilon;
266: xc = -2.0*epsilon*(1.0/(dx*dx)+1.0/(dy*dy));
267: xl = 0.5*a/dx+epsilon/(dx*dx);
268: xr = -0.5*a/dx+epsilon/(dx*dx);
269: yl = 0.5*a/dy+epsilon/(dy*dy);
270: yr = -0.5*a/dy+epsilon/(dy*dy);
271:
272: /* Get the length of parallel vector */
273: VecGetSize(globalin,&len);
275: /* Set the index sets */
276: PetscMalloc(len*sizeof(int),&idx);
277: for(i=0; i<len; i++) idx[i]=i;
278:
279: /* Create local sequential vectors */
280: VecCreateSeq(PETSC_COMM_SELF,len,&tmp_in);
281: VecDuplicate(tmp_in,&tmp_out);
283: /* Create scatter context */
284: ISCreateGeneral(PETSC_COMM_SELF,len,idx,&from);
285: ISCreateGeneral(PETSC_COMM_SELF,len,idx,&to);
286: VecScatterCreate(globalin,from,tmp_in,to,&scatter);
287: VecScatterBegin(globalin,tmp_in,INSERT_VALUES,SCATTER_FORWARD,scatter);
288:
290:
291: VecScatterEnd(globalin,tmp_in,INSERT_VALUES,SCATTER_FORWARD,scatter);
292:
294: /*Extract income array */
295: VecGetArray(tmp_in,&inptr);
297: /* Extract outcome array*/
298: VecGetArray(tmp_out,&outptr);
300: outptr[0] = xc*inptr[0]+xr*inptr[1]+yr*inptr[m];
301: outptr[m-1] = 2.0*xl*inptr[m-2]+xc*inptr[m-1]+yr*inptr[m-1+m];
302: for (i=1; i<m-1; i++) {
303: outptr[i] = xc*inptr[i]+xl*inptr[i-1]+xr*inptr[i+1]
304: +yr*inptr[i+m];
305: }
307: for (j=1; j<n-1; j++) {
308: outptr[j*m] = xc*inptr[j*m]+xr*inptr[j*m+1]+
309: yl*inptr[j*m-m]+yr*inptr[j*m+m];
310: outptr[j*m+m-1] = xc*inptr[j*m+m-1]+2.0*xl*inptr[j*m+m-1-1]+
311: yl*inptr[j*m+m-1-m]+yr*inptr[j*m+m-1+m];
312: for(i=1; i<m-1; i++) {
313: outptr[j*m+i] = xc*inptr[j*m+i]+xl*inptr[j*m+i-1]+xr*inptr[j*m+i+1]
314: +yl*inptr[j*m+i-m]+yr*inptr[j*m+i+m];
315: }
316: }
318: outptr[mn-m] = xc*inptr[mn-m]+xr*inptr[mn-m+1]+2.0*yl*inptr[mn-m-m];
319: outptr[mn-1] = 2.0*xl*inptr[mn-2]+xc*inptr[mn-1]+2.0*yl*inptr[mn-1-m];
320: for (i=1; i<m-1; i++) {
321: outptr[mn-m+i] = xc*inptr[mn-m+i]+xl*inptr[mn-m+i-1]+xr*inptr[mn-m+i+1]
322: +2*yl*inptr[mn-m+i-m];
323: }
325: VecRestoreArray(tmp_in,&inptr);
326: VecRestoreArray(tmp_out,&outptr);
328: VecScatterCreate(tmp_out,from,globalout,to,&scatter);
329: VecScatterBegin(tmp_out,globalout,INSERT_VALUES,SCATTER_FORWARD,scatter
330: );
331:
332: VecScatterEnd(tmp_out,globalout,INSERT_VALUES,SCATTER_FORWARD,scatter);
333:
334:
335: /* Destroy idx aand scatter */
336: ISDestroy(from);
337: ISDestroy(to);
338: VecScatterDestroy(scatter);
340: PetscFree(idx);
341: return 0;
342: }
344: int FormJacobian(SNES snes,Vec x,Mat *AA,Mat *BB,MatStructure *flag,void *ptr)
345: {
346: Data *data = (Data*)ptr;
347: Mat A = *AA;
348: Scalar v[1],one = 1.0;
349: int idx[1],i,j,row,ierr;
350: int m,n,mn;
352: m = data->m;
353: n = data->n;
354: mn = (data->m)*(data->n);
355:
356: for(i=0; i<mn; i++) {
357: idx[0] = i;
358: v[0] = one;
359: MatSetValues(A,1,&i,1,idx,v,INSERT_VALUES);
360: }
362: for(i=0; i<mn-m; i++) {
363: idx[0] = i+m;
364: v[0]= one;
365: MatSetValues(A,1,&i,1,idx,v,INSERT_VALUES);
366: }
368: for(i=m; i<mn; i++) {
369: idx[0] = i-m;
370: v[0] = one;
371: MatSetValues(A,1,&i,1,idx,v,INSERT_VALUES);
372: }
374: for(j=0; j<n; j++) {
375: for(i=0; i<m-1; i++) {
376: row = j*m+i;
377: idx[0] = j*m+i+1;
378: v[0] = one;
379: MatSetValues(A,1,&row,1,idx,v,INSERT_VALUES);
380: }
381: }
383: for(j=0; j<n; j++) {
384: for(i=1; i<m; i++) {
385: row = j*m+i;
386: idx[0] = j*m+i-1;
387: v[0] = one;
388: MatSetValues(A,1,&row,1,idx,v,INSERT_VALUES);
389: }
390: }
391:
392: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
393: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
396: *flag = SAME_NONZERO_PATTERN;
397: return 0;
398: }
400: int RHSJacobian(TS ts,double t,Vec x,Mat *AA,Mat *BB,MatStructure *flag,void *ptr)
401: {
402: Data *data = (Data*)ptr;
403: Mat A = *AA;
404: Scalar v[5];
405: int idx[5],i,j,row,ierr;
406: int m,n,mn;
407: double dx,dy,a,epsilon,xc,xl,xr,yl,yr;
409: m = data->m;
410: n = data->n;
411: mn = m*n;
412: dx = data->dx;
413: dy = data->dy;
414: a = data->a;
415: epsilon = data->epsilon;
417: xc = -2.0*epsilon*(1.0/(dx*dx)+1.0/(dy*dy));
418: xl = 0.5*a/dx+epsilon/(dx*dx);
419: xr = -0.5*a/dx+epsilon/(dx*dx);
420: yl = 0.5*a/dy+epsilon/(dy*dy);
421: yr = -0.5*a/dy+epsilon/(dy*dy);
423: row=0;
424: v[0] = xc; v[1]=xr; v[2]=yr;
425: idx[0]=0; idx[1]=2; idx[2]=m;
426: MatSetValues(A,1,&row,3,idx,v,INSERT_VALUES);
428: row=m-1;
429: v[0]=2.0*xl; v[1]=xc; v[2]=yr;
430: idx[0]=m-2; idx[1]=m-1; idx[2]=m-1+m;
431: MatSetValues(A,1,&row,3,idx,v,INSERT_VALUES);
433: for (i=1; i<m-1; i++) {
434: row=i;
435: v[0]=xl; v[1]=xc; v[2]=xr; v[3]=yr;
436: idx[0]=i-1; idx[1]=i; idx[2]=i+1; idx[3]=i+m;
437: MatSetValues(A,1,&row,4,idx,v,INSERT_VALUES);
438: }
440: for (j=1; j<n-1; j++) {
441: row=j*m;
442: v[0]=xc; v[1]=xr; v[2]=yl; v[3]=yr;
443: idx[0]=j*m; idx[1]=j*m; idx[2]=j*m-m; idx[3]=j*m+m;
444: MatSetValues(A,1,&row,4,idx,v,INSERT_VALUES);
445:
446: row=j*m+m-1;
447: v[0]=xc; v[1]=2.0*xl; v[2]=yl; v[3]=yr;
448: idx[0]=j*m+m-1; idx[1]=j*m+m-1-1; idx[2]=j*m+m-1-m; idx[3]=j*m+m-1+m;
449: MatSetValues(A,1,&row,4,idx,v,INSERT_VALUES);
451: for(i=1; i<m-1; i++) {
452: row=j*m+i;
453: v[0]=xc; v[1]=xl; v[2]=xr; v[3]=yl; v[4]=yr;
454: idx[0]=j*m+i; idx[1]=j*m+i-1; idx[2]=j*m+i+1; idx[3]=j*m+i-m;
455: idx[4]=j*m+i+m;
456: MatSetValues(A,1,&row,5,idx,v,INSERT_VALUES);
457: }
458: }
460: row=mn-m;
461: v[0] = xc; v[1]=xr; v[2]=2.0*yl;
462: idx[0]=mn-m; idx[1]=mn-m+1; idx[2]=mn-m-m;
463: MatSetValues(A,1,&row,3,idx,v,INSERT_VALUES);
464:
465: row=mn-1;
466: v[0] = xc; v[1]=2.0*xl; v[2]=2.0*yl;
467: idx[0]=mn-1; idx[1]=mn-2; idx[2]=mn-1-m;
468: MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
470: for (i=1; i<m-1; i++) {
471: row=mn-m+i;
472: v[0]=xl; v[1]=xc; v[2]=xr; v[3]=2.0*yl;
473: idx[0]=mn-m+i-1; idx[1]=mn-m+i; idx[2]=mn-m+i+1; idx[3]=mn-m+i-m;
474: MatSetValues(A,1,&row,4,idx,v,INSERT_VALUES);
475: }
478: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
479: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
482: *flag = SAME_NONZERO_PATTERN;
483: return 0;
484: }
486: int RHSFunction(TS ts,double t,Vec globalin,Vec globalout,void *ctx)
487: {
489: SNES snes = PETSC_NULL;
491: FormFunction(snes,globalin,globalout,ctx);
494: return 0;
495: }