Actual source code: ex4.c
1: /*
2: The Problem:
3: Solve the convection-diffusion equation:
4:
5: u_t+a*(u_x+u_y)=epsilon*(u_xx+u_yy)
6: u=0 at x=0, y=0
7: u_x=0 at x=1
8: u_y=0 at y=1
9: u = exp(-20.0*(pow(x-0.5,2.0)+pow(y-0.5,2.0))) at t=0
10:
11: This program tests the routine of computing the Jacobian by the
12: finite difference method as well as PETSc with SUNDIALS.
14: */
16: static char help[] = "Solve the convection-diffusion equation. \n\n";
18: #include petscts.h
20: typedef struct
21: {
22: PetscInt m; /* the number of mesh points in x-direction */
23: PetscInt n; /* the number of mesh points in y-direction */
24: PetscReal dx; /* the grid space in x-direction */
25: PetscReal dy; /* the grid space in y-direction */
26: PetscReal a; /* the convection coefficient */
27: PetscReal epsilon; /* the diffusion coefficient */
28: } Data;
38: int main(int argc,char **argv)
39: {
41: PetscInt time_steps=100,steps,iout,NOUT=1;
42: PetscMPIInt size;
43: Vec global;
44: PetscReal dt,ftime;
45: TS ts;
46: PetscViewer viewfile;
47: MatStructure J_structure;
48: Mat J = 0;
49: Vec x;
50: Data data;
51: PetscInt mn;
52: PetscTruth flg;
53: ISColoring iscoloring;
54: MatFDColoring matfdcoloring = 0;
55: PetscTruth fd_jacobian_coloring = PETSC_FALSE;
56: #if defined(PETSC_HAVE_SUNDIALS)
57: PC pc;
58: PetscViewer viewer;
59: char pcinfo[120],tsinfo[120];
60: const TSType tstype;
61: PetscTruth sundials;
62: #endif
64: PetscInitialize(&argc,&argv,(char*)0,help);
65: MPI_Comm_size(PETSC_COMM_WORLD,&size);
66:
67: /* set data */
68: data.m = 9;
69: data.n = 9;
70: data.a = 1.0;
71: data.epsilon = 0.1;
72: data.dx = 1.0/(data.m+1.0);
73: data.dy = 1.0/(data.n+1.0);
74: mn = (data.m)*(data.n);
75: PetscOptionsGetInt(PETSC_NULL,"-time",&time_steps,PETSC_NULL);
76:
77: /* set initial conditions */
78: VecCreate(PETSC_COMM_WORLD,&global);
79: VecSetSizes(global,PETSC_DECIDE,mn);
80: VecSetFromOptions(global);
81: Initial(global,&data);
82: VecDuplicate(global,&x);
84: /* create timestep context */
85: TSCreate(PETSC_COMM_WORLD,&ts);
86: TSSetProblemType(ts,TS_NONLINEAR); /* Need to be TS_NONLINEAR for Sundials */
87: TSMonitorSet(ts,Monitor,PETSC_NULL,PETSC_NULL);
89: /* set user provided RHSFunction and RHSJacobian */
90: TSSetRHSFunction(ts,RHSFunction,&data);
91: MatCreate(PETSC_COMM_WORLD,&J);
92: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,mn,mn);
93: MatSetFromOptions(J);
94: MatSeqAIJSetPreallocation(J,5,PETSC_NULL);
95: MatMPIAIJSetPreallocation(J,5,PETSC_NULL,5,PETSC_NULL);
97: PetscOptionsHasName(PETSC_NULL,"-ts_fd",&flg);
98: if (!flg){
99: /* RHSJacobian(ts,0.0,global,&J,&J,&J_structure,&data); */
100: TSSetRHSJacobian(ts,J,J,RHSJacobian,&data);
101: } else {
102: PetscOptionsHasName(PETSC_NULL,"-fd_color",&fd_jacobian_coloring);
103: if (fd_jacobian_coloring){ /* Use finite differences with coloring */
104: /* Get data structure of J */
105: PetscTruth pc_diagonal;
106: PetscOptionsHasName(PETSC_NULL,"-pc_diagonal",&pc_diagonal);
107: if (pc_diagonal){ /* the preconditioner of J is a diagonal matrix */
108: PetscInt rstart,rend,i;
109: PetscScalar zero=0.0;
110: MatGetOwnershipRange(J,&rstart,&rend);
111: for (i=rstart; i<rend; i++){
112: MatSetValues(J,1,&i,1,&i,&zero,INSERT_VALUES);
113: }
114: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
115: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
116: } else { /* the preconditioner of J has same data structure as J */
117: TSDefaultComputeJacobian(ts,0.0,global,&J,&J,&J_structure,&data);
118: }
119:
120: /* create coloring context */
121: MatGetColoring(J,MATCOLORING_SL,&iscoloring);
122: MatFDColoringCreate(J,iscoloring,&matfdcoloring);
123: MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))RHSFunction,&data);
124: MatFDColoringSetFromOptions(matfdcoloring);
125: TSSetRHSJacobian(ts,J,J,TSDefaultComputeJacobianColor,matfdcoloring);
126: ISColoringDestroy(iscoloring);
128: PetscTruth view_J;
129: PetscOptionsHasName(PETSC_NULL,"-view_J",&view_J);
130: if (view_J){
131: PetscPrintf(PETSC_COMM_SELF,"J computed from TSDefaultComputeJacobianColor():\n");
132: TSDefaultComputeJacobianColor(ts,0.0,global,&J,&J,&J_structure,matfdcoloring);
133: MatView(J,PETSC_VIEWER_STDOUT_WORLD);
134: }
135: } else { /* Use finite differences (slow) */
136: TSSetRHSJacobian(ts,J,J,TSDefaultComputeJacobian,&data);
137: }
138: }
140: /* Use SUNDIALS */
141: #if defined(PETSC_HAVE_SUNDIALS)
142: TSSetType(ts,TSSUNDIALS);
143: #else
144: TSSetType(ts,TSEULER);
145: #endif
146: dt = 0.1;
147: TSSetInitialTimeStep(ts,0.0,dt);
148: TSSetDuration(ts,time_steps,1);
149: TSSetSolution(ts,global);
150:
151: /* Test TSSetPostStep() */
152: PetscOptionsHasName(PETSC_NULL,"-test_PostStep",&flg);
153: if (flg){
154: TSSetPostStep(ts,PostStep);
155: }
157: /* Pick up a Petsc preconditioner */
158: /* one can always set method or preconditioner during the run time */
159: #if defined(PETSC_HAVE_SUNDIALS)
160: TSSundialsGetPC(ts,&pc);
161: PCSetType(pc,PCJACOBI);
162: #endif
163: TSSetFromOptions(ts);
164: TSSetUp(ts);
166: PetscOptionsGetInt(PETSC_NULL,"-NOUT",&NOUT,PETSC_NULL);
167: for (iout=1; iout<=NOUT; iout++){
168: TSSetDuration(ts,time_steps,iout*1.0/NOUT);
169: TSStep(ts,&steps,&ftime);
170: TSSetInitialTimeStep(ts,ftime,dt);
171: }
173: PetscOptionsHasName(PETSC_NULL,"-matlab_view",&flg);
174: if (flg){ /* print solution into a MATLAB file */
175: TSGetSolution(ts,&global);
176: PetscViewerASCIIOpen(PETSC_COMM_WORLD,"out.m",&viewfile);
177: PetscViewerSetFormat(viewfile,PETSC_VIEWER_ASCII_MATLAB);
178: VecView(global,viewfile);
179: PetscViewerDestroy(viewfile);
180: }
182: #if defined(PETSC_HAVE_SUNDIALS)
183: /* extracts the PC from ts */
184: TSSundialsGetPC(ts,&pc);
185: TSGetType(ts,&tstype);
186: PetscTypeCompare((PetscObject)ts,TSSUNDIALS,&sundials);
187: if (sundials){
188: PetscViewerStringOpen(PETSC_COMM_WORLD,tsinfo,120,&viewer);
189: TSView(ts,viewer);
190: PetscViewerDestroy(viewer);
191: PetscViewerStringOpen(PETSC_COMM_WORLD,pcinfo,120,&viewer);
192: PCView(pc,viewer);
193: PetscPrintf(PETSC_COMM_WORLD,"%d Procs,%s TSType, %s Preconditioner\n",
194: size,tsinfo,pcinfo);
195: PetscViewerDestroy(viewer);
196: }
197: #endif
199: /* free the memories */
200: TSDestroy(ts);
201: VecDestroy(global);
202: VecDestroy(x);
203: ierr= MatDestroy(J);
204: if (fd_jacobian_coloring){MatFDColoringDestroy(matfdcoloring);}
205: PetscFinalize();
206: return 0;
207: }
209: /* -------------------------------------------------------------------*/
210: /* the initial function */
211: PetscReal f_ini(PetscReal x,PetscReal y)
212: {
213: PetscReal f;
215: f=exp(-20.0*(pow(x-0.5,2.0)+pow(y-0.5,2.0)));
216: return f;
217: }
221: PetscErrorCode Initial(Vec global,void *ctx)
222: {
223: Data *data = (Data*)ctx;
224: PetscInt m,row,col;
225: PetscReal x,y,dx,dy;
226: PetscScalar *localptr;
227: PetscInt i,mybase,myend,locsize;
231: /* make the local copies of parameters */
232: m = data->m;
233: dx = data->dx;
234: dy = data->dy;
236: /* determine starting point of each processor */
237: VecGetOwnershipRange(global,&mybase,&myend);
238: VecGetLocalSize(global,&locsize);
240: /* Initialize the array */
241: VecGetArray(global,&localptr);
243: for (i=0; i<locsize; i++) {
244: row = 1+(mybase+i)-((mybase+i)/m)*m;
245: col = (mybase+i)/m+1;
246: x = dx*row;
247: y = dy*col;
248: localptr[i] = f_ini(x,y);
249: }
250:
251: VecRestoreArray(global,&localptr);
252: return(0);
253: }
257: PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec global,void *ctx)
258: {
259: VecScatter scatter;
260: IS from,to;
261: PetscInt i,n,*idx,nsteps,maxsteps;
262: Vec tmp_vec;
264: PetscScalar *tmp;
265: PetscReal maxtime;
266:
268: TSGetTimeStepNumber(ts,&nsteps);
269: /* display output at selected time steps */
270: TSGetDuration(ts, &maxsteps, &maxtime);
271: if (nsteps % 10 != 0 && time < maxtime) return(0);
273: /* Get the size of the vector */
274: VecGetSize(global,&n);
276: /* Set the index sets */
277: PetscMalloc(n*sizeof(PetscInt),&idx);
278: for(i=0; i<n; i++) idx[i]=i;
279:
280: /* Create local sequential vectors */
281: VecCreateSeq(PETSC_COMM_SELF,n,&tmp_vec);
283: /* Create scatter context */
284: ISCreateGeneral(PETSC_COMM_SELF,n,idx,&from);
285: ISCreateGeneral(PETSC_COMM_SELF,n,idx,&to);
286: VecScatterCreate(global,from,tmp_vec,to,&scatter);
287: VecScatterBegin(scatter,global,tmp_vec,INSERT_VALUES,SCATTER_FORWARD);
288: VecScatterEnd(scatter,global,tmp_vec,INSERT_VALUES,SCATTER_FORWARD);
290: VecGetArray(tmp_vec,&tmp);
291: PetscPrintf(PETSC_COMM_WORLD,"At t[%d] =%14.2e u= %14.2e at the center \n",nsteps,time,PetscRealPart(tmp[n/2]));
292: VecRestoreArray(tmp_vec,&tmp);
294: PetscFree(idx);
295: ISDestroy(from);
296: ISDestroy(to);
297: VecScatterDestroy(scatter);
298: VecDestroy(tmp_vec);
299: return(0);
300: }
304: PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec x,Mat *AA,Mat *BB,MatStructure *flag,void *ptr)
305: {
306: Data *data = (Data*)ptr;
307: Mat A = *AA;
308: PetscScalar v[5];
309: PetscInt idx[5],i,j,row;
311: PetscInt m,n,mn;
312: PetscReal dx,dy,a,epsilon,xc,xl,xr,yl,yr;
315: m = data->m;
316: n = data->n;
317: mn = m*n;
318: dx = data->dx;
319: dy = data->dy;
320: a = data->a;
321: epsilon = data->epsilon;
323: xc = -2.0*epsilon*(1.0/(dx*dx)+1.0/(dy*dy));
324: xl = 0.5*a/dx+epsilon/(dx*dx);
325: xr = -0.5*a/dx+epsilon/(dx*dx);
326: yl = 0.5*a/dy+epsilon/(dy*dy);
327: yr = -0.5*a/dy+epsilon/(dy*dy);
329: row=0;
330: v[0] = xc; v[1]=xr; v[2]=yr;
331: idx[0]=0; idx[1]=2; idx[2]=m;
332: MatSetValues(A,1,&row,3,idx,v,INSERT_VALUES);
334: row=m-1;
335: v[0]=2.0*xl; v[1]=xc; v[2]=yr;
336: idx[0]=m-2; idx[1]=m-1; idx[2]=m-1+m;
337: MatSetValues(A,1,&row,3,idx,v,INSERT_VALUES);
339: for (i=1; i<m-1; i++) {
340: row=i;
341: v[0]=xl; v[1]=xc; v[2]=xr; v[3]=yr;
342: idx[0]=i-1; idx[1]=i; idx[2]=i+1; idx[3]=i+m;
343: MatSetValues(A,1,&row,4,idx,v,INSERT_VALUES);
344: }
346: for (j=1; j<n-1; j++) {
347: row=j*m;
348: v[0]=xc; v[1]=xr; v[2]=yl; v[3]=yr;
349: idx[0]=j*m; idx[1]=j*m; idx[2]=j*m-m; idx[3]=j*m+m;
350: MatSetValues(A,1,&row,4,idx,v,INSERT_VALUES);
351:
352: row=j*m+m-1;
353: v[0]=xc; v[1]=2.0*xl; v[2]=yl; v[3]=yr;
354: 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;
355: MatSetValues(A,1,&row,4,idx,v,INSERT_VALUES);
357: for(i=1; i<m-1; i++) {
358: row=j*m+i;
359: v[0]=xc; v[1]=xl; v[2]=xr; v[3]=yl; v[4]=yr;
360: idx[0]=j*m+i; idx[1]=j*m+i-1; idx[2]=j*m+i+1; idx[3]=j*m+i-m;
361: idx[4]=j*m+i+m;
362: MatSetValues(A,1,&row,5,idx,v,INSERT_VALUES);
363: }
364: }
366: row=mn-m;
367: v[0] = xc; v[1]=xr; v[2]=2.0*yl;
368: idx[0]=mn-m; idx[1]=mn-m+1; idx[2]=mn-m-m;
369: MatSetValues(A,1,&row,3,idx,v,INSERT_VALUES);
370:
371: row=mn-1;
372: v[0] = xc; v[1]=2.0*xl; v[2]=2.0*yl;
373: idx[0]=mn-1; idx[1]=mn-2; idx[2]=mn-1-m;
374: MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
376: for (i=1; i<m-1; i++) {
377: row=mn-m+i;
378: v[0]=xl; v[1]=xc; v[2]=xr; v[3]=2.0*yl;
379: idx[0]=mn-m+i-1; idx[1]=mn-m+i; idx[2]=mn-m+i+1; idx[3]=mn-m+i-m;
380: MatSetValues(A,1,&row,4,idx,v,INSERT_VALUES);
381: }
383: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
384: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
386: /* *flag = SAME_NONZERO_PATTERN; */
387: *flag = DIFFERENT_NONZERO_PATTERN;
388: return(0);
389: }
391: /* globalout = -a*(u_x+u_y) + epsilon*(u_xx+u_yy) */
394: PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec globalin,Vec globalout,void *ctx)
395: {
396: Data *data = (Data*)ctx;
397: PetscInt m,n,mn;
398: PetscReal dx,dy;
399: PetscReal xc,xl,xr,yl,yr;
400: PetscReal a,epsilon;
401: PetscScalar *inptr,*outptr;
402: PetscInt i,j,len;
404: IS from,to;
405: PetscInt *idx;
406: VecScatter scatter;
407: Vec tmp_in,tmp_out;
410: m = data->m;
411: n = data->n;
412: mn = m*n;
413: dx = data->dx;
414: dy = data->dy;
415: a = data->a;
416: epsilon = data->epsilon;
418: xc = -2.0*epsilon*(1.0/(dx*dx)+1.0/(dy*dy));
419: xl = 0.5*a/dx+epsilon/(dx*dx);
420: xr = -0.5*a/dx+epsilon/(dx*dx);
421: yl = 0.5*a/dy+epsilon/(dy*dy);
422: yr = -0.5*a/dy+epsilon/(dy*dy);
423:
424: /* Get the length of parallel vector */
425: VecGetSize(globalin,&len);
427: /* Set the index sets */
428: PetscMalloc(len*sizeof(PetscInt),&idx);
429: for(i=0; i<len; i++) idx[i]=i;
430:
431: /* Create local sequential vectors */
432: VecCreateSeq(PETSC_COMM_SELF,len,&tmp_in);
433: VecDuplicate(tmp_in,&tmp_out);
435: /* Create scatter context */
436: ISCreateGeneral(PETSC_COMM_SELF,len,idx,&from);
437: ISCreateGeneral(PETSC_COMM_SELF,len,idx,&to);
438: VecScatterCreate(globalin,from,tmp_in,to,&scatter);
439: VecScatterBegin(scatter,globalin,tmp_in,INSERT_VALUES,SCATTER_FORWARD);
440: VecScatterEnd(scatter,globalin,tmp_in,INSERT_VALUES,SCATTER_FORWARD);
441: VecScatterDestroy(scatter);
443: /*Extract income array - include ghost points */
444: VecGetArray(tmp_in,&inptr);
446: /* Extract outcome array*/
447: VecGetArray(tmp_out,&outptr);
449: outptr[0] = xc*inptr[0]+xr*inptr[1]+yr*inptr[m];
450: outptr[m-1] = 2.0*xl*inptr[m-2]+xc*inptr[m-1]+yr*inptr[m-1+m];
451: for (i=1; i<m-1; i++) {
452: outptr[i] = xc*inptr[i]+xl*inptr[i-1]+xr*inptr[i+1]
453: +yr*inptr[i+m];
454: }
456: for (j=1; j<n-1; j++) {
457: outptr[j*m] = xc*inptr[j*m]+xr*inptr[j*m+1]+
458: yl*inptr[j*m-m]+yr*inptr[j*m+m];
459: outptr[j*m+m-1] = xc*inptr[j*m+m-1]+2.0*xl*inptr[j*m+m-1-1]+
460: yl*inptr[j*m+m-1-m]+yr*inptr[j*m+m-1+m];
461: for(i=1; i<m-1; i++) {
462: outptr[j*m+i] = xc*inptr[j*m+i]+xl*inptr[j*m+i-1]+xr*inptr[j*m+i+1]
463: +yl*inptr[j*m+i-m]+yr*inptr[j*m+i+m];
464: }
465: }
467: outptr[mn-m] = xc*inptr[mn-m]+xr*inptr[mn-m+1]+2.0*yl*inptr[mn-m-m];
468: outptr[mn-1] = 2.0*xl*inptr[mn-2]+xc*inptr[mn-1]+2.0*yl*inptr[mn-1-m];
469: for (i=1; i<m-1; i++) {
470: outptr[mn-m+i] = xc*inptr[mn-m+i]+xl*inptr[mn-m+i-1]+xr*inptr[mn-m+i+1]
471: +2*yl*inptr[mn-m+i-m];
472: }
474: VecRestoreArray(tmp_in,&inptr);
475: VecRestoreArray(tmp_out,&outptr);
477: VecScatterCreate(tmp_out,from,globalout,to,&scatter);
478: VecScatterBegin(scatter,tmp_out,globalout,INSERT_VALUES,SCATTER_FORWARD);
479: VecScatterEnd(scatter,tmp_out,globalout,INSERT_VALUES,SCATTER_FORWARD);
480:
481: /* Destroy idx aand scatter */
482: VecDestroy(tmp_in);
483: VecDestroy(tmp_out);
484: ISDestroy(from);
485: ISDestroy(to);
486: VecScatterDestroy(scatter);
488: PetscFree(idx);
489: return(0);
490: }
494: PetscErrorCode PostStep(TS ts)
495: {
496: PetscErrorCode ierr;
497: PetscReal t;
498:
500: TSGetTime(ts,&t);
501: PetscPrintf(PETSC_COMM_SELF," PostStep, t: %g\n",t);
502: return(0);
503: }