Actual source code: ex4.c
petsc-3.4.5 2014-06-29
1: /*
2: The Problem:
3: Solve the convection-diffusion equation:
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
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: PetscReal tfinal;
29: } Data;
31: extern PetscErrorCode Monitor(TS,PetscInt,PetscReal,Vec,void*);
32: extern PetscErrorCode Initial(Vec,void*);
33: extern PetscErrorCode RHSFunction(TS,PetscReal,Vec,Vec,void*);
34: extern PetscErrorCode RHSJacobian(TS,PetscReal,Vec,Mat*,Mat*,MatStructure*,void*);
35: extern PetscErrorCode PostStep(TS);
39: int main(int argc,char **argv)
40: {
42: PetscInt time_steps=100,iout,NOUT=1;
43: PetscMPIInt size;
44: Vec global;
45: PetscReal dt,ftime,ftime_original;
46: TS ts;
47: PetscViewer viewfile;
48: MatStructure J_structure;
49: Mat J = 0;
50: Vec x;
51: Data data;
52: PetscInt mn;
53: PetscBool flg;
54: ISColoring iscoloring;
55: MatFDColoring matfdcoloring = 0;
56: PetscBool fd_jacobian_coloring = PETSC_FALSE;
57: SNES snes;
58: KSP ksp;
59: PC pc;
60: PetscViewer viewer;
61: char pcinfo[120],tsinfo[120];
62: TSType tstype;
63: PetscBool sundials;
65: PetscInitialize(&argc,&argv,(char*)0,help);
66: MPI_Comm_size(PETSC_COMM_WORLD,&size);
68: /* set data */
69: data.m = 9;
70: data.n = 9;
71: data.a = 1.0;
72: data.epsilon = 0.1;
73: data.dx = 1.0/(data.m+1.0);
74: data.dy = 1.0/(data.n+1.0);
75: mn = (data.m)*(data.n);
76: PetscOptionsGetInt(NULL,"-time",&time_steps,NULL);
78: /* set initial conditions */
79: VecCreate(PETSC_COMM_WORLD,&global);
80: VecSetSizes(global,PETSC_DECIDE,mn);
81: VecSetFromOptions(global);
82: Initial(global,&data);
83: VecDuplicate(global,&x);
85: /* create timestep context */
86: TSCreate(PETSC_COMM_WORLD,&ts);
87: TSMonitorSet(ts,Monitor,&data,NULL);
88: #if defined(PETSC_HAVE_SUNDIALS)
89: TSSetType(ts,TSSUNDIALS);
90: #else
91: TSSetType(ts,TSEULER);
92: #endif
93: dt = 0.1;
94: ftime_original = data.tfinal = 1.0;
96: TSSetInitialTimeStep(ts,0.0,dt);
97: TSSetDuration(ts,time_steps,ftime_original);
98: TSSetSolution(ts,global);
100: /* set user provided RHSFunction and RHSJacobian */
101: TSSetRHSFunction(ts,NULL,RHSFunction,&data);
102: MatCreate(PETSC_COMM_WORLD,&J);
103: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,mn,mn);
104: MatSetFromOptions(J);
105: MatSeqAIJSetPreallocation(J,5,NULL);
106: MatMPIAIJSetPreallocation(J,5,NULL,5,NULL);
108: PetscOptionsHasName(NULL,"-ts_fd",&flg);
109: if (!flg) {
110: TSSetRHSJacobian(ts,J,J,RHSJacobian,&data);
111: } else {
112: TSGetSNES(ts,&snes);
113: PetscOptionsHasName(NULL,"-fd_color",&fd_jacobian_coloring);
114: if (fd_jacobian_coloring) { /* Use finite differences with coloring */
115: /* Get data structure of J */
116: PetscBool pc_diagonal;
117: PetscOptionsHasName(NULL,"-pc_diagonal",&pc_diagonal);
118: if (pc_diagonal) { /* the preconditioner of J is a diagonal matrix */
119: PetscInt rstart,rend,i;
120: PetscScalar zero=0.0;
121: MatGetOwnershipRange(J,&rstart,&rend);
122: for (i=rstart; i<rend; i++) {
123: MatSetValues(J,1,&i,1,&i,&zero,INSERT_VALUES);
124: }
125: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
126: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
127: } else {
128: /* Fill the structure using the expensive SNESComputeJacobianDefault. Temporarily set up the TS so we can call this function */
129: TSSetType(ts,TSBEULER);
130: TSSetUp(ts);
131: SNESComputeJacobianDefault(snes,x,&J,&J,&J_structure,ts);
132: }
134: /* create coloring context */
135: MatGetColoring(J,MATCOLORINGSL,&iscoloring);
136: MatFDColoringCreate(J,iscoloring,&matfdcoloring);
137: MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);
138: MatFDColoringSetFromOptions(matfdcoloring);
139: SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);
140: ISColoringDestroy(&iscoloring);
141: } else { /* Use finite differences (slow) */
142: SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL);
143: }
144: }
146: /* Pick up a Petsc preconditioner */
147: /* one can always set method or preconditioner during the run time */
148: TSGetSNES(ts,&snes);
149: SNESGetKSP(snes,&ksp);
150: KSPGetPC(ksp,&pc);
151: PCSetType(pc,PCJACOBI);
153: TSSetFromOptions(ts);
154: TSSetUp(ts);
156: /* Test TSSetPostStep() */
157: PetscOptionsHasName(NULL,"-test_PostStep",&flg);
158: if (flg) {
159: TSSetPostStep(ts,PostStep);
160: }
162: PetscOptionsGetInt(NULL,"-NOUT",&NOUT,NULL);
163: for (iout=1; iout<=NOUT; iout++) {
164: TSSetDuration(ts,time_steps,iout*ftime_original/NOUT);
165: TSSolve(ts,global);
166: TSGetSolveTime(ts,&ftime);
167: TSSetInitialTimeStep(ts,ftime,dt);
168: }
169: /* Interpolate solution at tfinal */
170: TSGetSolution(ts,&global);
171: TSInterpolate(ts,ftime_original,global);
173: PetscOptionsHasName(NULL,"-matlab_view",&flg);
174: if (flg) { /* print solution into a MATLAB file */
175: PetscViewerASCIIOpen(PETSC_COMM_WORLD,"out.m",&viewfile);
176: PetscViewerSetFormat(viewfile,PETSC_VIEWER_ASCII_MATLAB);
177: VecView(global,viewfile);
178: PetscViewerDestroy(&viewfile);
179: }
181: /* display solver info for Sundials */
182: TSGetType(ts,&tstype);
183: PetscObjectTypeCompare((PetscObject)ts,TSSUNDIALS,&sundials);
184: if (sundials) {
185: PetscViewerStringOpen(PETSC_COMM_WORLD,tsinfo,120,&viewer);
186: TSView(ts,viewer);
187: PetscViewerDestroy(&viewer);
188: PetscViewerStringOpen(PETSC_COMM_WORLD,pcinfo,120,&viewer);
189: PCView(pc,viewer);
190: PetscPrintf(PETSC_COMM_WORLD,"%d Procs,%s TSType, %s Preconditioner\n",
191: size,tsinfo,pcinfo);
192: PetscViewerDestroy(&viewer);
193: }
195: /* free the memories */
196: TSDestroy(&ts);
197: VecDestroy(&global);
198: VecDestroy(&x);
199: MatDestroy(&J);
200: if (fd_jacobian_coloring) {MatFDColoringDestroy(&matfdcoloring);}
201: PetscFinalize();
202: return 0;
203: }
205: /* -------------------------------------------------------------------*/
206: /* the initial function */
207: PetscReal f_ini(PetscReal x,PetscReal y)
208: {
209: PetscReal f;
211: f=exp(-20.0*(pow(x-0.5,2.0)+pow(y-0.5,2.0)));
212: return f;
213: }
217: PetscErrorCode Initial(Vec global,void *ctx)
218: {
219: Data *data = (Data*)ctx;
220: PetscInt m,row,col;
221: PetscReal x,y,dx,dy;
222: PetscScalar *localptr;
223: PetscInt i,mybase,myend,locsize;
227: /* make the local copies of parameters */
228: m = data->m;
229: dx = data->dx;
230: dy = data->dy;
232: /* determine starting point of each processor */
233: VecGetOwnershipRange(global,&mybase,&myend);
234: VecGetLocalSize(global,&locsize);
236: /* Initialize the array */
237: VecGetArray(global,&localptr);
239: for (i=0; i<locsize; i++) {
240: row = 1+(mybase+i)-((mybase+i)/m)*m;
241: col = (mybase+i)/m+1;
242: x = dx*row;
243: y = dy*col;
244: localptr[i] = f_ini(x,y);
245: }
247: VecRestoreArray(global,&localptr);
248: return(0);
249: }
253: PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec global,void *ctx)
254: {
255: VecScatter scatter;
256: IS from,to;
257: PetscInt i,n,*idx,nsteps,maxsteps;
258: Vec tmp_vec;
260: PetscScalar *tmp;
261: PetscReal maxtime;
262: Data *data = (Data*)ctx;
263: PetscReal tfinal = data->tfinal;
266: if (time > tfinal) return(0);
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;
280: /* Create local sequential vectors */
281: VecCreateSeq(PETSC_COMM_SELF,n,&tmp_vec);
283: /* Create scatter context */
284: ISCreateGeneral(PETSC_COMM_SELF,n,idx,PETSC_COPY_VALUES,&from);
285: ISCreateGeneral(PETSC_COMM_SELF,n,idx,PETSC_COPY_VALUES,&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);
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);
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);
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;
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,PETSC_COPY_VALUES,&from);
437: ISCreateGeneral(PETSC_COMM_SELF,len,idx,PETSC_COPY_VALUES,&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);
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: {
497: PetscReal t;
500: TSGetTime(ts,&t);
501: PetscPrintf(PETSC_COMM_SELF," PostStep, t: %g\n",t);
502: return(0);
503: }