Actual source code: ex1.c
1: /*$Id: ex1.c,v 1.50 2001/09/07 20:12:09 bsmith Exp $*/
2: /*
3: Formatted test for TS routines.
5: Solves U_t = U_xx
6: F(t,u) = (u_i+1 - 2u_i + u_i-1)/h^2
7: using several different schemes.
8: */
10: static char help[] = "Solves 1D heat equation.nn";
12: #include petscda.h
13: #include petscsys.h
14: #include petscts.h
16: #define PETSC_NEAR(a,b,c) (!(PetscAbsReal((a)-(b)) > (c)*PetscMax(PetscAbsReal(a),PetscAbsReal(b))))
18: typedef struct {
19: Vec global,local,localwork,solution; /* location for local work (with ghost points) vector */
20: DA da; /* manages ghost point communication */
21: PetscViewer viewer1,viewer2;
22: int M; /* total number of grid points */
23: PetscReal h; /* mesh width h = 1/(M-1) */
24: PetscReal norm_2,norm_max;
25: int nox; /* indicates problem is to be run without graphics */
26: } AppCtx;
28: extern int Monitor(TS,int,PetscReal,Vec,void *);
29: extern int RHSFunctionHeat(TS,PetscReal,Vec,Vec,void*);
30: extern int RHSMatrixFree(Mat,Vec,Vec);
31: extern int Initial(Vec,void*);
32: extern int RHSMatrixHeat(TS,PetscReal,Mat *,Mat *,MatStructure *,void *);
33: extern int RHSJacobianHeat(TS,PetscReal,Vec,Mat*,Mat*,MatStructure *,void*);
35: #define linear_no_matrix 0
36: #define linear_no_time 1
37: #define linear 2
38: #define nonlinear_no_jacobian 3
39: #define nonlinear 4
41: int main(int argc,char **argv)
42: {
43: int ierr,time_steps = 100,steps,size,m;
44: int problem = linear_no_matrix;
45: PetscTruth flg;
46: AppCtx appctx;
47: PetscReal dt,ftime;
48: TS ts;
49: Mat A = 0;
50: MatStructure A_structure;
51: TSProblemType tsproblem = TS_LINEAR;
52: PetscDraw draw;
53: PetscViewer viewer;
54: char tsinfo[120];
55:
56: PetscInitialize(&argc,&argv,(char*)0,help);
57: MPI_Comm_size(PETSC_COMM_WORLD,&size);
59: appctx.M = 60;
60: PetscOptionsGetInt(PETSC_NULL,"-M",&appctx.M,PETSC_NULL);
61: PetscOptionsGetInt(PETSC_NULL,"-time",&time_steps,PETSC_NULL);
62:
63: PetscOptionsHasName(PETSC_NULL,"-nox",&flg);
64: if (flg) appctx.nox = 1; else appctx.nox = 0;
65: appctx.norm_2 = 0.0; appctx.norm_max = 0.0;
67: /* Set up the ghost point communication pattern */
68: DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,appctx.M,1,1,PETSC_NULL,&appctx.da);
69: DACreateGlobalVector(appctx.da,&appctx.global);
70: VecGetLocalSize(appctx.global,&m);
71: DACreateLocalVector(appctx.da,&appctx.local);
73: /* Set up display to show wave graph */
75: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"",80,380,400,160,&appctx.viewer1);
76: PetscViewerDrawGetDraw(appctx.viewer1,0,&draw);
77: PetscDrawSetDoubleBuffer(draw);
78: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"",80,0,400,160,&appctx.viewer2);
79: PetscViewerDrawGetDraw(appctx.viewer2,0,&draw);
80: PetscDrawSetDoubleBuffer(draw);
83: /* make work array for evaluating right hand side function */
84: VecDuplicate(appctx.local,&appctx.localwork);
86: /* make work array for storing exact solution */
87: VecDuplicate(appctx.global,&appctx.solution);
89: appctx.h = 1.0/(appctx.M-1.0);
91: /* set initial conditions */
92: Initial(appctx.global,&appctx);
93:
94: /*
95: This example is written to allow one to easily test parts
96: of TS, we do not expect users to generally need to use more
97: then a single TSProblemType
98: */
99: PetscOptionsHasName(PETSC_NULL,"-linear_no_matrix",&flg);
100: if (flg) {
101: tsproblem = TS_LINEAR;
102: problem = linear_no_matrix;
103: }
104: PetscOptionsHasName(PETSC_NULL,"-linear_constant_matrix",&flg);
105: if (flg) {
106: tsproblem = TS_LINEAR;
107: problem = linear_no_time;
108: }
109: PetscOptionsHasName(PETSC_NULL,"-linear_variable_matrix",&flg);
110: if (flg) {
111: tsproblem = TS_LINEAR;
112: problem = linear;
113: }
114: PetscOptionsHasName(PETSC_NULL,"-nonlinear_no_jacobian",&flg);
115: if (flg) {
116: tsproblem = TS_NONLINEAR;
117: problem = nonlinear_no_jacobian;
118: }
119: PetscOptionsHasName(PETSC_NULL,"-nonlinear_jacobian",&flg);
120: if (flg) {
121: tsproblem = TS_NONLINEAR;
122: problem = nonlinear;
123: }
124:
125: /* make timestep context */
126: TSCreate(PETSC_COMM_WORLD,&ts);
127: TSSetProblemType(ts,tsproblem);
128: TSSetMonitor(ts,Monitor,&appctx,PETSC_NULL);
130: dt = appctx.h*appctx.h/2.01;
132: if (problem == linear_no_matrix) {
133: /*
134: The user provides the RHS as a Shell matrix.
135: */
136: MatCreateShell(PETSC_COMM_WORLD,m,appctx.M,appctx.M,appctx.M,&appctx,&A);
137: MatShellSetOperation(A,MATOP_MULT,(void(*)(void))RHSMatrixFree);
138: TSSetRHSMatrix(ts,A,A,PETSC_NULL,&appctx);
139: } else if (problem == linear_no_time) {
140: /*
141: The user provides the RHS as a matrix
142: */
143: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,appctx.M,appctx.M,&A);
144: MatSetFromOptions(A);
145: RHSMatrixHeat(ts,0.0,&A,&A,&A_structure,&appctx);
146: TSSetRHSMatrix(ts,A,A,PETSC_NULL,&appctx);
147: } else if (problem == linear) {
148: /*
149: The user provides the RHS as a time dependent matrix
150: */
151: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,appctx.M,appctx.M,&A);
152: MatSetFromOptions(A);
153: RHSMatrixHeat(ts,0.0,&A,&A,&A_structure,&appctx);
154: TSSetRHSMatrix(ts,A,A,RHSMatrixHeat,&appctx);
155: } else if (problem == nonlinear_no_jacobian) {
156: /*
157: The user provides the RHS and a Shell Jacobian
158: */
159: TSSetRHSFunction(ts,RHSFunctionHeat,&appctx);
160: MatCreateShell(PETSC_COMM_WORLD,m,appctx.M,appctx.M,appctx.M,&appctx,&A);
161: MatShellSetOperation(A,MATOP_MULT,(void(*)(void))RHSMatrixFree);
162: TSSetRHSJacobian(ts,A,A,PETSC_NULL,&appctx);
163: } else if (problem == nonlinear) {
164: /*
165: The user provides the RHS and Jacobian
166: */
167: TSSetRHSFunction(ts,RHSFunctionHeat,&appctx);
168: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,appctx.M,appctx.M,&A);
169: MatSetFromOptions(A);
170: RHSMatrixHeat(ts,0.0,&A,&A,&A_structure,&appctx);
171: TSSetRHSJacobian(ts,A,A,RHSJacobianHeat,&appctx);
172: }
174: TSSetFromOptions(ts);
176: TSSetInitialTimeStep(ts,0.0,dt);
177: TSSetDuration(ts,time_steps,100.);
178: TSSetSolution(ts,appctx.global);
181: TSSetUp(ts);
182: TSStep(ts,&steps,&ftime);
183: PetscViewerStringOpen(PETSC_COMM_WORLD,tsinfo,120,&viewer);
184: TSView(ts,viewer);
186: PetscOptionsHasName(PETSC_NULL,"-test",&flg);
187: if (flg) {
188: PetscTruth iseuler;
189: PetscTypeCompare((PetscObject)ts,"euler",&iseuler);
190: if (iseuler) {
191: if (!PETSC_NEAR(appctx.norm_2/steps,0.00257244,1.e-4)) {
192: fprintf(stdout,"Error in Euler method: 2-norm %g expecting: 0.00257244n",appctx.norm_2/steps);
193: }
194: } else {
195: if (!PETSC_NEAR(appctx.norm_2/steps,0.00506174,1.e-4)) {
196: fprintf(stdout,"Error in %s method: 2-norm %g expecting: 0.00506174n",tsinfo,appctx.norm_2/steps);
197: }
198: }
199: } else {
200: PetscPrintf(PETSC_COMM_WORLD,"%d Procs Avg. error 2 norm %g max norm %g %sn",
201: size,appctx.norm_2/steps,appctx.norm_max/steps,tsinfo);
202: }
204: PetscViewerDestroy(viewer);
205: TSDestroy(ts);
206: PetscViewerDestroy(appctx.viewer1);
207: PetscViewerDestroy(appctx.viewer2);
208: VecDestroy(appctx.localwork);
209: VecDestroy(appctx.solution);
210: VecDestroy(appctx.local);
211: VecDestroy(appctx.global);
212: DADestroy(appctx.da);
213: if (A) {ierr= MatDestroy(A);}
215: PetscFinalize();
216: return 0;
217: }
219: /* -------------------------------------------------------------------*/
220: int Initial(Vec global,void *ctx)
221: {
222: AppCtx *appctx = (AppCtx*) ctx;
223: PetscScalar *localptr,h = appctx->h;
224: int i,mybase,myend,ierr;
226: /* determine starting point of each processor */
227: VecGetOwnershipRange(global,&mybase,&myend);
229: /* Initialize the array */
230: VecGetArray(global,&localptr);
231: for (i=mybase; i<myend; i++) {
232: localptr[i-mybase] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h);
233: }
234: VecRestoreArray(global,&localptr);
235: return 0;
236: }
238: /*
239: Exact solution
240: */
241: int Solution(PetscReal t,Vec solution,void *ctx)
242: {
243: AppCtx *appctx = (AppCtx*) ctx;
244: PetscScalar *localptr,h = appctx->h,ex1,ex2,sc1,sc2;
245: int i,mybase,myend,ierr;
247: /* determine starting point of each processor */
248: VecGetOwnershipRange(solution,&mybase,&myend);
250: ex1 = exp(-36.*PETSC_PI*PETSC_PI*t);
251: ex2 = exp(-4.*PETSC_PI*PETSC_PI*t);
252: sc1 = PETSC_PI*6.*h; sc2 = PETSC_PI*2.*h;
253: VecGetArray(solution,&localptr);
254: for (i=mybase; i<myend; i++) {
255: localptr[i-mybase] = PetscSinScalar(sc1*(PetscReal)i)*ex1 + 3.*PetscSinScalar(sc2*(PetscReal)i)*ex2;
256: }
257: VecRestoreArray(solution,&localptr);
258: return 0;
259: }
261: int Monitor(TS ts,int step,PetscReal ltime,Vec global,void *ctx)
262: {
263: AppCtx *appctx = (AppCtx*) ctx;
264: int ierr;
265: PetscReal norm_2,norm_max;
266: PetscScalar mone = -1.0;
267: MPI_Comm comm;
269: PetscObjectGetComm((PetscObject)ts,&comm);
271: VecView(global,appctx->viewer2);
273: Solution(ltime,appctx->solution,ctx);
274: VecAXPY(&mone,global,appctx->solution);
275: VecNorm(appctx->solution,NORM_2,&norm_2);
276: norm_2 = sqrt(appctx->h)*norm_2;
277: VecNorm(appctx->solution,NORM_MAX,&norm_max);
279: if (!appctx->nox) {
280: PetscPrintf(comm,"timestep %d time %g norm of error %g %gn",step,ltime,norm_2,norm_max);
281: }
283: appctx->norm_2 += norm_2;
284: appctx->norm_max += norm_max;
286: VecView(appctx->solution,appctx->viewer1);
288: return 0;
289: }
291: /* -----------------------------------------------------------------------*/
292: int RHSMatrixFree(Mat mat,Vec x,Vec y)
293: {
294: int ierr;
295: void *ctx;
297: MatShellGetContext(mat,(void **)&ctx);
298: RHSFunctionHeat(0,0.0,x,y,ctx);
299: return 0;
300: }
302: int RHSFunctionHeat(TS ts,PetscReal t,Vec globalin,Vec globalout,void *ctx)
303: {
304: AppCtx *appctx = (AppCtx*) ctx;
305: DA da = appctx->da;
306: Vec local = appctx->local,localwork = appctx->localwork;
307: int ierr,i,localsize;
308: PetscScalar *copyptr,*localptr,sc;
310: /*Extract local array */
311: DAGlobalToLocalBegin(da,globalin,INSERT_VALUES,local);
312: DAGlobalToLocalEnd(da,globalin,INSERT_VALUES,local);
313: VecGetArray(local,&localptr);
315: /* Extract work vector */
316: VecGetArray(localwork,©ptr);
318: /* Update Locally - Make array of new values */
319: /* Note: For the first and last entry I copy the value */
320: /* if this is an interior node it is irrelevant */
321: sc = 1.0/(appctx->h*appctx->h);
322: VecGetLocalSize(local,&localsize);
323: copyptr[0] = localptr[0];
324: for (i=1; i<localsize-1; i++) {
325: copyptr[i] = sc * (localptr[i+1] + localptr[i-1] - 2.0*localptr[i]);
326: }
327: copyptr[localsize-1] = localptr[localsize-1];
328: VecRestoreArray(local,&localptr);
329: VecRestoreArray(localwork,©ptr);
331: /* Local to Global */
332: DALocalToGlobal(da,localwork,INSERT_VALUES,globalout);
333: return 0;
334: }
336: /* ---------------------------------------------------------------------*/
337: int RHSMatrixHeat(TS ts,PetscReal t,Mat *AA,Mat *BB,MatStructure *str,void *ctx)
338: {
339: Mat A = *AA;
340: AppCtx *appctx = (AppCtx*) ctx;
341: int ierr,i,mstart,mend,rank,size,idx[3];
342: PetscScalar v[3],stwo = -2./(appctx->h*appctx->h),sone = -.5*stwo;
344: *str = SAME_NONZERO_PATTERN;
346: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
347: MPI_Comm_size(PETSC_COMM_WORLD,&size);
349: MatGetOwnershipRange(A,&mstart,&mend);
350: if (mstart == 0) {
351: v[0] = 1.0;
352: MatSetValues(A,1,&mstart,1,&mstart,v,INSERT_VALUES);
353: mstart++;
354: }
355: if (mend == appctx->M) {
356: mend--;
357: v[0] = 1.0;
358: MatSetValues(A,1,&mend,1,&mend,v,INSERT_VALUES);
359: }
361: /*
362: Construct matrice one row at a time
363: */
364: v[0] = sone; v[1] = stwo; v[2] = sone;
365: for (i=mstart; i<mend; i++) {
366: idx[0] = i-1; idx[1] = i; idx[2] = i+1;
367: MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
368: }
370: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
371: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
372: return 0;
373: }
375: int RHSJacobianHeat(TS ts,PetscReal t,Vec x,Mat *AA,Mat *BB,MatStructure *str,void *ctx)
376: {
377: return RHSMatrixHeat(ts,t,AA,BB,str,ctx);
378: }