Actual source code: ex58.c
petsc-3.9.4 2018-09-11
2: #include <petscsnes.h>
3: #include <petscdm.h>
4: #include <petscdmda.h>
6: static const char help[] = "Parallel version of the minimum surface area problem in 2D using DMDA.\n\
7: It solves a system of nonlinear equations in mixed\n\
8: complementarity form.This example is based on a\n\
9: problem from the MINPACK-2 test suite. Given a rectangular 2-D domain and\n\
10: boundary values along the edges of the domain, the objective is to find the\n\
11: surface with the minimal area that satisfies the boundary conditions.\n\
12: This application solves this problem using complimentarity -- We are actually\n\
13: solving the system (grad f)_i >= 0, if x_i == l_i \n\
14: (grad f)_i = 0, if l_i < x_i < u_i \n\
15: (grad f)_i <= 0, if x_i == u_i \n\
16: where f is the function to be minimized. \n\
17: \n\
18: The command line options are:\n\
19: -da_grid_x <nx>, where <nx> = number of grid points in the 1st coordinate direction\n\
20: -da_grid_y <ny>, where <ny> = number of grid points in the 2nd coordinate direction\n\
21: -start <st>, where <st> =0 for zero vector, and an average of the boundary conditions otherwise\n\
22: -lb <value>, lower bound on the variables\n\
23: -ub <value>, upper bound on the variables\n\n";
25: /*
26: User-defined application context - contains data needed by the
27: application-provided call-back routines, FormJacobian() and
28: FormFunction().
29: */
31: /*
32: This is a new version of the ../tests/ex8.c code
34: Run, for example, with the options ./ex58 -snes_vi_monitor -ksp_monitor -mg_levels_ksp_monitor -pc_type mg -pc_mg_levels 2 -pc_mg_galerkin pmat -ksp_type fgmres
36: Or to run with grid sequencing on the nonlinear problem (note that you do not need to provide the number of
37: multigrid levels, it will be determined automatically based on the number of refinements done)
39: ./ex58 -pc_type mg -ksp_monitor -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3
40: -mg_levels_ksp_monitor -snes_vi_monitor -mg_levels_pc_type sor -pc_mg_type full
43: */
45: typedef struct {
46: PetscScalar *bottom, *top, *left, *right;
47: PetscScalar lb,ub;
48: } AppCtx;
51: /* -------- User-defined Routines --------- */
53: extern PetscErrorCode FormBoundaryConditions(SNES,AppCtx**);
54: extern PetscErrorCode DestroyBoundaryConditions(AppCtx**);
55: extern PetscErrorCode ComputeInitialGuess(SNES, Vec,void*);
56: extern PetscErrorCode FormGradient(SNES, Vec, Vec, void*);
57: extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void*);
58: extern PetscErrorCode FormBounds(SNES,Vec,Vec);
60: int main(int argc, char **argv)
61: {
63: Vec x,r; /* solution and residual vectors */
64: SNES snes; /* nonlinear solver context */
65: Mat J; /* Jacobian matrix */
66: DM da;
68: PetscInitialize(&argc, &argv, (char*)0, help);if (ierr) return ierr;
70: /* Create distributed array to manage the 2d grid */
71: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
72: DMSetFromOptions(da);
73: DMSetUp(da);
75: /* Extract global vectors from DMDA; */
76: DMCreateGlobalVector(da,&x);
77: VecDuplicate(x, &r);
79: DMSetMatType(da,MATAIJ);
80: DMCreateMatrix(da,&J);
82: /* Create nonlinear solver context */
83: SNESCreate(PETSC_COMM_WORLD,&snes);
84: SNESSetDM(snes,da);
86: /* Set function evaluation and Jacobian evaluation routines */
87: SNESSetFunction(snes,r,FormGradient,NULL);
88: SNESSetJacobian(snes,J,J,FormJacobian,NULL);
90: SNESSetComputeApplicationContext(snes,(PetscErrorCode (*)(SNES,void**))FormBoundaryConditions,(PetscErrorCode (*)(void**))DestroyBoundaryConditions);
92: SNESSetComputeInitialGuess(snes,ComputeInitialGuess,NULL);
94: SNESVISetComputeVariableBounds(snes,FormBounds);
96: SNESSetFromOptions(snes);
98: /* Solve the application */
99: SNESSolve(snes,NULL,x);
101: /* Free memory */
102: VecDestroy(&x);
103: VecDestroy(&r);
104: MatDestroy(&J);
105: SNESDestroy(&snes);
107: /* Free user-created data structures */
108: DMDestroy(&da);
110: PetscFinalize();
111: return ierr;
112: }
114: /* -------------------------------------------------------------------- */
116: /* FormBounds - sets the upper and lower bounds
118: Input Parameters:
119: . snes - the SNES context
121: Output Parameters:
122: . xl - lower bounds
123: . xu - upper bounds
124: */
125: PetscErrorCode FormBounds(SNES snes, Vec xl, Vec xu)
126: {
128: AppCtx *ctx;
131: SNESGetApplicationContext(snes,&ctx);
132: VecSet(xl,ctx->lb);
133: VecSet(xu,ctx->ub);
134: return(0);
135: }
137: /* -------------------------------------------------------------------- */
139: /* FormGradient - Evaluates gradient of f.
141: Input Parameters:
142: . snes - the SNES context
143: . X - input vector
144: . ptr - optional user-defined context, as set by SNESSetFunction()
146: Output Parameters:
147: . G - vector containing the newly evaluated gradient
148: */
149: PetscErrorCode FormGradient(SNES snes, Vec X, Vec G, void *ptr)
150: {
151: AppCtx *user;
152: int ierr;
153: PetscInt i,j;
154: PetscInt mx, my;
155: PetscScalar hx,hy, hydhx, hxdhy;
156: PetscScalar f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
157: PetscScalar df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc;
158: PetscScalar **g, **x;
159: PetscInt xs,xm,ys,ym;
160: Vec localX;
161: DM da;
164: SNESGetDM(snes,&da);
165: SNESGetApplicationContext(snes,(void**)&user);
166: DMDAGetInfo(da,PETSC_IGNORE,&mx,&my,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
167: hx = 1.0/(mx+1);hy=1.0/(my+1); hydhx=hy/hx; hxdhy=hx/hy;
169: VecSet(G,0.0);
171: /* Get local vector */
172: DMGetLocalVector(da,&localX);
173: /* Get ghost points */
174: DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
175: DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
176: /* Get pointer to local vector data */
177: DMDAVecGetArray(da,localX, &x);
178: DMDAVecGetArray(da,G, &g);
180: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
181: /* Compute function over the locally owned part of the mesh */
182: for (j=ys; j < ys+ym; j++) {
183: for (i=xs; i< xs+xm; i++) {
185: xc = x[j][i];
186: xlt=xrb=xl=xr=xb=xt=xc;
188: if (i==0) { /* left side */
189: xl = user->left[j+1];
190: xlt = user->left[j+2];
191: } else xl = x[j][i-1];
193: if (j==0) { /* bottom side */
194: xb = user->bottom[i+1];
195: xrb = user->bottom[i+2];
196: } else xb = x[j-1][i];
198: if (i+1 == mx) { /* right side */
199: xr = user->right[j+1];
200: xrb = user->right[j];
201: } else xr = x[j][i+1];
203: if (j+1==0+my) { /* top side */
204: xt = user->top[i+1];
205: xlt = user->top[i];
206: } else xt = x[j+1][i];
208: if (i>0 && j+1<my) xlt = x[j+1][i-1]; /* left top side */
209: if (j>0 && i+1<mx) xrb = x[j-1][i+1]; /* right bottom */
211: d1 = (xc-xl);
212: d2 = (xc-xr);
213: d3 = (xc-xt);
214: d4 = (xc-xb);
215: d5 = (xr-xrb);
216: d6 = (xrb-xb);
217: d7 = (xlt-xl);
218: d8 = (xt-xlt);
220: df1dxc = d1*hydhx;
221: df2dxc = (d1*hydhx + d4*hxdhy);
222: df3dxc = d3*hxdhy;
223: df4dxc = (d2*hydhx + d3*hxdhy);
224: df5dxc = d2*hydhx;
225: df6dxc = d4*hxdhy;
227: d1 /= hx;
228: d2 /= hx;
229: d3 /= hy;
230: d4 /= hy;
231: d5 /= hy;
232: d6 /= hx;
233: d7 /= hy;
234: d8 /= hx;
236: f1 = PetscSqrtScalar(1.0 + d1*d1 + d7*d7);
237: f2 = PetscSqrtScalar(1.0 + d1*d1 + d4*d4);
238: f3 = PetscSqrtScalar(1.0 + d3*d3 + d8*d8);
239: f4 = PetscSqrtScalar(1.0 + d3*d3 + d2*d2);
240: f5 = PetscSqrtScalar(1.0 + d2*d2 + d5*d5);
241: f6 = PetscSqrtScalar(1.0 + d4*d4 + d6*d6);
243: df1dxc /= f1;
244: df2dxc /= f2;
245: df3dxc /= f3;
246: df4dxc /= f4;
247: df5dxc /= f5;
248: df6dxc /= f6;
250: g[j][i] = (df1dxc+df2dxc+df3dxc+df4dxc+df5dxc+df6dxc)/2.0;
252: }
253: }
255: /* Restore vectors */
256: DMDAVecRestoreArray(da,localX, &x);
257: DMDAVecRestoreArray(da,G, &g);
258: DMRestoreLocalVector(da,&localX);
259: PetscLogFlops(67*mx*my);
260: return(0);
261: }
263: /* ------------------------------------------------------------------- */
264: /*
265: FormJacobian - Evaluates Jacobian matrix.
267: Input Parameters:
268: . snes - SNES context
269: . X - input vector
270: . ptr - optional user-defined context, as set by SNESSetJacobian()
272: Output Parameters:
273: . tH - Jacobian matrix
275: */
276: PetscErrorCode FormJacobian(SNES snes, Vec X, Mat H, Mat tHPre, void *ptr)
277: {
278: AppCtx *user;
280: PetscInt i,j,k;
281: PetscInt mx, my;
282: MatStencil row,col[7];
283: PetscScalar hx, hy, hydhx, hxdhy;
284: PetscScalar f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
285: PetscScalar hl,hr,ht,hb,hc,htl,hbr;
286: PetscScalar **x, v[7];
287: PetscBool assembled;
288: PetscInt xs,xm,ys,ym;
289: Vec localX;
290: DM da;
293: SNESGetDM(snes,&da);
294: SNESGetApplicationContext(snes,(void**)&user);
295: DMDAGetInfo(da,PETSC_IGNORE,&mx,&my,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
296: hx = 1.0/(mx+1); hy=1.0/(my+1); hydhx=hy/hx; hxdhy=hx/hy;
298: /* Set various matrix options */
299: MatAssembled(H,&assembled);
300: if (assembled) {MatZeroEntries(H);}
302: /* Get local vector */
303: DMGetLocalVector(da,&localX);
304: /* Get ghost points */
305: DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
306: DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
308: /* Get pointers to vector data */
309: DMDAVecGetArray(da,localX, &x);
311: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
312: /* Compute Jacobian over the locally owned part of the mesh */
313: for (j=ys; j< ys+ym; j++) {
314: for (i=xs; i< xs+xm; i++) {
315: xc = x[j][i];
316: xlt=xrb=xl=xr=xb=xt=xc;
318: /* Left */
319: if (i==0) {
320: xl = user->left[j+1];
321: xlt = user->left[j+2];
322: } else xl = x[j][i-1];
324: /* Bottom */
325: if (j==0) {
326: xb =user->bottom[i+1];
327: xrb = user->bottom[i+2];
328: } else xb = x[j-1][i];
330: /* Right */
331: if (i+1 == mx) {
332: xr =user->right[j+1];
333: xrb = user->right[j];
334: } else xr = x[j][i+1];
336: /* Top */
337: if (j+1==my) {
338: xt =user->top[i+1];
339: xlt = user->top[i];
340: } else xt = x[j+1][i];
342: /* Top left */
343: if (i>0 && j+1<my) xlt = x[j+1][i-1];
345: /* Bottom right */
346: if (j>0 && i+1<mx) xrb = x[j-1][i+1];
348: d1 = (xc-xl)/hx;
349: d2 = (xc-xr)/hx;
350: d3 = (xc-xt)/hy;
351: d4 = (xc-xb)/hy;
352: d5 = (xrb-xr)/hy;
353: d6 = (xrb-xb)/hx;
354: d7 = (xlt-xl)/hy;
355: d8 = (xlt-xt)/hx;
357: f1 = PetscSqrtScalar(1.0 + d1*d1 + d7*d7);
358: f2 = PetscSqrtScalar(1.0 + d1*d1 + d4*d4);
359: f3 = PetscSqrtScalar(1.0 + d3*d3 + d8*d8);
360: f4 = PetscSqrtScalar(1.0 + d3*d3 + d2*d2);
361: f5 = PetscSqrtScalar(1.0 + d2*d2 + d5*d5);
362: f6 = PetscSqrtScalar(1.0 + d4*d4 + d6*d6);
365: hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+
366: (-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
367: hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+
368: (-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
369: ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+
370: (-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
371: hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+
372: (-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);
374: hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6);
375: htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3);
377: hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) +
378: hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
379: (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2.0*d1*d4)/(f2*f2*f2) +
380: (hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2.0*d2*d3)/(f4*f4*f4);
382: hl/=2.0; hr/=2.0; ht/=2.0; hb/=2.0; hbr/=2.0; htl/=2.0; hc/=2.0;
384: k =0;
385: row.i = i;row.j= j;
386: /* Bottom */
387: if (j>0) {
388: v[k] =hb;
389: col[k].i = i; col[k].j=j-1; k++;
390: }
392: /* Bottom right */
393: if (j>0 && i < mx -1) {
394: v[k] =hbr;
395: col[k].i = i+1; col[k].j = j-1; k++;
396: }
398: /* left */
399: if (i>0) {
400: v[k] = hl;
401: col[k].i = i-1; col[k].j = j; k++;
402: }
404: /* Centre */
405: v[k]= hc; col[k].i= row.i; col[k].j = row.j; k++;
407: /* Right */
408: if (i < mx-1) {
409: v[k] = hr;
410: col[k].i= i+1; col[k].j = j;k++;
411: }
413: /* Top left */
414: if (i>0 && j < my-1) {
415: v[k] = htl;
416: col[k].i = i-1;col[k].j = j+1; k++;
417: }
419: /* Top */
420: if (j < my-1) {
421: v[k] = ht;
422: col[k].i = i; col[k].j = j+1; k++;
423: }
425: MatSetValuesStencil(H,1,&row,k,col,v,INSERT_VALUES);
426: }
427: }
429: /* Assemble the matrix */
430: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
431: DMDAVecRestoreArray(da,localX,&x);
432: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
433: DMRestoreLocalVector(da,&localX);
435: PetscLogFlops(199*mx*my);
436: return(0);
437: }
439: /* ------------------------------------------------------------------- */
440: /*
441: FormBoundaryConditions - Calculates the boundary conditions for
442: the region.
444: Input Parameter:
445: . user - user-defined application context
447: Output Parameter:
448: . user - user-defined application context
449: */
450: PetscErrorCode FormBoundaryConditions(SNES snes,AppCtx **ouser)
451: {
453: PetscInt i,j,k,limit=0,maxits=5;
454: PetscInt mx,my;
455: PetscInt bsize=0, lsize=0, tsize=0, rsize=0;
456: PetscScalar one =1.0, two=2.0, three=3.0;
457: PetscScalar det,hx,hy,xt=0,yt=0;
458: PetscReal fnorm, tol=1e-10;
459: PetscScalar u1,u2,nf1,nf2,njac11,njac12,njac21,njac22;
460: PetscScalar b=-0.5, t=0.5, l=-0.5, r=0.5;
461: PetscScalar *boundary;
462: AppCtx *user;
463: DM da;
466: SNESGetDM(snes,&da);
467: PetscNew(&user);
468: *ouser = user;
469: user->lb = .05;
470: user->ub = PETSC_INFINITY;
471: DMDAGetInfo(da,PETSC_IGNORE,&mx,&my,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
473: /* Check if lower and upper bounds are set */
474: PetscOptionsGetScalar(NULL,NULL, "-lb", &user->lb, 0);
475: PetscOptionsGetScalar(NULL,NULL, "-ub", &user->ub, 0);
476: bsize=mx+2; lsize=my+2; rsize=my+2; tsize=mx+2;
478: PetscMalloc1(bsize, &user->bottom);
479: PetscMalloc1(tsize, &user->top);
480: PetscMalloc1(lsize, &user->left);
481: PetscMalloc1(rsize, &user->right);
483: hx= (r-l)/(mx+1.0); hy=(t-b)/(my+1.0);
485: for (j=0; j<4; j++) {
486: if (j==0) {
487: yt = b;
488: xt = l;
489: limit = bsize;
490: boundary = user->bottom;
491: } else if (j==1) {
492: yt = t;
493: xt = l;
494: limit = tsize;
495: boundary = user->top;
496: } else if (j==2) {
497: yt = b;
498: xt = l;
499: limit = lsize;
500: boundary = user->left;
501: } else { /* if (j==3) */
502: yt = b;
503: xt = r;
504: limit = rsize;
505: boundary = user->right;
506: }
508: for (i=0; i<limit; i++) {
509: u1=xt;
510: u2=-yt;
511: for (k=0; k<maxits; k++) {
512: nf1 = u1 + u1*u2*u2 - u1*u1*u1/three-xt;
513: nf2 = -u2 - u1*u1*u2 + u2*u2*u2/three-yt;
514: fnorm = PetscRealPart(PetscSqrtScalar(nf1*nf1+nf2*nf2));
515: if (fnorm <= tol) break;
516: njac11=one+u2*u2-u1*u1;
517: njac12=two*u1*u2;
518: njac21=-two*u1*u2;
519: njac22=-one - u1*u1 + u2*u2;
520: det = njac11*njac22-njac21*njac12;
521: u1 = u1-(njac22*nf1-njac12*nf2)/det;
522: u2 = u2-(njac11*nf2-njac21*nf1)/det;
523: }
525: boundary[i]=u1*u1-u2*u2;
526: if (j==0 || j==1) xt=xt+hx;
527: else yt=yt+hy; /* if (j==2 || j==3) */
528: }
529: }
530: return(0);
531: }
533: PetscErrorCode DestroyBoundaryConditions(AppCtx **ouser)
534: {
536: AppCtx *user = *ouser;
539: PetscFree(user->bottom);
540: PetscFree(user->top);
541: PetscFree(user->left);
542: PetscFree(user->right);
543: PetscFree(*ouser);
544: return(0);
545: }
548: /* ------------------------------------------------------------------- */
549: /*
550: ComputeInitialGuess - Calculates the initial guess
552: Input Parameters:
553: . user - user-defined application context
554: . X - vector for initial guess
556: Output Parameters:
557: . X - newly computed initial guess
558: */
559: PetscErrorCode ComputeInitialGuess(SNES snes, Vec X,void *dummy)
560: {
562: PetscInt i,j,mx,my;
563: DM da;
564: AppCtx *user;
565: PetscScalar **x;
566: PetscInt xs,xm,ys,ym;
569: SNESGetDM(snes,&da);
570: SNESGetApplicationContext(snes,(void**)&user);
572: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
573: DMDAGetInfo(da,PETSC_IGNORE,&mx,&my,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
575: /* Get pointers to vector data */
576: DMDAVecGetArray(da,X,&x);
577: /* Perform local computations */
578: for (j=ys; j<ys+ym; j++) {
579: for (i=xs; i< xs+xm; i++) {
580: x[j][i] = (((j+1.0)*user->bottom[i+1]+(my-j+1.0)*user->top[i+1])/(my+2.0)+((i+1.0)*user->left[j+1]+(mx-i+1.0)*user->right[j+1])/(mx+2.0))/2.0;
581: }
582: }
583: /* Restore vectors */
584: DMDAVecRestoreArray(da,X,&x);
585: return(0);
586: }
589: /*TEST
591: test:
592: args: -snes_type vinewtonrsls -pc_type mg -ksp_monitor_short -pc_mg_galerkin pmat -da_refine 5 -snes_vi_monitor -pc_mg_type full -snes_max_it 100 -snes_converged_reason
593: requires: !single
595: test:
596: suffix: 2
597: args: -snes_type vinewtonssls -pc_type mg -ksp_monitor_short -pc_mg_galerkin pmat -da_refine 5 -snes_vi_monitor -pc_mg_type full -snes_max_it 100 -snes_converged_reason
598: requires: !single
600: TEST*/