Actual source code: ex29.c
2: /*#define HAVE_DA_HDF*/
4: /* solve the equations for the perturbed magnetic field only */
5: #define EQ
7: /* turning this on causes instability?!? */
8: /* #define UPWINDING */
10: static char help[] = "Hall MHD with in two dimensions with time stepping and multigrid.\n\n\
11: -options_file ex29.options\n\
12: other PETSc options\n\
13: -resistivity <eta>\n\
14: -viscosity <nu>\n\
15: -skin_depth <d_e>\n\
16: -larmor_radius <rho_s>\n\
17: -contours : draw contour plots of solution\n\n";
19: /*T
20: Concepts: SNES^solving a system of nonlinear equations (parallel multicomponent example);
21: Concepts: DA^using distributed arrays;
22: Concepts: multicomponent
23: Processors: n
24: T*/
26: /* ------------------------------------------------------------------------
28: We thank Kai Germaschewski for contributing the FormFunctionLocal()
30: ------------------------------------------------------------------------- */
32: /*
33: Include "petscda.h" so that we can use distributed arrays (DAs).
34: Include "petscsnes.h" so that we can use SNES solvers.
35: Include "petscmg.h" to control the multigrid solvers.
36: Note that these automatically include:
37: petsc.h - base PETSc routines petscvec.h - vectors
38: petscsys.h - system routines petscmat.h - matrices
39: petscis.h - index sets petscksp.h - Krylov subspace methods
40: petscviewer.h - viewers petscpc.h - preconditioners
41: petscksp.h - linear solvers
42: */
43: #include petscsnes.h
44: #include petscda.h
45: #include petscmg.h
46: #include petscdmmg.h
48: #ifdef HAVE_DA_HDF
49: PetscInt DAVecHDFOutput(DA,Vec,char*);
50: #endif
52: #define D_x(x,m,i,j) (p5 * (x[(j)][(i)+1].m - x[(j)][(i)-1].m) * dhx)
53: #define D_xm(x,m,i,j) ((x[(j)][(i)].m - x[(j)][(i)-1].m) * dhx)
54: #define D_xp(x,m,i,j) ((x[(j)][(i+1)].m - x[(j)][(i)].m) * dhx)
55: #define D_y(x,m,i,j) (p5 * (x[(j)+1][(i)].m - x[(j)-1][(i)].m) * dhy)
56: #define D_ym(x,m,i,j) ((x[(j)][(i)].m - x[(j)-1][(i)].m) * dhy)
57: #define D_yp(x,m,i,j) ((x[(j)+1][(i)].m - x[(j)][(i)].m) * dhy)
58: #define D_xx(x,m,i,j) ((x[(j)][(i)+1].m - two*x[(j)][(i)].m + x[(j)][(i)-1].m) * hydhx * dhxdhy)
59: #define D_yy(x,m,i,j) ((x[(j)+1][(i)].m - two*x[(j)][(i)].m + x[(j)-1][(i)].m) * hxdhy * dhxdhy)
60: #define Lapl(x,m,i,j) (D_xx(x,m,i,j) + D_yy(x,m,i,j))
61: #define lx (2.*3.1415926)
62: #define ly (4.*3.1415926)
63: #define sqr(a) ((a)*(a))
65: /*
66: User-defined routines and data structures
67: */
69: typedef struct {
70: PetscReal fnorm_ini,dt_ini;
71: PetscReal dt,dt_out;
72: PetscReal ptime;
73: PetscReal max_time;
74: PetscReal fnorm_ratio;
75: PetscInt ires,itstep;
76: PetscInt max_steps,print_freq;
77: PetscReal t;
78: PetscReal fnorm;
80: PetscTruth ts_monitor; /* print information about each time step */
81: PetscReal dump_time; /* time to dump solution to a file */
82: PetscViewer socketviewer; /* socket to dump solution at each timestep for visualization */
83: } TstepCtx;
85: typedef struct {
86: PetscScalar phi,psi,U,F;
87: } Field;
89: typedef struct {
90: PassiveScalar phi,psi,U,F;
91: } PassiveField;
93: typedef struct {
94: PetscInt mglevels;
95: PetscInt cycles; /* number of time steps for integration */
96: PassiveReal nu,eta,d_e,rho_s; /* physical parameters */
97: PetscTruth draw_contours; /* flag - 1 indicates drawing contours */
98: PetscTruth second_order;
99: PetscTruth PreLoading;
100: } Parameters;
102: typedef struct {
103: Vec Xoldold,Xold;
104: TstepCtx *tsCtx;
105: Parameters *param;
106: } AppCtx;
120: int main(int argc,char **argv)
121: {
123: DMMG *dmmg; /* multilevel grid structure */
124: AppCtx *user; /* user-defined work context (one for each level) */
125: TstepCtx tsCtx; /* time-step parameters (one total) */
126: Parameters param; /* physical parameters (one total) */
127: PetscInt i,m,n,mx,my;
128: DA da;
129: PetscReal dt_ratio;
130: PetscInt dfill[16] = {1,0,1,0,
131: 0,1,0,1,
132: 0,0,1,1,
133: 0,1,1,1};
134: PetscInt ofill[16] = {1,0,0,0,
135: 0,1,0,0,
136: 1,1,1,1,
137: 1,1,1,1};
139: PetscInitialize(&argc,&argv,(char *)0,help);
142: PreLoadBegin(PETSC_TRUE,"SetUp");
144: param.PreLoading = PreLoading;
145: DMMGCreate(PETSC_COMM_WORLD,1,&user,&dmmg);
146: param.mglevels = DMMGGetLevels(dmmg);
148: /*
149: Create distributed array multigrid object (DMMG) to manage
150: parallel grid and vectors for principal unknowns (x) and
151: governing residuals (f)
152: */
153: DACreate2d(PETSC_COMM_WORLD, DA_XYPERIODIC, DA_STENCIL_STAR, -5, -5,
154: PETSC_DECIDE, PETSC_DECIDE, 4, 1, 0, 0, &da);
156: /* overwrite the default sparsity pattern toone specific for
157: this code's nonzero structure */
158: DASetBlockFills(da,dfill,ofill);
160: DMMGSetDM(dmmg,(DM)da);
161: DADestroy(da);
163: /* default physical parameters */
164: param.nu = 0;
165: param.eta = 1e-3;
166: param.d_e = 0.2;
167: param.rho_s = 0;
168: param.second_order = PETSC_FALSE;
170: PetscOptionsGetReal(PETSC_NULL, "-viscosity", ¶m.nu,PETSC_NULL);
172: PetscOptionsGetReal(PETSC_NULL, "-resistivity", ¶m.eta,PETSC_NULL);
174: PetscOptionsGetReal(PETSC_NULL, "-skin_depth", ¶m.d_e,PETSC_NULL);
176: PetscOptionsGetReal(PETSC_NULL, "-larmor_radius", ¶m.rho_s,PETSC_NULL);
178: PetscOptionsHasName(PETSC_NULL, "-contours", ¶m.draw_contours);
180: PetscOptionsHasName(PETSC_NULL, "-second_order", ¶m.second_order);
182: DASetFieldName(DMMGGetDA(dmmg), 0, "phi");
184: DASetFieldName(DMMGGetDA(dmmg), 1, "psi");
186: DASetFieldName(DMMGGetDA(dmmg), 2, "U");
188: DASetFieldName(DMMGGetDA(dmmg), 3, "F");
190: /*======================================================================*/
191: /* Initialize stuff related to time stepping */
192: /*======================================================================*/
194: DAGetInfo(DMMGGetDA(dmmg),0,&mx,&my,0,0,0,0,0,0,0,0);
196: tsCtx.fnorm_ini = 0;
197: tsCtx.max_steps = 1000000;
198: tsCtx.max_time = 1.0e+12;
199: /* use for dt = min(dx,dy); multiplied by dt_ratio below */
200: tsCtx.dt = PetscMin(lx/mx,ly/my);
201: tsCtx.fnorm_ratio = 1.0e+10;
202: tsCtx.t = 0;
203: tsCtx.dt_out = 10;
204: tsCtx.print_freq = tsCtx.max_steps;
205: tsCtx.ts_monitor = PETSC_FALSE;
206: tsCtx.dump_time = -1.0;
208: PetscOptionsGetInt(PETSC_NULL, "-max_st", &tsCtx.max_steps,PETSC_NULL);
209: PetscOptionsGetReal(PETSC_NULL, "-ts_rtol", &tsCtx.fnorm_ratio,PETSC_NULL);
210: PetscOptionsGetInt(PETSC_NULL, "-print_freq", &tsCtx.print_freq,PETSC_NULL);
212: dt_ratio = 1.0;
213: PetscOptionsGetReal(PETSC_NULL, "-dt_ratio", &dt_ratio,PETSC_NULL);
214: tsCtx.dt *= dt_ratio;
216: PetscOptionsHasName(PETSC_NULL, "-ts_monitor", &tsCtx.ts_monitor);
217: PetscOptionsGetReal(PETSC_NULL, "-dump", &tsCtx.dump_time,PETSC_NULL);
220: tsCtx.socketviewer = 0;
221: #if defined(PETSC_USE_SOCKET_VIEWER)
222: {
223: PetscTruth flg;
224: PetscOptionsHasName(PETSC_NULL, "-socket_viewer", &flg);
225: if (flg && !PreLoading) {
226: tsCtx.ts_monitor = PETSC_TRUE;
227: PetscViewerSocketOpen(PETSC_COMM_WORLD,0,PETSC_DECIDE,&tsCtx.socketviewer);
228: }
229: }
230: #endif
232: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
233: Create user context, set problem data, create vector data structures.
234: Also, compute the initial guess.
235: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
236: /* create application context for each level */
237: PetscMalloc(param.mglevels*sizeof(AppCtx),&user);
238: for (i=0; i<param.mglevels; i++) {
239: /* create work vectors to hold previous time-step solution and
240: function value */
241: VecDuplicate(dmmg[i]->x, &user[i].Xoldold);
242: VecDuplicate(dmmg[i]->x, &user[i].Xold);
243: user[i].tsCtx = &tsCtx;
244: user[i].param = ¶m;
245: DMMGSetUser(dmmg,i,&user[i]);
246: }
247:
248: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
249: Create nonlinear solver context
250:
251: Process adiC(20): AddTSTermLocal AddTSTermLocal2 FormFunctionLocal FormFunctionLocali
252: Process blockadiC(4): FormFunctionLocali4
253: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
254: DMMGSetSNESLocal(dmmg, FormFunctionLocal, 0,ad_FormFunctionLocal, admf_FormFunctionLocal);
255: DMMGSetFromOptions(dmmg);
256: DMMGSetSNESLocali(dmmg,FormFunctionLocali,0,admf_FormFunctionLocali);
257: DMMGSetSNESLocalib(dmmg,FormFunctionLocali4,0,admfb_FormFunctionLocali4);
258:
259: /* attach nullspace to each level of the preconditioner */
260: DMMGSetNullSpace(dmmg,PETSC_FALSE,1,CreateNullSpace);
261:
262: PetscPrintf(PETSC_COMM_WORLD, "finish setupNull!");
264: if (PreLoading) {
265: PetscPrintf(PETSC_COMM_WORLD, "# viscosity = %G, resistivity = %G, "
266: "skin_depth # = %G, larmor_radius # = %G\n",
267: param.nu, param.eta, param.d_e, param.rho_s);
268: DAGetInfo(DMMGGetDA(dmmg),0,&m,&n,0,0,0,0,0,0,0,0);
269: PetscPrintf(PETSC_COMM_WORLD,"Problem size %D by %D\n",m,n);
270: PetscPrintf(PETSC_COMM_WORLD,"dx %G dy %G dt %G ratio dt/min(dx,dy) %G\n",lx/mx,ly/my,tsCtx.dt,dt_ratio);
271: }
273:
274:
275: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
276: Solve the nonlinear system
277: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
278:
279: PreLoadStage("Solve");
281: if (param.draw_contours) {
282: VecView(((AppCtx*)DMMGGetUser(dmmg,param.mglevels-1))->Xold,PETSC_VIEWER_DRAW_WORLD);
283: }
285: Update(dmmg);
287: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
288: Free work space. All PETSc objects should be destroyed when they
289: are no longer needed.
290: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
291:
292: for (i=0; i<param.mglevels; i++) {
293: VecDestroy(user[i].Xoldold);
294: VecDestroy(user[i].Xold);
295: }
296: PetscFree(user);
297: DMMGDestroy(dmmg);
299: PreLoadEnd();
300:
301: PetscFinalize();
302: return 0;
303: }
305: /* ------------------------------------------------------------------- */
308: /* ------------------------------------------------------------------- */
309: PetscErrorCode Gnuplot(DA da, Vec X, double mtime)
310: {
311: PetscInt i,j,xs,ys,xm,ym;
312: PetscInt xints,xinte,yints,yinte;
314: Field **x;
315: FILE *f;
316: char fname[PETSC_MAX_PATH_LEN];
317: PetscMPIInt rank;
319: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
321: sprintf(fname, "out-%g-%d.dat", mtime, rank);
323: f = fopen(fname, "w");
325: DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);
327: DAVecGetArray(da,X,&x);
329: xints = xs; xinte = xs+xm; yints = ys; yinte = ys+ym;
331: for (j=yints; j<yinte; j++) {
332: for (i=xints; i<xinte; i++) {
333: PetscFPrintf(PETSC_COMM_WORLD, f,
334: "%D %D %G %G %G %G %G %G\n",
335: i, j, 0.0, 0.0,
336: PetscAbsScalar(x[j][i].U), PetscAbsScalar(x[j][i].F),
337: PetscAbsScalar(x[j][i].phi), PetscAbsScalar(x[j][i].psi));
338: }
339: PetscFPrintf(PETSC_COMM_WORLD,f, "\n");
340: }
341: DAVecRestoreArray(da,X,&x);
342: fclose(f);
343: return 0;
344: }
346: /* ------------------------------------------------------------------- */
349: /* ------------------------------------------------------------------- */
350: PetscErrorCode Initialize(DMMG *dmmg)
351: {
352: AppCtx *appCtx = (AppCtx*)DMMGGetUser(dmmg,0);
353: Parameters *param = appCtx->param;
354: DA da;
356: PetscInt i,j,mx,my,xs,ys,xm,ym;
357: PetscReal two = 2.0,one = 1.0;
358: PetscReal hx,hy,dhx,dhy,hxdhy,hydhx,hxhy,dhxdhy;
359: PetscReal d_e,rho_s,de2,xx,yy;
360: Field **x, **localx;
361: Vec localX;
362: PetscTruth flg;
365: PetscOptionsHasName(0,"-restart",&flg);
366: if (flg) {
367: PetscViewer viewer;
368: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"binaryoutput",FILE_MODE_READ,&viewer);
369: VecLoadIntoVector(viewer,dmmg[param->mglevels-1]->x);
370: PetscViewerDestroy(viewer);
371: return(0);
372: }
374: d_e = param->d_e;
375: rho_s = param->rho_s;
376: de2 = sqr(param->d_e);
378: da = (DA)(dmmg[param->mglevels-1]->dm);
379: DAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0);
381: dhx = mx/lx; dhy = my/ly;
382: hx = one/dhx; hy = one/dhy;
383: hxdhy = hx*dhy; hydhx = hy*dhx;
384: hxhy = hx*hy; dhxdhy = dhx*dhy;
386: /*
387: Get local grid boundaries (for 2-dimensional DA):
388: xs, ys - starting grid indices (no ghost points)
389: xm, ym - widths of local grid (no ghost points)
390: */
391: DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);
393: DAGetLocalVector(da,&localX);
394: /*
395: Get a pointer to vector data.
396: - For default PETSc vectors, VecGetArray() returns a pointer to
397: the data array. Otherwise, the routine is implementation dependent.
398: - You MUST call VecRestoreArray() when you no longer need access to
399: the array.
400: */
401: DAVecGetArray(da,dmmg[param->mglevels-1]->x,&x);
402: DAVecGetArray(da,localX,&localx);
404: /*
405: Compute initial solution over the locally owned part of the grid
406: */
407: #if defined (PETSC_HAVE_ERF)
408: {
409: PetscReal eps = lx/ly;
410: PetscReal pert = 1e-4;
411: PetscReal k = 1.*eps;
412: PetscReal gam;
414: if (d_e < rho_s) d_e = rho_s;
415: gam = k * d_e;
416: for (j=ys-1; j<ys+ym+1; j++) {
417: yy = j * hy;
418: for (i=xs-1; i<xs+xm+1; i++) {
419: xx = i * hx;
420: if (xx < -3.1416926/2) {
421: localx[j][i].phi = pert * gam / k * erf((xx + 3.1415926) / (sqrt(2.0) * d_e)) * (-sin(k*yy));
422: } else if (xx < 3.1415926/2) {
423: localx[j][i].phi = - pert * gam / k * erf(xx / (sqrt(2.0) * d_e)) * (-sin(k*yy));
424: } else if (xx < 3*3.1415926/2){
425: localx[j][i].phi = pert * gam / k * erf((xx - 3.1415926) / (sqrt(2.0) * d_e)) * (-sin(k*yy));
426: } else {
427: localx[j][i].phi = - pert * gam / k * erf((xx - 2.*3.1415926) / (sqrt(2.0) * d_e)) * (-sin(k*yy));
428: }
429: #ifdef EQ
430: localx[j][i].psi = 0.;
431: #else
432: localx[j][i].psi = cos(xx);
433: #endif
434: }
435: }
437: for (j=ys; j<ys+ym; j++) {
438: for (i=xs; i<xs+xm; i++) {
439: x[j][i].U = Lapl(localx,phi,i,j);
440: x[j][i].F = localx[j][i].psi - de2 * Lapl(localx,psi,i,j);
441: x[j][i].phi = localx[j][i].phi;
442: x[j][i].psi = localx[j][i].psi;
443: }
444: }
445: }
446: #else
447: SETERRQ(1,"erf() not available on this machine");
448: #endif
450: /*
451: Restore vector
452: */
453: DAVecRestoreArray(da,dmmg[param->mglevels-1]->x,&x);
454:
455: DAVecRestoreArray(da,localX,&localx);
456:
457: DARestoreLocalVector(da,&localX);
458:
460: return(0);
461: }
465: PetscErrorCode ComputeMaxima(DA da, Vec X, PetscReal t)
466: {
468: PetscInt i,j,mx,my,xs,ys,xm,ym;
469: PetscInt xints,xinte,yints,yinte;
470: Field **x;
471: double norm[4] = {0,0,0,0};
472: double gnorm[4];
473: MPI_Comm comm;
477: DAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0);
479: DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);
480:
482: xints = xs; xinte = xs+xm; yints = ys; yinte = ys+ym;
484: DAVecGetArray(da, X, &x);
486: for (j=yints; j<yinte; j++) {
487: for (i=xints; i<xinte; i++) {
488: norm[0] = PetscMax(norm[0],PetscAbsScalar(x[j][i].U));
489: norm[1] = PetscMax(norm[1],PetscAbsScalar(x[j][i].F));
490: norm[2] = PetscMax(norm[2],PetscAbsScalar(x[j][i].phi));
491: norm[3] = PetscMax(norm[3],PetscAbsScalar(x[j][i].psi));
492: }
493: }
495: DAVecRestoreArray(da,X,&x);
497: PetscObjectGetComm((PetscObject)da, &comm);
498: MPI_Allreduce(norm, gnorm, 4, MPI_DOUBLE, MPI_MAX, comm);
500: PetscFPrintf(PETSC_COMM_WORLD, stderr,"%G\t%G\t%G\t%G\t%G\n",t, gnorm[0], gnorm[1], gnorm[2], gnorm[3]);
502: return(0);
503: }
507: PetscErrorCode FormFunctionLocal(DALocalInfo *info,Field **x,Field **f,void *ptr)
508: {
509: AppCtx *user = (AppCtx*)ptr;
510: TstepCtx *tsCtx = user->tsCtx;
511: Parameters *param = user->param;
513: PetscInt xints,xinte,yints,yinte,i,j;
514: PassiveReal hx,hy,dhx,dhy,hxdhy,hydhx,hxhy,dhxdhy;
515: PassiveReal de2,rhos2,nu,eta,dde2;
516: PassiveReal two = 2.0,one = 1.0,p5 = 0.5;
517: PassiveReal F_eq_x,By_eq;
518: PetscScalar xx;
519: PetscScalar vx,vy,avx,avy,vxp,vxm,vyp,vym;
520: PetscScalar Bx,By,aBx,aBy,Bxp,Bxm,Byp,Bym;
523: de2 = sqr(param->d_e);
524: rhos2 = sqr(param->rho_s);
525: nu = param->nu;
526: eta = param->eta;
527: dde2 = one/de2;
529: /*
530: Define mesh intervals ratios for uniform grid.
531: [Note: FD formulae below are normalized by multiplying through by
532: local volume element to obtain coefficients O(1) in two dimensions.]
533: */
534: dhx = info->mx/lx; dhy = info->my/ly;
535: hx = one/dhx; hy = one/dhy;
536: hxdhy = hx*dhy; hydhx = hy*dhx;
537: hxhy = hx*hy; dhxdhy = dhx*dhy;
539: xints = info->xs; xinte = info->xs+info->xm;
540: yints = info->ys; yinte = info->ys+info->ym;
542: /* Compute over the interior points */
543: for (j=yints; j<yinte; j++) {
544: for (i=xints; i<xinte; i++) {
545: #ifdef EQ
546: xx = i * hx;
547: F_eq_x = - (1. + de2) * sin(PetscAbsScalar(xx));
548: By_eq = sin(PetscAbsScalar(xx));
549: #else
550: F_eq_x = 0.;
551: By_eq = 0.;
552: #endif
554: /*
555: * convective coefficients for upwinding
556: */
558: vx = - D_y(x,phi,i,j);
559: vy = D_x(x,phi,i,j);
560: avx = PetscAbsScalar(vx); vxp = p5*(vx+avx); vxm = p5*(vx-avx);
561: avy = PetscAbsScalar(vy); vyp = p5*(vy+avy); vym = p5*(vy-avy);
562: #ifndef UPWINDING
563: vxp = vxm = p5*vx;
564: vyp = vym = p5*vy;
565: #endif
567: Bx = D_y(x,psi,i,j);
568: By = - D_x(x,psi,i,j) + By_eq;
569: aBx = PetscAbsScalar(Bx); Bxp = p5*(Bx+aBx); Bxm = p5*(Bx-aBx);
570: aBy = PetscAbsScalar(By); Byp = p5*(By+aBy); Bym = p5*(By-aBy);
571: #ifndef UPWINDING
572: Bxp = Bxm = p5*Bx;
573: Byp = Bym = p5*By;
574: #endif
576: /* Lap(phi) - U */
577: f[j][i].phi = (Lapl(x,phi,i,j) - x[j][i].U) * hxhy;
579: /* psi - d_e^2 * Lap(psi) - F */
580: f[j][i].psi = (x[j][i].psi - de2 * Lapl(x,psi,i,j) - x[j][i].F) * hxhy;
582: /* vx * U_x + vy * U_y - (B_x * F_x + B_y * F_y) / d_e^2
583: - nu Lap(U) */
584: f[j][i].U =
585: ((vxp * (D_xm(x,U,i,j)) + vxm * (D_xp(x,U,i,j)) +
586: vyp * (D_ym(x,U,i,j)) + vym * (D_yp(x,U,i,j))) -
587: (Bxp * (D_xm(x,F,i,j) + F_eq_x) + Bxm * (D_xp(x,F,i,j) + F_eq_x) +
588: Byp * (D_ym(x,F,i,j)) + Bym * (D_yp(x,F,i,j))) * dde2 -
589: nu * Lapl(x,U,i,j)) * hxhy;
590:
591: /* vx * F_x + vy * F_y - rho_s^2 * (B_x * U_x + B_y * U_y)
592: - eta * Lap(psi) */
593: f[j][i].F =
594: ((vxp * (D_xm(x,F,i,j) + F_eq_x) + vxm * (D_xp(x,F,i,j) + F_eq_x) +
595: vyp * (D_ym(x,F,i,j)) + vym * (D_yp(x,F,i,j))) -
596: (Bxp * (D_xm(x,U,i,j)) + Bxm * (D_xp(x,U,i,j)) +
597: Byp * (D_ym(x,U,i,j)) + Bym * (D_yp(x,U,i,j))) * rhos2 -
598: eta * Lapl(x,psi,i,j)) * hxhy;
599: }
600: }
602: /* Add time step contribution */
603: if (tsCtx->ires) {
604: if ((param->second_order) && (tsCtx->itstep > 0)){
605: AddTSTermLocal2(info,x,f,user);
606: } else {
607: AddTSTermLocal(info,x,f,user);
608: }
609: }
611: /*
612: Flop count (multiply-adds are counted as 2 operations)
613: */
614: /* PetscLogFlops(84*info->ym*info->xm); FIXME */
615: return(0);
616: }
618: /*---------------------------------------------------------------------*/
621: PetscErrorCode Update(DMMG *dmmg)
622: /*---------------------------------------------------------------------*/
623: {
624: AppCtx *user = (AppCtx *) DMMGGetUser(dmmg,0);
625: TstepCtx *tsCtx = user->tsCtx;
626: Parameters *param = user->param;
627: SNES snes;
628: PetscErrorCode ierr;
629: PetscInt its,lits,i;
630: PetscInt max_steps;
631: PetscInt nfailsCum = 0,nfails = 0;
632: static PetscInt ic_out;
633: PetscTruth ts_monitor = (tsCtx->ts_monitor && !param->PreLoading) ? PETSC_TRUE : PETSC_FALSE;
637: if (param->PreLoading)
638: max_steps = 1;
639: else
640: max_steps = tsCtx->max_steps;
641:
642: Initialize(dmmg);
644: snes = DMMGGetSNES(dmmg);
646: for (tsCtx->itstep = 0; tsCtx->itstep < max_steps; tsCtx->itstep++) {
647:
648: PetscPrintf(PETSC_COMM_WORLD, "time step=%d!\n",tsCtx->itstep);
649: if ((param->second_order) && (tsCtx->itstep > 0))
650: {
651: for (i=param->mglevels-1; i>=0 ;i--)
652: {
653: VecCopy(((AppCtx*)DMMGGetUser(dmmg,i))->Xold,((AppCtx*)DMMGGetUser(dmmg,i))->Xoldold);
654: }
655: }
657: for (i=param->mglevels-1; i>0 ;i--) {
658: MatRestrict(dmmg[i]->R, dmmg[i]->x, dmmg[i-1]->x);
659: VecPointwiseMult(dmmg[i-1]->x,dmmg[i-1]->x,dmmg[i]->Rscale);
660: VecCopy(dmmg[i]->x, ((AppCtx*)DMMGGetUser(dmmg,i))->Xold);
661: }
662: VecCopy(dmmg[0]->x, ((AppCtx*)DMMGGetUser(dmmg,0))->Xold);
664: DMMGSolve(dmmg);
668: if (tsCtx->itstep == 665000)
669: {
670: KSP ksp;
671: PC pc;
672: Mat mat, pmat;
673: MatStructure flag;
674: PetscViewer viewer;
675: char file[PETSC_MAX_PATH_LEN];
677: PetscStrcpy(file, "matrix");
679: PetscViewerBinaryOpen(PETSC_COMM_WORLD, file, FILE_MODE_WRITE, &viewer);
681: SNESGetKSP(snes, &ksp);
683: KSPGetPC(ksp, &pc);
685: PCGetOperators(pc, &mat, &pmat, &flag);
687: MatView(mat, viewer);
689: PetscViewerDestroy(viewer);
690: SETERRQ(1,"Done saving Jacobian");
691: }
694: tsCtx->t += tsCtx->dt;
696: /* save restart solution if requested at a particular time, then exit */
697: if (tsCtx->dump_time > 0.0 && tsCtx->t >= tsCtx->dump_time) {
698: Vec v = DMMGGetx(dmmg);
699: VecView(v,PETSC_VIEWER_BINARY_WORLD);
700: SETERRQ1(1,"Saved solution at time %G",tsCtx->t);
701: }
703: if (ts_monitor)
704: {
705: SNESGetIterationNumber(snes, &its);
706: SNESGetLinearSolveIterations(snes, &lits);
707: SNESGetNonlinearStepFailures(snes, &nfails);
708: SNESGetFunctionNorm(snes, &tsCtx->fnorm);
710: nfailsCum += nfails;
711: if (nfailsCum >= 2)
712: SETERRQ(1, "unable to find a newton step");
714: PetscPrintf(PETSC_COMM_WORLD,
715: "time step = %D, time = %G, number of nonlinear steps = %D, "
716: "number of linear steps = %D, norm of the function = %G\n",
717: tsCtx->itstep + 1, tsCtx->t, its, lits, PetscAbsScalar(tsCtx->fnorm));
719: /* send solution over to Matlab, to be visualized (using ex29.m) */
720: if (!param->PreLoading && tsCtx->socketviewer)
721: {
722: Vec v;
723: SNESGetSolution(snes, &v);
724: #if defined(PETSC_USE_SOCKET_VIEWER)
725: VecView(v, tsCtx->socketviewer);
726: #endif
727: }
728: }
730: if (!param->PreLoading) {
731: if (param->draw_contours) {
732: VecView(DMMGGetx(dmmg),PETSC_VIEWER_DRAW_WORLD);
733: }
735: if (1 && ts_monitor) {
736: /* compute maxima */
737: ComputeMaxima((DA) dmmg[param->mglevels-1]->dm,dmmg[param->mglevels-1]->x,tsCtx->t);
738: /* output */
739: if (ic_out++ == (int)(tsCtx->dt_out / tsCtx->dt + .5)) {
740: #ifdef HAVE_DA_HDF
741: char fname[PETSC_MAX_PATH_LEN];
743: sprintf(fname, "out-%G.hdf", tsCtx->t);
744: DAVecHDFOutput(DMMGGetDA(dmmg), DMMGGetx(dmmg), fname);
745: #else
746: /*
747: Gnuplot(DMMGGetDA(dmmg), DMMGGetx(dmmg), tsCtx->t);
748:
749: */
750: #endif
751: ic_out = 1;
752: }
753: }
754: }
755: } /* End of time step loop */
756:
757: if (!param->PreLoading){
758: SNESGetFunctionNorm(snes,&tsCtx->fnorm);
759: PetscPrintf(PETSC_COMM_WORLD, "timesteps %D fnorm = %G\n",
760: tsCtx->itstep, PetscAbsScalar(tsCtx->fnorm));
761: }
763: if (param->PreLoading) {
764: tsCtx->fnorm_ini = 0.0;
765: }
766:
767: return(0);
768: }
770: /*---------------------------------------------------------------------*/
773: PetscErrorCode AddTSTermLocal(DALocalInfo* info,Field **x,Field **f,AppCtx *user)
774: /*---------------------------------------------------------------------*/
775: {
776: TstepCtx *tsCtx = user->tsCtx;
777: DA da = info->da;
779: PetscInt i,j;
780: PetscInt xints,xinte,yints,yinte;
781: PassiveReal hx,hy,dhx,dhy,hxhy;
782: PassiveReal one = 1.0;
783: PassiveScalar dtinv;
784: PassiveField **xold;
788: xints = info->xs; xinte = info->xs+info->xm;
789: yints = info->ys; yinte = info->ys+info->ym;
791: dhx = info->mx/lx; dhy = info->my/ly;
792: hx = one/dhx; hy = one/dhy;
793: hxhy = hx*hy;
795: dtinv = hxhy/(tsCtx->dt);
797: DAVecGetArray(da,user->Xold,&xold);
798: for (j=yints; j<yinte; j++) {
799: for (i=xints; i<xinte; i++) {
800: f[j][i].U += dtinv*(x[j][i].U-xold[j][i].U);
801: f[j][i].F += dtinv*(x[j][i].F-xold[j][i].F);
802: }
803: }
804: DAVecRestoreArray(da,user->Xold,&xold);
806: return(0);
807: }
809: /*---------------------------------------------------------------------*/
812: PetscErrorCode AddTSTermLocal2(DALocalInfo* info,Field **x,Field **f,AppCtx *user)
813: /*---------------------------------------------------------------------*/
814: {
815: TstepCtx *tsCtx = user->tsCtx;
816: DA da = info->da;
818: PetscInt i,j,xints,xinte,yints,yinte;
819: PassiveReal hx,hy,dhx,dhy,hxhy;
820: PassiveReal one = 1.0, onep5 = 1.5, two = 2.0, p5 = 0.5;
821: PassiveScalar dtinv;
822: PassiveField **xoldold,**xold;
826: xints = info->xs; xinte = info->xs+info->xm;
827: yints = info->ys; yinte = info->ys+info->ym;
829: dhx = info->mx/lx; dhy = info->my/ly;
830: hx = one/dhx; hy = one/dhy;
831: hxhy = hx*hy;
833: dtinv = hxhy/(tsCtx->dt);
835: DAVecGetArray(da,user->Xoldold,&xoldold);
836: DAVecGetArray(da,user->Xold,&xold);
837: for (j=yints; j<yinte; j++) {
838: for (i=xints; i<xinte; i++) {
839: f[j][i].U += dtinv * (onep5 * x[j][i].U - two * xold[j][i].U +
840: p5 * xoldold[j][i].U);
841: f[j][i].F += dtinv * (onep5 * x[j][i].F - two * xold[j][i].F +
842: p5 * xoldold[j][i].F);
843: }
844: }
845: DAVecRestoreArray(da,user->Xoldold,&xoldold);
846: DAVecRestoreArray(da,user->Xold,&xold);
848: return(0);
849: }
851: /* Creates the null space of the Jacobian for a particular level */
854: PetscErrorCode CreateNullSpace(DMMG dmmg,Vec *nulls)
855: {
857: PetscInt i,N,rstart,rend;
858: PetscScalar scale,*vx;
861: VecGetSize(nulls[0],&N);
862: scale = 2.0/sqrt((PetscReal)N);
863: VecGetArray(nulls[0],&vx);
864: VecGetOwnershipRange(nulls[0],&rstart,&rend);
865: for (i=rstart; i<rend; i++) {
866: if (!(i % 4)) vx[i-rstart] = scale;
867: else vx[i-rstart] = 0.0;
868: }
869: VecRestoreArray(nulls[0],&vx);
870: return(0);
871: }
873: /*
874: This is an experimental function and can be safely ignored.
875: */
876: PetscErrorCode FormFunctionLocali(DALocalInfo *info,MatStencil *st,Field **x,PetscScalar *f,void *ptr)
877: {
878: AppCtx *user = (AppCtx*)ptr;
879: TstepCtx *tsCtx = user->tsCtx;
880: Parameters *param = user->param;
882: PetscInt i,j,c;
883: PetscInt xints,xinte,yints,yinte;
884: PassiveReal hx,hy,dhx,dhy,hxdhy,hydhx,hxhy,dhxdhy;
885: PassiveReal de2,rhos2,nu,eta,dde2;
886: PassiveReal two = 2.0,one = 1.0,p5 = 0.5;
887: PassiveReal F_eq_x,By_eq,dtinv;
888: PetscScalar xx;
889: PetscScalar vx,vy,avx,avy,vxp,vxm,vyp,vym;
890: PetscScalar Bx,By,aBx,aBy,Bxp,Bxm,Byp,Bym;
891: PassiveField **xold;
894: de2 = sqr(param->d_e);
895: rhos2 = sqr(param->rho_s);
896: nu = param->nu;
897: eta = param->eta;
898: dde2 = one/de2;
900: /*
901: Define mesh intervals ratios for uniform grid.
902: [Note: FD formulae below are normalized by multiplying through by
903: local volume element to obtain coefficients O(1) in two dimensions.]
904: */
905: dhx = info->mx/lx; dhy = info->my/ly;
906: hx = one/dhx; hy = one/dhy;
907: hxdhy = hx*dhy; hydhx = hy*dhx;
908: hxhy = hx*hy; dhxdhy = dhx*dhy;
910: xints = info->xs; xinte = info->xs+info->xm;
911: yints = info->ys; yinte = info->ys+info->ym;
914: i = st->i; j = st->j; c = st->c;
916: #ifdef EQ
917: xx = i * hx;
918: F_eq_x = - (1. + de2) * sin(PetscAbsScalar(xx));
919: By_eq = sin(PetscAbsScalar(xx));
920: #else
921: F_eq_x = 0.;
922: By_eq = 0.;
923: #endif
925: /*
926: * convective coefficients for upwinding
927: */
929: vx = - D_y(x,phi,i,j);
930: vy = D_x(x,phi,i,j);
931: avx = PetscAbsScalar(vx); vxp = p5*(vx+avx); vxm = p5*(vx-avx);
932: avy = PetscAbsScalar(vy); vyp = p5*(vy+avy); vym = p5*(vy-avy);
933: #ifndef UPWINDING
934: vxp = vxm = p5*vx;
935: vyp = vym = p5*vy;
936: #endif
938: Bx = D_y(x,psi,i,j);
939: By = - D_x(x,psi,i,j) + By_eq;
940: aBx = PetscAbsScalar(Bx); Bxp = p5*(Bx+aBx); Bxm = p5*(Bx-aBx);
941: aBy = PetscAbsScalar(By); Byp = p5*(By+aBy); Bym = p5*(By-aBy);
942: #ifndef UPWINDING
943: Bxp = Bxm = p5*Bx;
944: Byp = Bym = p5*By;
945: #endif
947: DAVecGetArray(info->da,user->Xold,&xold);
948: dtinv = hxhy/(tsCtx->dt);
949: switch(c) {
951: case 0:
952: /* Lap(phi) - U */
953: *f = (Lapl(x,phi,i,j) - x[j][i].U) * hxhy;
954: break;
956: case 1:
957: /* psi - d_e^2 * Lap(psi) - F */
958: *f = (x[j][i].psi - de2 * Lapl(x,psi,i,j) - x[j][i].F) * hxhy;
959: break;
961: case 2:
962: /* vx * U_x + vy * U_y - (B_x * F_x + B_y * F_y) / d_e^2
963: - nu Lap(U) */
964: *f =
965: ((vxp * (D_xm(x,U,i,j)) + vxm * (D_xp(x,U,i,j)) +
966: vyp * (D_ym(x,U,i,j)) + vym * (D_yp(x,U,i,j))) -
967: (Bxp * (D_xm(x,F,i,j) + F_eq_x) + Bxm * (D_xp(x,F,i,j) + F_eq_x) +
968: Byp * (D_ym(x,F,i,j)) + Bym * (D_yp(x,F,i,j))) * dde2 -
969: nu * Lapl(x,U,i,j)) * hxhy;
970: *f += dtinv*(x[j][i].U-xold[j][i].U);
971: break;
973: case 3:
974: /* vx * F_x + vy * F_y - rho_s^2 * (B_x * U_x + B_y * U_y)
975: - eta * Lap(psi) */
976: *f =
977: ((vxp * (D_xm(x,F,i,j) + F_eq_x) + vxm * (D_xp(x,F,i,j) + F_eq_x) +
978: vyp * (D_ym(x,F,i,j)) + vym * (D_yp(x,F,i,j))) -
979: (Bxp * (D_xm(x,U,i,j)) + Bxm * (D_xp(x,U,i,j)) +
980: Byp * (D_ym(x,U,i,j)) + Bym * (D_yp(x,U,i,j))) * rhos2 -
981: eta * Lapl(x,psi,i,j)) * hxhy;
982: *f += dtinv*(x[j][i].F-xold[j][i].F);
983: break;
984: }
985: DAVecRestoreArray(info->da,user->Xold,&xold);
988: /*
989: Flop count (multiply-adds are counted as 2 operations)
990: */
991: /* PetscLogFlops(84*info->ym*info->xm); FIXME */
992: return(0);
993: }
994: /*
995: This is an experimental function and can be safely ignored.
996: */
997: PetscErrorCode FormFunctionLocali4(DALocalInfo *info,MatStencil *st,Field **x,PetscScalar *ff,void *ptr)
998: {
999: Field *f = (Field *)ff;
1000: AppCtx *user = (AppCtx*)ptr;
1001: TstepCtx *tsCtx = user->tsCtx;
1002: Parameters *param = user->param;
1004: PetscInt i,j;
1005: PetscInt xints,xinte,yints,yinte;
1006: PassiveReal hx,hy,dhx,dhy,hxdhy,hydhx,hxhy,dhxdhy;
1007: PassiveReal de2,rhos2,nu,eta,dde2;
1008: PassiveReal two = 2.0,one = 1.0,p5 = 0.5;
1009: PassiveReal F_eq_x,By_eq,dtinv;
1010: PetscScalar xx;
1011: PetscScalar vx,vy,avx,avy,vxp,vxm,vyp,vym;
1012: PetscScalar Bx,By,aBx,aBy,Bxp,Bxm,Byp,Bym;
1013: PassiveField **xold;
1016: de2 = sqr(param->d_e);
1017: rhos2 = sqr(param->rho_s);
1018: nu = param->nu;
1019: eta = param->eta;
1020: dde2 = one/de2;
1022: /*
1023: Define mesh intervals ratios for uniform grid.
1024: [Note: FD formulae below are normalized by multiplying through by
1025: local volume element to obtain coefficients O(1) in two dimensions.]
1026: */
1027: dhx = info->mx/lx; dhy = info->my/ly;
1028: hx = one/dhx; hy = one/dhy;
1029: hxdhy = hx*dhy; hydhx = hy*dhx;
1030: hxhy = hx*hy; dhxdhy = dhx*dhy;
1032: xints = info->xs; xinte = info->xs+info->xm;
1033: yints = info->ys; yinte = info->ys+info->ym;
1036: i = st->i; j = st->j;
1038: #ifdef EQ
1039: xx = i * hx;
1040: F_eq_x = - (1. + de2) * sin(PetscAbsScalar(xx));
1041: By_eq = sin(PetscAbsScalar(xx));
1042: #else
1043: F_eq_x = 0.;
1044: By_eq = 0.;
1045: #endif
1047: /*
1048: * convective coefficients for upwinding
1049: */
1051: vx = - D_y(x,phi,i,j);
1052: vy = D_x(x,phi,i,j);
1053: avx = PetscAbsScalar(vx); vxp = p5*(vx+avx); vxm = p5*(vx-avx);
1054: avy = PetscAbsScalar(vy); vyp = p5*(vy+avy); vym = p5*(vy-avy);
1055: #ifndef UPWINDING
1056: vxp = vxm = p5*vx;
1057: vyp = vym = p5*vy;
1058: #endif
1060: Bx = D_y(x,psi,i,j);
1061: By = - D_x(x,psi,i,j) + By_eq;
1062: aBx = PetscAbsScalar(Bx); Bxp = p5*(Bx+aBx); Bxm = p5*(Bx-aBx);
1063: aBy = PetscAbsScalar(By); Byp = p5*(By+aBy); Bym = p5*(By-aBy);
1064: #ifndef UPWINDING
1065: Bxp = Bxm = p5*Bx;
1066: Byp = Bym = p5*By;
1067: #endif
1069: DAVecGetArray(info->da,user->Xold,&xold);
1070: dtinv = hxhy/(tsCtx->dt);
1071:
1073:
1074: /* Lap(phi) - U */
1075: f->phi = (Lapl(x,phi,i,j) - x[j][i].U) * hxhy;
1076:
1078:
1079: /* psi - d_e^2 * Lap(psi) - F */
1080: f->psi = (x[j][i].psi - de2 * Lapl(x,psi,i,j) - x[j][i].F) * hxhy;
1081:
1083:
1084: /* vx * U_x + vy * U_y - (B_x * F_x + B_y * F_y) / d_e^2
1085: - nu Lap(U) */
1086: f->U =
1087: ((vxp * (D_xm(x,U,i,j)) + vxm * (D_xp(x,U,i,j)) +
1088: vyp * (D_ym(x,U,i,j)) + vym * (D_yp(x,U,i,j))) -
1089: (Bxp * (D_xm(x,F,i,j) + F_eq_x) + Bxm * (D_xp(x,F,i,j) + F_eq_x) +
1090: Byp * (D_ym(x,F,i,j)) + Bym * (D_yp(x,F,i,j))) * dde2 -
1091: nu * Lapl(x,U,i,j)) * hxhy;
1092: f->U += dtinv*(x[j][i].U-xold[j][i].U);
1093:
1095:
1096: /* vx * F_x + vy * F_y - rho_s^2 * (B_x * U_x + B_y * U_y)
1097: - eta * Lap(psi) */
1098: f->F =
1099: ((vxp * (D_xm(x,F,i,j) + F_eq_x) + vxm * (D_xp(x,F,i,j) + F_eq_x) +
1100: vyp * (D_ym(x,F,i,j)) + vym * (D_yp(x,F,i,j))) -
1101: (Bxp * (D_xm(x,U,i,j)) + Bxm * (D_xp(x,U,i,j)) +
1102: Byp * (D_ym(x,U,i,j)) + Bym * (D_yp(x,U,i,j))) * rhos2 -
1103: eta * Lapl(x,psi,i,j)) * hxhy;
1104: f->F += dtinv*(x[j][i].F-xold[j][i].F);
1105:
1106:
1107: DAVecRestoreArray(info->da,user->Xold,&xold);
1110: /*
1111: Flop count (multiply-adds are counted as 2 operations)
1112: */
1113: /* PetscLogFlops(84*info->ym*info->xm); FIXME */
1114: return(0);
1115: }