Actual source code: ex28.c
petsc-3.4.5 2014-06-29
1: static const char help[] = "1D multiphysics prototype with analytic Jacobians to solve individual problems and a coupled problem.\n\n";
3: /* Solve a PDE coupled to an algebraic system in 1D
4: *
5: * PDE (U):
6: * -(k u_x)_x = 1 on (0,1), subject to u(0) = 0, u(1) = 1
7: * Algebraic (K):
8: * exp(k-1) + k = u + 1/(1/(1+u) + 1/(1+u_x^2))
9: *
10: * The discretization places k at staggered points, and a separate DMDA is used for each "physics".
11: *
12: * This example is a prototype for coupling in multi-physics problems, therefore residual evaluation and assembly for
13: * each problem (referred to as U and K) are written separately. This permits the same "physics" code to be used for
14: * solving each uncoupled problem as well as the coupled system. In particular, run with -problem_type 0 to solve only
15: * problem U (with K fixed), -problem_type 1 to solve only K (with U fixed), and -problem_type 2 to solve both at once.
16: *
17: * In all cases, a fully-assembled analytic Jacobian is available, so the systems can be solved with a direct solve or
18: * any other standard method. Additionally, by running with
19: *
20: * -pack_dm_mat_type nest
21: *
22: * The same code assembles a coupled matrix where each block is stored separately, which allows the use of PCFieldSplit
23: * without copying values to extract submatrices.
24: */
26: #include <petscsnes.h>
27: #include <petscdmda.h>
28: #include <petscdmcomposite.h>
30: typedef struct _UserCtx *User;
31: struct _UserCtx {
32: PetscInt ptype;
33: DM pack;
34: Vec Uloc,Kloc;
35: };
39: static PetscErrorCode FormFunctionLocal_U(User user,DMDALocalInfo *info,const PetscScalar u[],const PetscScalar k[],PetscScalar f[])
40: {
41: PetscReal hx = 1./info->mx;
42: PetscInt i;
45: for (i=info->xs; i<info->xs+info->xm; i++) {
46: if (i == 0) f[i] = 1./hx*u[i];
47: else if (i == info->mx-1) f[i] = 1./hx*(u[i] - 1.0);
48: else f[i] = hx*((k[i-1]*(u[i]-u[i-1]) - k[i]*(u[i+1]-u[i]))/(hx*hx) - 1.0);
49: }
50: return(0);
51: }
55: static PetscErrorCode FormFunctionLocal_K(User user,DMDALocalInfo *info,const PetscScalar u[],const PetscScalar k[],PetscScalar f[])
56: {
57: PetscReal hx = 1./info->mx;
58: PetscInt i;
61: for (i=info->xs; i<info->xs+info->xm; i++) {
62: const PetscScalar
63: ubar = 0.5*(u[i+1]+u[i]),
64: gradu = (u[i+1]-u[i])/hx,
65: g = 1. + gradu*gradu,
66: w = 1./(1.+ubar) + 1./g;
67: f[i] = hx*(PetscExpScalar(k[i]-1.0) + k[i] - 1./w);
68: }
69: return(0);
70: }
74: static PetscErrorCode FormFunction_All(SNES snes,Vec X,Vec F,void *ctx)
75: {
76: User user = (User)ctx;
77: DM dau,dak;
78: DMDALocalInfo infou,infok;
79: PetscScalar *u,*k;
80: PetscScalar *fu,*fk;
82: Vec Uloc,Kloc,Fu,Fk;
85: DMCompositeGetEntries(user->pack,&dau,&dak);
86: DMDAGetLocalInfo(dau,&infou);
87: DMDAGetLocalInfo(dak,&infok);
88: DMCompositeGetLocalVectors(user->pack,&Uloc,&Kloc);
89: switch (user->ptype) {
90: case 0:
91: DMGlobalToLocalBegin(dau,X,INSERT_VALUES,Uloc);
92: DMGlobalToLocalEnd (dau,X,INSERT_VALUES,Uloc);
93: DMDAVecGetArray(dau,Uloc,&u);
94: DMDAVecGetArray(dak,user->Kloc,&k);
95: DMDAVecGetArray(dau,F,&fu);
96: FormFunctionLocal_U(user,&infou,u,k,fu);
97: DMDAVecRestoreArray(dau,F,&fu);
98: DMDAVecRestoreArray(dau,Uloc,&u);
99: DMDAVecRestoreArray(dak,user->Kloc,&k);
100: break;
101: case 1:
102: DMGlobalToLocalBegin(dak,X,INSERT_VALUES,Kloc);
103: DMGlobalToLocalEnd (dak,X,INSERT_VALUES,Kloc);
104: DMDAVecGetArray(dau,user->Uloc,&u);
105: DMDAVecGetArray(dak,Kloc,&k);
106: DMDAVecGetArray(dak,F,&fk);
107: FormFunctionLocal_K(user,&infok,u,k,fk);
108: DMDAVecRestoreArray(dak,F,&fk);
109: DMDAVecRestoreArray(dau,user->Uloc,&u);
110: DMDAVecRestoreArray(dak,Kloc,&k);
111: break;
112: case 2:
113: DMCompositeScatter(user->pack,X,Uloc,Kloc);
114: DMDAVecGetArray(dau,Uloc,&u);
115: DMDAVecGetArray(dak,Kloc,&k);
116: DMCompositeGetAccess(user->pack,F,&Fu,&Fk);
117: DMDAVecGetArray(dau,Fu,&fu);
118: DMDAVecGetArray(dak,Fk,&fk);
119: FormFunctionLocal_U(user,&infou,u,k,fu);
120: FormFunctionLocal_K(user,&infok,u,k,fk);
121: DMDAVecRestoreArray(dau,Fu,&fu);
122: DMDAVecRestoreArray(dak,Fk,&fk);
123: DMCompositeRestoreAccess(user->pack,F,&Fu,&Fk);
124: DMDAVecRestoreArray(dau,Uloc,&u);
125: DMDAVecRestoreArray(dak,Kloc,&k);
126: break;
127: }
128: DMCompositeRestoreLocalVectors(user->pack,&Uloc,&Kloc);
129: return(0);
130: }
134: static PetscErrorCode FormJacobianLocal_U(User user,DMDALocalInfo *info,const PetscScalar u[],const PetscScalar k[],Mat Buu)
135: {
136: PetscReal hx = 1./info->mx;
138: PetscInt i;
141: for (i=info->xs; i<info->xs+info->xm; i++) {
142: PetscInt row = i-info->gxs,cols[] = {row-1,row,row+1};
143: PetscScalar val = 1./hx;
144: if (i == 0) {
145: MatSetValuesLocal(Buu,1,&row,1,&row,&val,INSERT_VALUES);
146: } else if (i == info->mx-1) {
147: MatSetValuesLocal(Buu,1,&row,1,&row,&val,INSERT_VALUES);
148: } else {
149: PetscScalar vals[] = {-k[i-1]/hx,(k[i-1]+k[i])/hx,-k[i]/hx};
150: MatSetValuesLocal(Buu,1,&row,3,cols,vals,INSERT_VALUES);
151: }
152: }
153: return(0);
154: }
158: static PetscErrorCode FormJacobianLocal_K(User user,DMDALocalInfo *info,const PetscScalar u[],const PetscScalar k[],Mat Bkk)
159: {
160: PetscReal hx = 1./info->mx;
162: PetscInt i;
165: for (i=info->xs; i<info->xs+info->xm; i++) {
166: PetscInt row = i-info->gxs;
167: PetscScalar vals[] = {hx*(PetscExpScalar(k[i]-1.)+1.)};
168: MatSetValuesLocal(Bkk,1,&row,1,&row,vals,INSERT_VALUES);
169: }
170: return(0);
171: }
175: static PetscErrorCode FormJacobianLocal_UK(User user,DMDALocalInfo *info,DMDALocalInfo *infok,const PetscScalar u[],const PetscScalar k[],Mat Buk)
176: {
177: PetscReal hx = 1./info->mx;
179: PetscInt i;
180: PetscInt row,cols[2];
181: PetscScalar vals[2];
184: if (!Buk) return(0); /* Not assembling this block */
185: for (i=info->xs; i<info->xs+info->xm; i++) {
186: if (i == 0 || i == info->mx-1) continue;
187: row = i-info->gxs;
188: cols[0] = i-1-infok->gxs; vals[0] = (u[i]-u[i-1])/hx;
189: cols[1] = i-infok->gxs; vals[1] = (u[i]-u[i+1])/hx;
190: MatSetValuesLocal(Buk,1,&row,2,cols,vals,INSERT_VALUES);
191: }
192: return(0);
193: }
197: static PetscErrorCode FormJacobianLocal_KU(User user,DMDALocalInfo *info,DMDALocalInfo *infok,const PetscScalar u[],const PetscScalar k[],Mat Bku)
198: {
200: PetscInt i;
201: PetscReal hx = 1./(info->mx-1);
204: if (!Bku) return(0); /* Not assembling this block */
205: for (i=infok->xs; i<infok->xs+infok->xm; i++) {
206: PetscInt row = i-infok->gxs,cols[2];
207: PetscScalar vals[2];
208: const PetscScalar
209: ubar = 0.5*(u[i]+u[i+1]),
210: ubar_L = 0.5,
211: ubar_R = 0.5,
212: gradu = (u[i+1]-u[i])/hx,
213: gradu_L = -1./hx,
214: gradu_R = 1./hx,
215: g = 1. + PetscSqr(gradu),
216: g_gradu = 2.*gradu,
217: w = 1./(1.+ubar) + 1./g,
218: w_ubar = -1./PetscSqr(1.+ubar),
219: w_gradu = -g_gradu/PetscSqr(g),
220: iw = 1./w,
221: iw_ubar = -w_ubar * PetscSqr(iw),
222: iw_gradu = -w_gradu * PetscSqr(iw);
223: cols[0] = i-info->gxs; vals[0] = -hx*(iw_ubar*ubar_L + iw_gradu*gradu_L);
224: cols[1] = i+1-info->gxs; vals[1] = -hx*(iw_ubar*ubar_R + iw_gradu*gradu_R);
225: MatSetValuesLocal(Bku,1,&row,2,cols,vals,INSERT_VALUES);
226: }
227: return(0);
228: }
232: static PetscErrorCode FormJacobian_All(SNES snes,Vec X,Mat *J,Mat *B,MatStructure *mstr,void *ctx)
233: {
234: User user = (User)ctx;
235: DM dau,dak;
236: DMDALocalInfo infou,infok;
237: PetscScalar *u,*k;
239: Vec Uloc,Kloc;
242: DMCompositeGetEntries(user->pack,&dau,&dak);
243: DMDAGetLocalInfo(dau,&infou);
244: DMDAGetLocalInfo(dak,&infok);
245: DMCompositeGetLocalVectors(user->pack,&Uloc,&Kloc);
246: switch (user->ptype) {
247: case 0:
248: DMGlobalToLocalBegin(dau,X,INSERT_VALUES,Uloc);
249: DMGlobalToLocalEnd (dau,X,INSERT_VALUES,Uloc);
250: DMDAVecGetArray(dau,Uloc,&u);
251: DMDAVecGetArray(dak,user->Kloc,&k);
252: FormJacobianLocal_U(user,&infou,u,k,*B);
253: DMDAVecRestoreArray(dau,Uloc,&u);
254: DMDAVecRestoreArray(dak,user->Kloc,&k);
255: break;
256: case 1:
257: DMGlobalToLocalBegin(dak,X,INSERT_VALUES,Kloc);
258: DMGlobalToLocalEnd (dak,X,INSERT_VALUES,Kloc);
259: DMDAVecGetArray(dau,user->Uloc,&u);
260: DMDAVecGetArray(dak,Kloc,&k);
261: FormJacobianLocal_K(user,&infok,u,k,*B);
262: DMDAVecRestoreArray(dau,user->Uloc,&u);
263: DMDAVecRestoreArray(dak,Kloc,&k);
264: break;
265: case 2: {
266: Mat Buu,Buk,Bku,Bkk;
267: IS *is;
268: DMCompositeScatter(user->pack,X,Uloc,Kloc);
269: DMDAVecGetArray(dau,Uloc,&u);
270: DMDAVecGetArray(dak,Kloc,&k);
271: DMCompositeGetLocalISs(user->pack,&is);
272: MatGetLocalSubMatrix(*B,is[0],is[0],&Buu);
273: MatGetLocalSubMatrix(*B,is[0],is[1],&Buk);
274: MatGetLocalSubMatrix(*B,is[1],is[0],&Bku);
275: MatGetLocalSubMatrix(*B,is[1],is[1],&Bkk);
276: FormJacobianLocal_U(user,&infou,u,k,Buu);
277: FormJacobianLocal_UK(user,&infou,&infok,u,k,Buk);
278: FormJacobianLocal_KU(user,&infou,&infok,u,k,Bku);
279: FormJacobianLocal_K(user,&infok,u,k,Bkk);
280: MatRestoreLocalSubMatrix(*B,is[0],is[0],&Buu);
281: MatRestoreLocalSubMatrix(*B,is[0],is[1],&Buk);
282: MatRestoreLocalSubMatrix(*B,is[1],is[0],&Bku);
283: MatRestoreLocalSubMatrix(*B,is[1],is[1],&Bkk);
284: DMDAVecRestoreArray(dau,Uloc,&u);
285: DMDAVecRestoreArray(dak,Kloc,&k);
287: ISDestroy(&is[0]);
288: ISDestroy(&is[1]);
289: PetscFree(is);
290: } break;
291: }
292: DMCompositeRestoreLocalVectors(user->pack,&Uloc,&Kloc);
293: MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
294: MatAssemblyEnd (*B,MAT_FINAL_ASSEMBLY);
295: if (*J != *B) {
296: MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
297: MatAssemblyEnd (*J,MAT_FINAL_ASSEMBLY);
298: }
299: *mstr = DIFFERENT_NONZERO_PATTERN;
300: return(0);
301: }
305: static PetscErrorCode FormInitial_Coupled(User user,Vec X)
306: {
308: DM dau,dak;
309: DMDALocalInfo infou,infok;
310: Vec Xu,Xk;
311: PetscScalar *u,*k,hx;
312: PetscInt i;
315: DMCompositeGetEntries(user->pack,&dau,&dak);
316: DMCompositeGetAccess(user->pack,X,&Xu,&Xk);
317: DMDAVecGetArray(dau,Xu,&u);
318: DMDAVecGetArray(dak,Xk,&k);
319: DMDAGetLocalInfo(dau,&infou);
320: DMDAGetLocalInfo(dak,&infok);
321: hx = 1./(infok.mx);
322: for (i=infou.xs; i<infou.xs+infou.xm; i++) u[i] = (PetscScalar)i*hx * (1.-(PetscScalar)i*hx);
323: for (i=infok.xs; i<infok.xs+infok.xm; i++) k[i] = 1.0 + 0.5*(PetscScalar)sin((double)2*PETSC_PI*i*hx);
324: DMDAVecRestoreArray(dau,Xu,&u);
325: DMDAVecRestoreArray(dak,Xk,&k);
326: DMCompositeRestoreAccess(user->pack,X,&Xu,&Xk);
327: DMCompositeScatter(user->pack,X,user->Uloc,user->Kloc);
328: return(0);
329: }
333: int main(int argc, char *argv[])
334: {
336: DM dau,dak,pack;
337: const PetscInt *lxu;
338: PetscInt *lxk,m,nprocs;
339: User user;
340: SNES snes;
341: Vec X,F,Xu,Xk,Fu,Fk;
342: Mat B;
343: IS *isg;
344: PetscBool view_draw,pass_dm;
346: PetscInitialize(&argc,&argv,0,help);
347: DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,-10,1,1,NULL,&dau);
348: DMSetOptionsPrefix(dau,"u_");
349: DMSetFromOptions(dau);
350: DMDAGetOwnershipRanges(dau,&lxu,0,0);
351: DMDAGetInfo(dau,0, &m,0,0, &nprocs,0,0, 0,0,0,0,0,0);
352: PetscMalloc(nprocs*sizeof(*lxk),&lxk);
353: PetscMemcpy(lxk,lxu,nprocs*sizeof(*lxk));
354: lxk[0]--;
355: DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,m-1,1,1,lxk,&dak);
356: DMSetOptionsPrefix(dak,"k_");
357: DMSetFromOptions(dau);
358: PetscFree(lxk);
360: DMCompositeCreate(PETSC_COMM_WORLD,&pack);
361: DMSetOptionsPrefix(pack,"pack_");
362: DMCompositeAddDM(pack,dau);
363: DMCompositeAddDM(pack,dak);
364: DMDASetFieldName(dau,0,"u");
365: DMDASetFieldName(dak,0,"k");
366: DMSetFromOptions(pack);
368: DMCreateGlobalVector(pack,&X);
369: VecDuplicate(X,&F);
371: PetscNew(struct _UserCtx,&user);
373: user->pack = pack;
375: DMCompositeGetGlobalISs(pack,&isg);
376: DMCompositeGetLocalVectors(pack,&user->Uloc,&user->Kloc);
377: DMCompositeScatter(pack,X,user->Uloc,user->Kloc);
379: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Coupled problem options","SNES");
380: {
381: user->ptype = 0; view_draw = PETSC_FALSE; pass_dm = PETSC_TRUE;
383: PetscOptionsInt("-problem_type","0: solve for u only, 1: solve for k only, 2: solve for both",0,user->ptype,&user->ptype,0);
384: PetscOptionsBool("-view_draw","Draw the final coupled solution regardless of whether only one physics was solved",0,view_draw,&view_draw,0);
385: PetscOptionsBool("-pass_dm","Pass the packed DM to SNES to use when determining splits and forward into splits",0,pass_dm,&pass_dm,0);
386: }
387: PetscOptionsEnd();
389: FormInitial_Coupled(user,X);
391: SNESCreate(PETSC_COMM_WORLD,&snes);
392: switch (user->ptype) {
393: case 0:
394: DMCompositeGetAccess(pack,X,&Xu,0);
395: DMCompositeGetAccess(pack,F,&Fu,0);
396: DMCreateMatrix(dau,NULL,&B);
397: SNESSetFunction(snes,Fu,FormFunction_All,user);
398: SNESSetJacobian(snes,B,B,FormJacobian_All,user);
399: SNESSetFromOptions(snes);
400: SNESSetDM(snes,dau);
401: SNESSolve(snes,NULL,Xu);
402: DMCompositeRestoreAccess(pack,X,&Xu,0);
403: DMCompositeRestoreAccess(pack,F,&Fu,0);
404: break;
405: case 1:
406: DMCompositeGetAccess(pack,X,0,&Xk);
407: DMCompositeGetAccess(pack,F,0,&Fk);
408: DMCreateMatrix(dak,NULL,&B);
409: SNESSetFunction(snes,Fk,FormFunction_All,user);
410: SNESSetJacobian(snes,B,B,FormJacobian_All,user);
411: SNESSetFromOptions(snes);
412: SNESSetDM(snes,dak);
413: SNESSolve(snes,NULL,Xk);
414: DMCompositeRestoreAccess(pack,X,0,&Xk);
415: DMCompositeRestoreAccess(pack,F,0,&Fk);
416: break;
417: case 2:
418: DMCreateMatrix(pack,NULL,&B);
419: /* This example does not correctly allocate off-diagonal blocks. These options allows new nonzeros (slow). */
420: MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
421: MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
422: SNESSetFunction(snes,F,FormFunction_All,user);
423: SNESSetJacobian(snes,B,B,FormJacobian_All,user);
424: SNESSetFromOptions(snes);
425: if (!pass_dm) { /* Manually provide index sets and names for the splits */
426: KSP ksp;
427: PC pc;
428: SNESGetKSP(snes,&ksp);
429: KSPGetPC(ksp,&pc);
430: PCFieldSplitSetIS(pc,"u",isg[0]);
431: PCFieldSplitSetIS(pc,"k",isg[1]);
432: } else {
433: /* The same names come from the options prefix for dau and dak. This option can support geometric multigrid inside
434: * of splits, but it requires using a DM (perhaps your own implementation). */
435: SNESSetDM(snes,pack);
436: }
437: SNESSolve(snes,NULL,X);
438: break;
439: }
440: if (view_draw) {VecView(X,PETSC_VIEWER_DRAW_WORLD);}
441: if (0) {
442: PetscInt col = 0;
443: PetscBool mult_dup = PETSC_FALSE,view_dup = PETSC_FALSE;
444: Mat D;
445: Vec Y;
447: PetscOptionsGetInt(0,"-col",&col,0);
448: PetscOptionsGetBool(0,"-mult_dup",&mult_dup,0);
449: PetscOptionsGetBool(0,"-view_dup",&view_dup,0);
451: VecDuplicate(X,&Y);
452: /* MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY); */
453: /* MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY); */
454: MatConvert(B,MATAIJ,MAT_INITIAL_MATRIX,&D);
455: VecZeroEntries(X);
456: VecSetValue(X,col,1.0,INSERT_VALUES);
457: VecAssemblyBegin(X);
458: VecAssemblyEnd(X);
459: MatMult(mult_dup ? D : B,X,Y);
460: MatView(view_dup ? D : B,PETSC_VIEWER_STDOUT_WORLD);
461: /* VecView(X,PETSC_VIEWER_STDOUT_WORLD); */
462: VecView(Y,PETSC_VIEWER_STDOUT_WORLD);
463: MatDestroy(&D);
464: VecDestroy(&Y);
465: }
467: DMCompositeRestoreLocalVectors(pack,&user->Uloc,&user->Kloc);
468: PetscFree(user);
470: ISDestroy(&isg[0]);
471: ISDestroy(&isg[1]);
472: PetscFree(isg);
473: VecDestroy(&X);
474: VecDestroy(&F);
475: MatDestroy(&B);
476: DMDestroy(&dau);
477: DMDestroy(&dak);
478: DMDestroy(&pack);
479: SNESDestroy(&snes);
480: PetscFinalize();
481: return 0;
482: }