Actual source code: ex30.c

petsc-3.4.4 2014-03-13
  1: static const char help[] = "Steady-state 2D subduction flow, pressure and temperature solver.\n\
  2:        The flow is driven by the subducting slab.\n\
  3: ---------------------------------ex30 help---------------------------------\n\
  4:   -OPTION <DEFAULT> = (UNITS) DESCRIPTION.\n\n\
  5:   -width <320> = (km) width of domain.\n\
  6:   -depth <300> = (km) depth of domain.\n\
  7:   -slab_dip <45> = (degrees) dip angle of the slab (determines the grid aspect ratio).\n\
  8:   -lid_depth <35> = (km) depth of the static conductive lid.\n\
  9:   -fault_depth <35> = (km) depth of slab-wedge mechanical coupling\n\
 10:      (fault dept >= lid depth).\n\
 11: \n\
 12:   -ni <82> = grid cells in x-direction. (nj adjusts to accommodate\n\
 13:       the slab dip & depth). DO NOT USE -da_grid_x option!!!\n\
 14:   -ivisc <3> = rheology option.\n\
 15:       0 --- constant viscosity.\n\
 16:       1 --- olivine diffusion creep rheology (T&P-dependent, newtonian).\n\
 17:       2 --- olivine dislocation creep rheology (T&P-dependent, non-newtonian).\n\
 18:       3 --- Full mantle rheology, combination of 1 & 2.\n\
 19: \n\
 20:   -slab_velocity <5> = (cm/year) convergence rate of slab into subduction zone.\n\
 21:   -slab_age <50> = (million yrs) age of slab for thermal profile boundary condition.\n\
 22:   -lid_age <50> = (million yrs) age of lid for thermal profile boundary condition.\n\
 23: \n\
 24:   FOR OTHER PARAMETER OPTIONS AND THEIR DEFAULT VALUES, see SetParams() in ex30.c.\n\
 25: ---------------------------------ex30 help---------------------------------\n";



This PETSc 2.2.0 example by Richard F. Katz
http://www.ldeo.columbia.edu/~katz/

The problem is modeled by the partial differential equation system

\begin{eqnarray}
-\nabla P + \nabla \cdot [\eta (\nabla v + \nabla v^T)] & = & 0 \\
\nabla \cdot v & = & 0 \\
dT/dt + \nabla \cdot (vT) - 1/Pe \triangle^2(T) & = & 0 \\
\end{eqnarray}

\begin{eqnarray}
\eta(T,Eps\_dot) & = & \hbox{constant } \hbox{if ivisc} ==0 \\
& = & \hbox{diffusion creep (T,P-dependent) } \hbox{if ivisc} ==1 \\
& = & \hbox{dislocation creep (T,P,v-dependent)} \hbox{if ivisc} ==2 \\
& = & \hbox{mantle viscosity (difn and disl) } \hbox{if ivisc} ==3
\end{eqnarray}

which is uniformly discretized on a staggered mesh:
-------$w_{ij}$------
$u_{i-1j}$ $P,T_{ij}$ $u_{ij}$
------$w_{ij-1}$-----

 55: #include <petscsnes.h>
 56: #include <petscdmda.h>

 58: #define VISC_CONST   0
 59: #define VISC_DIFN    1
 60: #define VISC_DISL    2
 61: #define VISC_FULL    3
 62: #define CELL_CENTER  0
 63: #define CELL_CORNER  1
 64: #define BC_ANALYTIC  0
 65: #define BC_NOSTRESS  1
 66: #define BC_EXPERMNT  2
 67: #define ADVECT_FV    0
 68: #define ADVECT_FROMM 1
 69: #define PLATE_SLAB   0
 70: #define PLATE_LID    1
 71: #define EPS_ZERO     0.00000001

 73: typedef struct { /* holds the variables to be solved for */
 74:   PetscScalar u,w,p,T;
 75: } Field;

 77: typedef struct { /* parameters needed to compute viscosity */
 78:   PetscReal A,n,Estar,Vstar;
 79: } ViscParam;

 81: typedef struct { /* physical and miscelaneous parameters */
 82:   PetscReal width, depth, scaled_width, scaled_depth, peclet, potentialT;
 83:   PetscReal slab_dip, slab_age, slab_velocity, kappa, z_scale;
 84:   PetscReal c, d, sb, cb, skt, visc_cutoff, lid_age, eta0, continuation;
 85:   PetscReal L, V, lid_depth, fault_depth;
 86:   ViscParam diffusion, dislocation;
 87:   PetscInt  ivisc, adv_scheme, ibound, output_ivisc;
 88:   PetscBool quiet, param_test, output_to_file, pv_analytic;
 89:   PetscBool interrupted, stop_solve, toggle_kspmon, kspmon;
 90:   char      filename[PETSC_MAX_PATH_LEN];
 91: } Parameter;

 93: typedef struct { /* grid parameters */
 94:   DMDABoundaryType bx,by;
 95:   DMDAStencilType  stencil;
 96:   PetscInt         corner,ni,nj,jlid,jfault,inose;
 97:   PetscInt         dof,stencil_width,mglevels;
 98:   PetscReal        dx,dz;
 99: } GridInfo;

101: typedef struct { /* application context */
102:   Vec       x,Xguess;
103:   Parameter *param;
104:   GridInfo  *grid;
105: } AppCtx;

107: /* Callback functions (static interface) */
108: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,Field**,Field**,void*);

110: /* Main routines */
111: extern PetscErrorCode SetParams(Parameter*, GridInfo*);
112: extern PetscErrorCode ReportParams(Parameter*, GridInfo*);
113: extern PetscErrorCode Initialize(DM);
114: extern PetscErrorCode UpdateSolution(SNES,AppCtx*, PetscInt*);
115: extern PetscErrorCode DoOutput(SNES,PetscInt);

117: /* Post-processing & misc */
118: extern PetscErrorCode ViscosityField(DM,Vec,Vec);
119: extern PetscErrorCode StressField(DM);
120: extern PetscErrorCode SNESConverged_Interactive(SNES, PetscInt, PetscReal, PetscReal, PetscReal, SNESConvergedReason*, void*);
121: extern PetscErrorCode InteractiveHandler(int, void*);
122: extern PetscBool  OptionsHasName(const char pre[],const char name[]);

124: /*-----------------------------------------------------------------------*/
127: int main(int argc,char **argv)
128: /*-----------------------------------------------------------------------*/
129: {
130:   SNES           snes;
131:   AppCtx         *user;               /* user-defined work context */
132:   Parameter      param;
133:   GridInfo       grid;
134:   PetscInt       nits;
136:   MPI_Comm       comm;
137:   DM             da;

139:   PetscInitialize(&argc,&argv,(char*)0,help);
140:   PetscOptionsSetValue("-file","ex30_output");
141:   PetscOptionsSetValue("-snes_monitor_short",NULL);
142:   PetscOptionsSetValue("-snes_max_it","20");
143:   PetscOptionsSetValue("-ksp_max_it","1500");
144:   PetscOptionsSetValue("-ksp_gmres_restart","300");
145:   PetscOptionsInsert(&argc,&argv,NULL);

147:   comm = PETSC_COMM_WORLD;

149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150:      Set up the problem parameters.
151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152:   SetParams(&param,&grid);
153:   ReportParams(&param,&grid);

155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
157:   SNESCreate(comm,&snes);
158:   DMDACreate2d(comm,grid.bx,grid.by,grid.stencil,grid.ni,grid.nj,PETSC_DECIDE,PETSC_DECIDE,grid.dof,grid.stencil_width,0,0,&da);
159:   SNESSetDM(snes,da);
160:   DMDASetFieldName(da,0,"x-velocity");
161:   DMDASetFieldName(da,1,"y-velocity");
162:   DMDASetFieldName(da,2,"pressure");
163:   DMDASetFieldName(da,3,"temperature");


166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167:      Create user context, set problem data, create vector data structures.
168:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169:   PetscMalloc(sizeof(AppCtx),&user);
170:   user->param = &param;
171:   user->grid  = &grid;
172:   DMSetApplicationContext(da,user);
173:   DMCreateGlobalVector(da,&(user->Xguess));


176:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177:      Set up the SNES solver with callback functions.
178:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
179:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,(void*)user);
180:   SNESSetFromOptions(snes);


183:   SNESSetConvergenceTest(snes,SNESConverged_Interactive,(void*)user,NULL);
184:   PetscPushSignalHandler(InteractiveHandler,(void*)user);

186:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187:      Initialize and solve the nonlinear system
188:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
189:   Initialize(da);
190:   UpdateSolution(snes,user,&nits);

192:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193:      Output variables.
194:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195:   DoOutput(snes,nits);

197:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198:      Free work space.
199:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200:   VecDestroy(&user->Xguess);
201:   VecDestroy(&user->x);
202:   PetscFree(user);
203:   SNESDestroy(&snes);
204:   DMDestroy(&da);
205:   PetscPopSignalHandler();
206:   PetscFinalize();
207:   return 0;
208: }

210: /*=====================================================================
211:   PETSc INTERACTION FUNCTIONS (initialize & call SNESSolve)
212:   =====================================================================*/

214: /*---------------------------------------------------------------------*/
217: /*  manages solve: adaptive continuation method  */
218: PetscErrorCode UpdateSolution(SNES snes, AppCtx *user, PetscInt *nits)
219: {
220:   KSP                 ksp;
221:   PC                  pc;
222:   SNESConvergedReason reason;
223:   Parameter           *param   = user->param;
224:   PetscReal           cont_incr=0.3;
225:   PetscInt            its;
226:   PetscErrorCode      ierr;
227:   PetscBool           q = PETSC_FALSE;
228:   DM                  dm;

231:   SNESGetDM(snes,&dm);
232:   DMCreateGlobalVector(dm,&user->x);
233:   SNESGetKSP(snes,&ksp);
234:   KSPGetPC(ksp, &pc);
235:   KSPSetComputeSingularValues(ksp, PETSC_TRUE);

237:   *nits=0;

239:   /* Isoviscous solve */
240:   if (param->ivisc == VISC_CONST && !param->stop_solve) {
241:     param->ivisc = VISC_CONST;

243:     SNESSolve(snes,0,user->x);
244:     SNESGetConvergedReason(snes,&reason);
245:     SNESGetIterationNumber(snes,&its);
246:     *nits += its;
247:     VecCopy(user->x,user->Xguess);
248:     if (param->stop_solve) goto done;
249:   }

251:   /* Olivine diffusion creep */
252:   if (param->ivisc >= VISC_DIFN && !param->stop_solve) {
253:     if (!q) PetscPrintf(PETSC_COMM_WORLD,"Computing Variable Viscosity Solution\n");

255:     /* continuation method on viscosity cutoff */
256:     for (param->continuation=0.0;; param->continuation+=cont_incr) {
257:       if (!q) PetscPrintf(PETSC_COMM_WORLD," Continuation parameter = %G\n", param->continuation);

259:       /* solve the non-linear system */
260:       VecCopy(user->Xguess,user->x);
261:       SNESSolve(snes,0,user->x);
262:       SNESGetConvergedReason(snes,&reason);
263:       SNESGetIterationNumber(snes,&its);
264:       *nits += its;
265:       if (!q) PetscPrintf(PETSC_COMM_WORLD," SNES iterations: %D, Cumulative: %D\n", its, *nits);
266:       if (param->stop_solve) goto done;

268:       if (reason<0) {
269:         /* NOT converged */
270:         cont_incr = -fabs(cont_incr)/2.0;
271:         if (fabs(cont_incr)<0.01) goto done;

273:       } else {
274:         /* converged */
275:         VecCopy(user->x,user->Xguess);
276:         if (param->continuation >= 1.0) goto done;
277:         if (its<=3)      cont_incr = 0.30001;
278:         else if (its<=8) cont_incr = 0.15001;
279:         else             cont_incr = 0.10001;

281:         if (param->continuation+cont_incr > 1.0) cont_incr = 1.0 - param->continuation;
282:       } /* endif reason<0 */
283:     }
284:   }
285: done:
286:   if (param->stop_solve && !q) PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: stopping solve.\n");
287:   if (reason<0 && !q) PetscPrintf(PETSC_COMM_WORLD,"FAILED TO CONVERGE: stopping solve.\n");
288:   return(0);
289: }


292: /*=====================================================================
293:   PHYSICS FUNCTIONS (compute the discrete residual)
294:   =====================================================================*/


297: /*---------------------------------------------------------------------*/
300: PETSC_STATIC_INLINE PetscScalar UInterp(Field **x, PetscInt i, PetscInt j)
301: /*---------------------------------------------------------------------*/
302: {
303:   return 0.25*(x[j][i].u+x[j+1][i].u+x[j][i+1].u+x[j+1][i+1].u);
304: }

306: /*---------------------------------------------------------------------*/
309: PETSC_STATIC_INLINE PetscScalar WInterp(Field **x, PetscInt i, PetscInt j)
310: /*---------------------------------------------------------------------*/
311: {
312:   return 0.25*(x[j][i].w+x[j+1][i].w+x[j][i+1].w+x[j+1][i+1].w);
313: }

315: /*---------------------------------------------------------------------*/
318: PETSC_STATIC_INLINE PetscScalar PInterp(Field **x, PetscInt i, PetscInt j)
319: /*---------------------------------------------------------------------*/
320: {
321:   return 0.25*(x[j][i].p+x[j+1][i].p+x[j][i+1].p+x[j+1][i+1].p);
322: }

324: /*---------------------------------------------------------------------*/
327: PETSC_STATIC_INLINE PetscScalar TInterp(Field **x, PetscInt i, PetscInt j)
328: /*---------------------------------------------------------------------*/
329: {
330:   return 0.25*(x[j][i].T+x[j+1][i].T+x[j][i+1].T+x[j+1][i+1].T);
331: }

333: /*---------------------------------------------------------------------*/
336: /*  isoviscous analytic solution for IC */
337: PETSC_STATIC_INLINE PassiveScalar HorizVelocity(PetscInt i, PetscInt j, AppCtx *user)
338: /*---------------------------------------------------------------------*/
339: {
340:   Parameter   *param = user->param;
341:   GridInfo    *grid  = user->grid;
342:   PetscScalar st, ct, th, c=param->c, d=param->d;
343:   PetscReal   x, z,r;

345:   x  = (i - grid->jlid)*grid->dx;  z = (j - grid->jlid - 0.5)*grid->dz;
346:   r  = PetscSqrtReal(x*x+z*z);
347:   st = z/r;
348:   ct = x/r;
349:   th = atan(z/x);
350:   return ct*(c*th*st+d*(st+th*ct)) + st*(c*(st-th*ct)+d*th*st);
351: }

353: /*---------------------------------------------------------------------*/
356: /*  isoviscous analytic solution for IC */
357: PETSC_STATIC_INLINE PetscScalar VertVelocity(PetscInt i, PetscInt j, AppCtx *user)
358: /*---------------------------------------------------------------------*/
359: {
360:   Parameter   *param = user->param;
361:   GridInfo    *grid  = user->grid;
362:   PetscScalar st, ct, th, c=param->c, d=param->d;
363:   PetscReal   x, z, r;

365:   x = (i - grid->jlid - 0.5)*grid->dx;  z = (j - grid->jlid)*grid->dz;
366:   r = PetscSqrtReal(x*x+z*z); st = z/r;  ct = x/r;  th = atan(z/x);
367:   return st*(c*th*st+d*(st+th*ct)) - ct*(c*(st-th*ct)+d*th*st);
368: }

370: /*---------------------------------------------------------------------*/
373: /*  isoviscous analytic solution for IC */
374: PETSC_STATIC_INLINE PetscScalar Pressure(PetscInt i, PetscInt j, AppCtx *user)
375: /*---------------------------------------------------------------------*/
376: {
377:   Parameter   *param = user->param;
378:   GridInfo    *grid  = user->grid;
379:   PetscScalar x, z, r, st, ct, c=param->c, d=param->d;

381:   x = (i - grid->jlid - 0.5)*grid->dx;  z = (j - grid->jlid - 0.5)*grid->dz;
382:   r = PetscSqrtReal(x*x+z*z);  st = z/r;  ct = x/r;
383:   return (-2.0*(c*ct-d*st)/r);
384: }

388: /*  computes the second invariant of the strain rate tensor */
389: PETSC_STATIC_INLINE PetscScalar CalcSecInv(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
390: /*---------------------------------------------------------------------*/
391: {
392:   Parameter   *param = user->param;
393:   GridInfo    *grid  = user->grid;
394:   PetscInt    ilim   =grid->ni-1, jlim=grid->nj-1;
395:   PetscScalar uN,uS,uE,uW,wN,wS,wE,wW;
396:   PetscScalar eps11, eps12, eps22;

398:   if (i<j) return EPS_ZERO;
399:   if (i==ilim) i--;
400:   if (j==jlim) j--;

402:   if (ipos==CELL_CENTER) { /* on cell center */
403:     if (j<=grid->jlid) return EPS_ZERO;

405:     uE = x[j][i].u; uW = x[j][i-1].u;
406:     wN = x[j][i].w; wS = x[j-1][i].w;
407:     wE = WInterp(x,i,j-1);
408:     if (i==j) {
409:       uN = param->cb; wW = param->sb;
410:     } else {
411:       uN = UInterp(x,i-1,j); wW = WInterp(x,i-1,j-1);
412:     }

414:     if (j==grid->jlid+1) uS = 0.0;
415:     else                 uS = UInterp(x,i-1,j-1);

417:   } else {       /* on CELL_CORNER */
418:     if (j<grid->jlid) return EPS_ZERO;

420:     uN = x[j+1][i].u;  uS = x[j][i].u;
421:     wE = x[j][i+1].w;  wW = x[j][i].w;
422:     if (i==j) {
423:       wN = param->sb;
424:       uW = param->cb;
425:     } else {
426:       wN = WInterp(x,i,j);
427:       uW = UInterp(x,i-1,j);
428:     }

430:     if (j==grid->jlid) {
431:       uE = 0.0;  uW = 0.0;
432:       uS = -uN;
433:       wS = -wN;
434:     } else {
435:       uE = UInterp(x,i,j);
436:       wS = WInterp(x,i,j-1);
437:     }
438:   }

440:   eps11 = (uE-uW)/grid->dx;  eps22 = (wN-wS)/grid->dz;
441:   eps12 = 0.5*((uN-uS)/grid->dz + (wE-wW)/grid->dx);

443:   return PetscSqrtReal(0.5*(eps11*eps11 + 2.0*eps12*eps12 + eps22*eps22));
444: }

446: /*---------------------------------------------------------------------*/
449: /*  computes the shear viscosity */
450: PETSC_STATIC_INLINE PetscScalar Viscosity(PetscScalar T, PetscScalar eps, PassiveScalar z, Parameter *param)
451: /*---------------------------------------------------------------------*/
452: {
453:   PetscReal   result   =0.0;
454:   ViscParam   difn     =param->diffusion, disl=param->dislocation;
455:   PetscInt    iVisc    =param->ivisc;
456:   PetscScalar eps_scale=param->V/(param->L*1000.0);
457:   PetscScalar strain_power, v1, v2, P;
458:   PetscScalar rho_g = 32340.0, R=8.3144;

460:   P = rho_g*(z*param->L*1000.0); /* Pa */

462:   if (iVisc==VISC_CONST) {
463:     /* constant viscosity */
464:     return 1.0;
465:   } else if (iVisc==VISC_DIFN) {
466:     /* diffusion creep rheology */
467:     result = PetscRealPart((difn.A*PetscExpScalar((difn.Estar + P*difn.Vstar)/R/(T+273.0))/param->eta0));
468:   } else if (iVisc==VISC_DISL) {
469:     /* dislocation creep rheology */
470:     strain_power = PetscPowScalar(eps*eps_scale, (1.0-disl.n)/disl.n);

472:     result = PetscRealPart(disl.A*PetscExpScalar((disl.Estar + P*disl.Vstar)/disl.n/R/(T+273.0))*strain_power/param->eta0);
473:   } else if (iVisc==VISC_FULL) {
474:     /* dislocation/diffusion creep rheology */
475:     strain_power = PetscPowScalar(eps*eps_scale, (1.0-disl.n)/disl.n);

477:     v1 = difn.A*PetscExpScalar((difn.Estar + P*difn.Vstar)/R/(T+273.0))/param->eta0;
478:     v2 = disl.A*PetscExpScalar((disl.Estar + P*disl.Vstar)/disl.n/R/(T+273.0))*strain_power/param->eta0;

480:     result = PetscRealPart(1.0/(1.0/v1 + 1.0/v2));
481:   }

483:   /* max viscosity is param->eta0 */
484:   result = PetscMin(result, 1.0);
485:   /* min viscosity is param->visc_cutoff */
486:   result = PetscMax(result, param->visc_cutoff);
487:   /* continuation method */
488:   result = PetscPowReal(result,param->continuation);
489:   return result;
490: }

492: /*---------------------------------------------------------------------*/
495: /*  computes the residual of the x-component of eqn (1) above */
496: PETSC_STATIC_INLINE PetscScalar XMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
497: /*---------------------------------------------------------------------*/
498: {
499:   Parameter   *param=user->param;
500:   GridInfo    *grid =user->grid;
501:   PetscScalar dx    = grid->dx, dz=grid->dz;
502:   PetscScalar etaN,etaS,etaE,etaW,epsN=0.0,epsS=0.0,epsE=0.0,epsW=0.0;
503:   PetscScalar TE=0.0,TN=0.0,TS=0.0,TW=0.0, dPdx, residual, z_scale;
504:   PetscScalar dudxW,dudxE,dudzN,dudzS,dwdxN,dwdxS;
505:   PetscInt    jlim = grid->nj-1;

507:   z_scale = param->z_scale;

509:   if (param->ivisc==VISC_DIFN || param->ivisc>=VISC_DISL) { /* viscosity is T-dependent */
510:     TS = param->potentialT * TInterp(x,i,j-1) * exp((j-1.0)*dz*z_scale);
511:     if (j==jlim) TN = TS;
512:     else         TN = param->potentialT * TInterp(x,i,j) * exp(j*dz*z_scale);
513:     TW = param->potentialT * x[j][i].T        * exp((j-0.5)*dz*z_scale);
514:     TE = param->potentialT * x[j][i+1].T      * exp((j-0.5)*dz*z_scale);
515:     if (param->ivisc>=VISC_DISL) { /* olivine dislocation creep */
516:       epsN = CalcSecInv(x,i,j,  CELL_CORNER,user);
517:       epsS = CalcSecInv(x,i,j-1,CELL_CORNER,user);
518:       epsE = CalcSecInv(x,i+1,j,CELL_CENTER,user);
519:       epsW = CalcSecInv(x,i,j,  CELL_CENTER,user);
520:     }
521:   }
522:   etaN = Viscosity(TN,epsN,dz*(j+0.5),param);
523:   etaS = Viscosity(TS,epsS,dz*(j-0.5),param);
524:   etaW = Viscosity(TW,epsW,dz*j,param);
525:   etaE = Viscosity(TE,epsE,dz*j,param);

527:   dPdx = (x[j][i+1].p - x[j][i].p)/dx;
528:   if (j==jlim) dudzN = etaN * (x[j][i].w   - x[j][i+1].w)/dx;
529:   else         dudzN = etaN * (x[j+1][i].u - x[j][i].u)  /dz;
530:   dudzS = etaS * (x[j][i].u    - x[j-1][i].u)/dz;
531:   dudxE = etaE * (x[j][i+1].u  - x[j][i].u)  /dx;
532:   dudxW = etaW * (x[j][i].u    - x[j][i-1].u)/dx;

534:   residual = -dPdx                          /* X-MOMENTUM EQUATION*/
535:              +(dudxE - dudxW)/dx
536:              +(dudzN - dudzS)/dz;

538:   if (param->ivisc!=VISC_CONST) {
539:     dwdxN = etaN * (x[j][i+1].w   - x[j][i].w)  /dx;
540:     dwdxS = etaS * (x[j-1][i+1].w - x[j-1][i].w)/dx;

542:     residual += (dudxE - dudxW)/dx + (dwdxN - dwdxS)/dz;
543:   }

545:   return residual;
546: }

548: /*---------------------------------------------------------------------*/
551: /*  computes the residual of the z-component of eqn (1) above */
552: PETSC_STATIC_INLINE PetscScalar ZMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
553: /*---------------------------------------------------------------------*/
554: {
555:   Parameter   *param=user->param;
556:   GridInfo    *grid =user->grid;
557:   PetscScalar dx    = grid->dx, dz=grid->dz;
558:   PetscScalar etaN  =0.0,etaS=0.0,etaE=0.0,etaW=0.0,epsN=0.0,epsS=0.0,epsE=0.0,epsW=0.0;
559:   PetscScalar TE    =0.0,TN=0.0,TS=0.0,TW=0.0, dPdz, residual,z_scale;
560:   PetscScalar dudzE,dudzW,dwdxW,dwdxE,dwdzN,dwdzS;
561:   PetscInt    ilim = grid->ni-1;

563:   /* geometric and other parameters */
564:   z_scale = param->z_scale;

566:   /* viscosity */
567:   if (param->ivisc==VISC_DIFN || param->ivisc>=VISC_DISL) { /* viscosity is T-dependent */
568:     TN = param->potentialT * x[j+1][i].T      * exp((j+0.5)*dz*z_scale);
569:     TS = param->potentialT * x[j][i].T        * exp((j-0.5)*dz*z_scale);
570:     TW = param->potentialT * TInterp(x,i-1,j) * exp(j*dz*z_scale);
571:     if (i==ilim) TE = TW;
572:     else         TE = param->potentialT * TInterp(x,i,j) * exp(j*dz*z_scale);
573:     if (param->ivisc>=VISC_DISL) { /* olivine dislocation creep */
574:       epsN = CalcSecInv(x,i,j+1,CELL_CENTER,user);
575:       epsS = CalcSecInv(x,i,j,  CELL_CENTER,user);
576:       epsE = CalcSecInv(x,i,j,  CELL_CORNER,user);
577:       epsW = CalcSecInv(x,i-1,j,CELL_CORNER,user);
578:     }
579:   }
580:   etaN = Viscosity(TN,epsN,dz*(j+1.0),param);
581:   etaS = Viscosity(TS,epsS,dz*(j+0.0),param);
582:   etaW = Viscosity(TW,epsW,dz*(j+0.5),param);
583:   etaE = Viscosity(TE,epsE,dz*(j+0.5),param);

585:   dPdz  = (x[j+1][i].p - x[j][i].p)/dz;
586:   dwdzN = etaN * (x[j+1][i].w - x[j][i].w)/dz;
587:   dwdzS = etaS * (x[j][i].w - x[j-1][i].w)/dz;
588:   if (i==ilim) dwdxE = etaE * (x[j][i].u   - x[j+1][i].u)/dz;
589:   else         dwdxE = etaE * (x[j][i+1].w - x[j][i].w)  /dx;
590:   dwdxW = 2.0*etaW * (x[j][i].w - x[j][i-1].w)/dx;

592:   /* Z-MOMENTUM */
593:   residual = -dPdz                 /* constant viscosity terms */
594:              +(dwdzN - dwdzS)/dz
595:              +(dwdxE - dwdxW)/dx;

597:   if (param->ivisc!=VISC_CONST) {
598:     dudzE = etaE * (x[j+1][i].u - x[j][i].u)/dz;
599:     dudzW = etaW * (x[j+1][i-1].u - x[j][i-1].u)/dz;

601:     residual += (dwdzN - dwdzS)/dz + (dudzE - dudzW)/dx;
602:   }

604:   return residual;
605: }

607: /*---------------------------------------------------------------------*/
610: /*  computes the residual of eqn (2) above */
611: PETSC_STATIC_INLINE PetscScalar ContinuityResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
612: /*---------------------------------------------------------------------*/
613: {
614:   GridInfo    *grid =user->grid;
615:   PetscScalar uE,uW,wN,wS,dudx,dwdz;

617:   uW = x[j][i-1].u; uE = x[j][i].u; dudx = (uE - uW)/grid->dx;
618:   wS = x[j-1][i].w; wN = x[j][i].w; dwdz = (wN - wS)/grid->dz;

620:   return dudx + dwdz;
621: }

623: /*---------------------------------------------------------------------*/
626: /*  computes the residual of eqn (3) above */
627: PETSC_STATIC_INLINE PetscScalar EnergyResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
628: /*---------------------------------------------------------------------*/
629: {
630:   Parameter   *param=user->param;
631:   GridInfo    *grid =user->grid;
632:   PetscScalar dx    = grid->dx, dz=grid->dz;
633:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, jlid=grid->jlid;
634:   PetscScalar TE, TN, TS, TW, residual;
635:   PetscScalar uE,uW,wN,wS;
636:   PetscScalar fN,fS,fE,fW,dTdxW,dTdxE,dTdzN,dTdzS;

638:   dTdzN = (x[j+1][i].T - x[j][i].T)  /dz;
639:   dTdzS = (x[j][i].T   - x[j-1][i].T)/dz;
640:   dTdxE = (x[j][i+1].T - x[j][i].T)  /dx;
641:   dTdxW = (x[j][i].T   - x[j][i-1].T)/dx;

643:   residual = ((dTdzN - dTdzS)/dz + /* diffusion term */
644:               (dTdxE - dTdxW)/dx)*dx*dz/param->peclet;

646:   if (j<=jlid && i>=j) {
647:     /* don't advect in the lid */
648:     return residual;
649:   } else if (i<j) {
650:     /* beneath the slab sfc */
651:     uW = uE = param->cb;
652:     wS = wN = param->sb;
653:   } else {
654:     /* advect in the slab and wedge */
655:     uW = x[j][i-1].u; uE = x[j][i].u;
656:     wS = x[j-1][i].w; wN = x[j][i].w;
657:   }

659:   if (param->adv_scheme==ADVECT_FV || i==ilim-1 || j==jlim-1 || i==1 || j==1) {
660:     /* finite volume advection */
661:     TS = (x[j][i].T + x[j-1][i].T)/2.0;
662:     TN = (x[j][i].T + x[j+1][i].T)/2.0;
663:     TE = (x[j][i].T + x[j][i+1].T)/2.0;
664:     TW = (x[j][i].T + x[j][i-1].T)/2.0;
665:     fN = wN*TN*dx; fS = wS*TS*dx;
666:     fE = uE*TE*dz; fW = uW*TW*dz;

668:   } else {
669:     /* Fromm advection scheme */
670:     fE =     (uE *(-x[j][i+2].T + 5.0*(x[j][i+1].T+x[j][i].T)-x[j][i-1].T)/8.0
671:               - PetscAbsScalar(uE)*(-x[j][i+2].T + 3.0*(x[j][i+1].T-x[j][i].T)+x[j][i-1].T)/8.0)*dz;
672:     fW =     (uW *(-x[j][i+1].T + 5.0*(x[j][i].T+x[j][i-1].T)-x[j][i-2].T)/8.0
673:               - PetscAbsScalar(uW)*(-x[j][i+1].T + 3.0*(x[j][i].T-x[j][i-1].T)+x[j][i-2].T)/8.0)*dz;
674:     fN =     (wN *(-x[j+2][i].T + 5.0*(x[j+1][i].T+x[j][i].T)-x[j-1][i].T)/8.0
675:               - PetscAbsScalar(wN)*(-x[j+2][i].T + 3.0*(x[j+1][i].T-x[j][i].T)+x[j-1][i].T)/8.0)*dx;
676:     fS =     (wS *(-x[j+1][i].T + 5.0*(x[j][i].T+x[j-1][i].T)-x[j-2][i].T)/8.0
677:               - PetscAbsScalar(wS)*(-x[j+1][i].T + 3.0*(x[j][i].T-x[j-1][i].T)+x[j-2][i].T)/8.0)*dx;
678:   }

680:   residual -= (fE - fW + fN - fS);

682:   return residual;
683: }

685: /*---------------------------------------------------------------------*/
688: /*  computes the shear stress---used on the boundaries */
689: PETSC_STATIC_INLINE PetscScalar ShearStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
690: /*---------------------------------------------------------------------*/
691: {
692:   Parameter   *param=user->param;
693:   GridInfo    *grid =user->grid;
694:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1;
695:   PetscScalar uN, uS, wE, wW;

697:   if (j<=grid->jlid || i<j || i==ilim || j==jlim) return EPS_ZERO;

699:   if (ipos==CELL_CENTER) { /* on cell center */

701:     wE = WInterp(x,i,j-1);
702:     if (i==j) {
703:       wW = param->sb;
704:       uN = param->cb;
705:     } else {
706:       wW = WInterp(x,i-1,j-1);
707:       uN = UInterp(x,i-1,j);
708:     }
709:     if (j==grid->jlid+1) uS = 0.0;
710:     else                 uS = UInterp(x,i-1,j-1);

712:   } else { /* on cell corner */

714:     uN = x[j+1][i].u;         uS = x[j][i].u;
715:     wW = x[j][i].w;           wE = x[j][i+1].w;

717:   }

719:   return (uN-uS)/grid->dz + (wE-wW)/grid->dx;
720: }

722: /*---------------------------------------------------------------------*/
725: /*  computes the normal stress---used on the boundaries */
726: PETSC_STATIC_INLINE PetscScalar XNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
727: /*---------------------------------------------------------------------*/
728: {
729:   Parameter   *param=user->param;
730:   GridInfo    *grid =user->grid;
731:   PetscScalar dx    = grid->dx, dz=grid->dz;
732:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, ivisc;
733:   PetscScalar epsC  =0.0, etaC, TC, uE, uW, pC, z_scale;
734:   if (i<j || j<=grid->jlid) return EPS_ZERO;

736:   ivisc=param->ivisc;  z_scale = param->z_scale;

738:   if (ipos==CELL_CENTER) { /* on cell center */

740:     TC = param->potentialT * x[j][i].T * exp((j-0.5)*dz*z_scale);
741:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CENTER,user);
742:     etaC = Viscosity(TC,epsC,dz*j,param);

744:     uW = x[j][i-1].u;   uE = x[j][i].u;
745:     pC = x[j][i].p;

747:   } else { /* on cell corner */
748:     if (i==ilim || j==jlim) return EPS_ZERO;

750:     TC = param->potentialT * TInterp(x,i,j) * exp(j*dz*z_scale);
751:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
752:     etaC = Viscosity(TC,epsC,dz*(j+0.5),param);

754:     if (i==j) uW = param->sb;
755:     else      uW = UInterp(x,i-1,j);
756:     uE = UInterp(x,i,j); pC = PInterp(x,i,j);
757:   }

759:   return 2.0*etaC*(uE-uW)/dx - pC;
760: }

762: /*---------------------------------------------------------------------*/
765: /*  computes the normal stress---used on the boundaries */
766: PETSC_STATIC_INLINE PetscScalar ZNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
767: /*---------------------------------------------------------------------*/
768: {
769:   Parameter   *param=user->param;
770:   GridInfo    *grid =user->grid;
771:   PetscScalar dz    =grid->dz;
772:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, ivisc;
773:   PetscScalar epsC  =0.0, etaC, TC;
774:   PetscScalar pC, wN, wS, z_scale;
775:   if (i<j || j<=grid->jlid) return EPS_ZERO;

777:   ivisc=param->ivisc;  z_scale = param->z_scale;

779:   if (ipos==CELL_CENTER) { /* on cell center */

781:     TC = param->potentialT * x[j][i].T * exp((j-0.5)*dz*z_scale);
782:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CENTER,user);
783:     etaC = Viscosity(TC,epsC,dz*j,param);
784:     wN   = x[j][i].w; wS = x[j-1][i].w; pC = x[j][i].p;

786:   } else { /* on cell corner */
787:     if ((i==ilim) || (j==jlim)) return EPS_ZERO;

789:     TC = param->potentialT * TInterp(x,i,j) * exp(j*dz*z_scale);
790:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
791:     etaC = Viscosity(TC,epsC,dz*(j+0.5),param);
792:     if (i==j) wN = param->sb;
793:     else      wN = WInterp(x,i,j);
794:     wS = WInterp(x,i,j-1); pC = PInterp(x,i,j);
795:   }

797:   return 2.0*etaC*(wN-wS)/dz - pC;
798: }

800: /*---------------------------------------------------------------------*/

802: /*=====================================================================
803:   INITIALIZATION, POST-PROCESSING AND OUTPUT FUNCTIONS
804:   =====================================================================*/

806: /*---------------------------------------------------------------------*/
809: /* initializes the problem parameters and checks for
810:    command line changes */
811: PetscErrorCode SetParams(Parameter *param, GridInfo *grid)
812: /*---------------------------------------------------------------------*/
813: {
814:   PetscErrorCode ierr, ierr_out=0;
815:   PetscReal      SEC_PER_YR                    = 3600.00*24.00*365.2500;
816:   PetscReal      PI                            = 3.14159265358979323846;
817:   PetscReal      alpha_g_on_cp_units_inverse_km=4.0e-5*9.8;

819:   /* domain geometry */
820:   param->slab_dip    = 45.0;
821:   param->width       = 320.0;                                              /* km */
822:   param->depth       = 300.0;                                              /* km */
823:   param->lid_depth   = 35.0;                                               /* km */
824:   param->fault_depth = 35.0;                                               /* km */

826:   PetscOptionsGetReal(NULL,"-slab_dip",&(param->slab_dip),NULL);
827:   PetscOptionsGetReal(NULL,"-width",&(param->width),NULL);
828:   PetscOptionsGetReal(NULL,"-depth",&(param->depth),NULL);
829:   PetscOptionsGetReal(NULL,"-lid_depth",&(param->lid_depth),NULL);
830:   PetscOptionsGetReal(NULL,"-fault_depth",&(param->fault_depth),NULL);

832:   param->slab_dip = param->slab_dip*PI/180.0;                    /* radians */

834:   /* grid information */
835:   PetscOptionsGetInt(NULL, "-jfault",&(grid->jfault),NULL);
836:   grid->ni = 82;
837:   PetscOptionsGetInt(NULL, "-ni",&(grid->ni),NULL);

839:   grid->dx            = param->width/((double)(grid->ni-2));               /* km */
840:   grid->dz            = grid->dx*tan(param->slab_dip);                     /* km */
841:   grid->nj            = (PetscInt)(param->depth/grid->dz + 3.0);         /* gridpoints*/
842:   param->depth        = grid->dz*(grid->nj-2);                             /* km */
843:   grid->inose         = 0;                                          /* gridpoints*/
844:   PetscOptionsGetInt(NULL,"-inose",&(grid->inose),NULL);
845:   grid->bx            = DMDA_BOUNDARY_NONE;
846:   grid->by            = DMDA_BOUNDARY_NONE;
847:   grid->stencil       = DMDA_STENCIL_BOX;
848:   grid->dof           = 4;
849:   grid->stencil_width = 2;
850:   grid->mglevels      = 1;

852:   /* boundary conditions */
853:   param->pv_analytic = PETSC_FALSE;
854:   param->ibound      = BC_NOSTRESS;
855:   PetscOptionsGetInt(NULL,"-ibound",&(param->ibound),NULL);

857:   /* physical constants */
858:   param->slab_velocity = 5.0;               /* cm/yr */
859:   param->slab_age      = 50.0;              /* Ma */
860:   param->lid_age       = 50.0;              /* Ma */
861:   param->kappa         = 0.7272e-6;         /* m^2/sec */
862:   param->potentialT    = 1300.0;            /* degrees C */

864:   PetscOptionsGetReal(NULL,"-slab_velocity",&(param->slab_velocity),NULL);
865:   PetscOptionsGetReal(NULL,"-slab_age",&(param->slab_age),NULL);
866:   PetscOptionsGetReal(NULL,"-lid_age",&(param->lid_age),NULL);
867:   PetscOptionsGetReal(NULL,"-kappa",&(param->kappa),NULL);
868:   PetscOptionsGetReal(NULL,"-potentialT",&(param->potentialT),NULL);

870:   /* viscosity */
871:   param->ivisc        = 3;                  /* 0=isovisc, 1=difn creep, 2=disl creep, 3=full */
872:   param->eta0         = 1e24;               /* Pa-s */
873:   param->visc_cutoff  = 0.0;                /* factor of eta_0 */
874:   param->continuation = 1.0;

876:   /* constants for diffusion creep */
877:   param->diffusion.A     = 1.8e7;             /* Pa-s */
878:   param->diffusion.n     = 1.0;               /* dim'less */
879:   param->diffusion.Estar = 375e3;             /* J/mol */
880:   param->diffusion.Vstar = 5e-6;              /* m^3/mol */

882:   /* constants for param->dislocationocation creep */
883:   param->dislocation.A     = 2.8969e4;        /* Pa-s */
884:   param->dislocation.n     = 3.5;             /* dim'less */
885:   param->dislocation.Estar = 530e3;           /* J/mol */
886:   param->dislocation.Vstar = 14e-6;           /* m^3/mol */

888:   PetscOptionsGetInt(NULL, "-ivisc",&(param->ivisc),NULL);
889:   PetscOptionsGetReal(NULL,"-visc_cutoff",&(param->visc_cutoff),NULL);

891:   param->output_ivisc = param->ivisc;

893:   PetscOptionsGetInt(NULL,"-output_ivisc",&(param->output_ivisc),NULL);
894:   PetscOptionsGetReal(NULL,"-vstar",&(param->dislocation.Vstar),NULL);

896:   /* output options */
897:   param->quiet      = PETSC_FALSE;
898:   param->param_test = PETSC_FALSE;

900:   PetscOptionsHasName(NULL,"-quiet",&(param->quiet));
901:   PetscOptionsHasName(NULL,"-test",&(param->param_test));
902:   PetscOptionsGetString(NULL,"-file",param->filename,PETSC_MAX_PATH_LEN,&(param->output_to_file));

904:   /* advection */
905:   param->adv_scheme = ADVECT_FROMM;       /* advection scheme: 0=finite vol, 1=Fromm */

907:   PetscOptionsGetInt(NULL,"-adv_scheme",&(param->adv_scheme),NULL);

909:   /* misc. flags */
910:   param->stop_solve    = PETSC_FALSE;
911:   param->interrupted   = PETSC_FALSE;
912:   param->kspmon        = PETSC_FALSE;
913:   param->toggle_kspmon = PETSC_FALSE;

915:   /* derived parameters for slab angle */
916:   param->sb = sin(param->slab_dip);
917:   param->cb = cos(param->slab_dip);
918:   param->c  =  param->slab_dip*param->sb/(param->slab_dip*param->slab_dip-param->sb*param->sb);
919:   param->d  = (param->slab_dip*param->cb-param->sb)/(param->slab_dip*param->slab_dip-param->sb*param->sb);

921:   /* length, velocity and time scale for non-dimensionalization */
922:   param->L = PetscMin(param->width,param->depth);               /* km */
923:   param->V = param->slab_velocity/100.0/SEC_PER_YR;             /* m/sec */

925:   /* other unit conversions and derived parameters */
926:   param->scaled_width = param->width/param->L;                  /* dim'less */
927:   param->scaled_depth = param->depth/param->L;                  /* dim'less */
928:   param->lid_depth    = param->lid_depth/param->L;              /* dim'less */
929:   param->fault_depth  = param->fault_depth/param->L;            /* dim'less */
930:   grid->dx            = grid->dx/param->L;                      /* dim'less */
931:   grid->dz            = grid->dz/param->L;                      /* dim'less */
932:   grid->jlid          = (PetscInt)(param->lid_depth/grid->dz);       /* gridcells */
933:   grid->jfault        = (PetscInt)(param->fault_depth/grid->dz);     /* gridcells */
934:   param->lid_depth    = grid->jlid*grid->dz;                    /* dim'less */
935:   param->fault_depth  = grid->jfault*grid->dz;                  /* dim'less */
936:   grid->corner        = grid->jlid+1;                           /* gridcells */
937:   param->peclet       = param->V                                /* m/sec */
938:                         * param->L*1000.0                       /* m */
939:                         / param->kappa;                         /* m^2/sec */
940:   param->z_scale = param->L * alpha_g_on_cp_units_inverse_km;
941:   param->skt     = PetscSqrtReal(param->kappa*param->slab_age*SEC_PER_YR);
942:   PetscOptionsGetReal(NULL,"-peclet",&(param->peclet),NULL);

944:   return ierr_out;
945: }

947: /*---------------------------------------------------------------------*/
950: /*  prints a report of the problem parameters to stdout */
951: PetscErrorCode ReportParams(Parameter *param, GridInfo *grid)
952: /*---------------------------------------------------------------------*/
953: {
954:   PetscErrorCode ierr, ierr_out=0;
955:   char           date[30];
956:   PetscReal      PI = 3.14159265358979323846;

958:   PetscGetDate(date,30);

960:   if (!(param->quiet)) {
961:     PetscPrintf(PETSC_COMM_WORLD,"---------------------BEGIN ex30 PARAM REPORT-------------------\n");
962:     /* PetscPrintf(PETSC_COMM_WORLD,"                   %s\n",&(date[0]));*/

964:     PetscPrintf(PETSC_COMM_WORLD,"Domain: \n");
965:     PetscPrintf(PETSC_COMM_WORLD,"  Width = %G km,         Depth = %G km\n",param->width,param->depth);
966:     PetscPrintf(PETSC_COMM_WORLD,"  Slab dip = %G degrees,  Slab velocity = %G cm/yr\n",param->slab_dip*180.0/PI,param->slab_velocity);
967:     PetscPrintf(PETSC_COMM_WORLD,"  Lid depth = %5.2f km,   Fault depth = %5.2f km\n",param->lid_depth*param->L,param->fault_depth*param->L);

969:     PetscPrintf(PETSC_COMM_WORLD,"\nGrid: \n");
970:     PetscPrintf(PETSC_COMM_WORLD,"  [ni,nj] = %D, %D       [dx,dz] = %G, %G km\n",grid->ni,grid->nj,grid->dx*param->L,grid->dz*param->L);
971:     PetscPrintf(PETSC_COMM_WORLD,"  jlid = %3D              jfault = %3D \n",grid->jlid,grid->jfault);
972:     PetscPrintf(PETSC_COMM_WORLD,"  Pe = %G\n",param->peclet);

974:     PetscPrintf(PETSC_COMM_WORLD,"\nRheology:");
975:     if (param->ivisc==VISC_CONST) {
976:       PetscPrintf(PETSC_COMM_WORLD,"                 Isoviscous \n");
977:       if (param->pv_analytic) {
978:         PetscPrintf(PETSC_COMM_WORLD,"                          Pressure and Velocity prescribed! \n");
979:       }
980:     } else if (param->ivisc==VISC_DIFN) {
981:       PetscPrintf(PETSC_COMM_WORLD,"                 Diffusion Creep (T-Dependent Newtonian) \n");
982:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %G--%G Pa-sec \n",param->eta0,param->visc_cutoff*param->eta0);
983:     } else if (param->ivisc==VISC_DISL) {
984:       PetscPrintf(PETSC_COMM_WORLD,"                 Dislocation Creep (T-Dependent Non-Newtonian) \n");
985:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %G--%G Pa-sec \n",param->eta0,param->visc_cutoff*param->eta0);
986:     } else if (param->ivisc==VISC_FULL) {
987:       PetscPrintf(PETSC_COMM_WORLD,"                 Full Rheology \n");
988:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %G--%G Pa-sec \n",param->eta0,param->visc_cutoff*param->eta0);
989:     } else {
990:       PetscPrintf(PETSC_COMM_WORLD,"                 Invalid! \n");
991:       ierr_out = 1;
992:     }

994:     PetscPrintf(PETSC_COMM_WORLD,"Boundary condition:");
995:     if (param->ibound==BC_ANALYTIC) {
996:       PetscPrintf(PETSC_COMM_WORLD,"       Isoviscous Analytic Dirichlet \n");
997:     } else if (param->ibound==BC_NOSTRESS) {
998:       PetscPrintf(PETSC_COMM_WORLD,"       Stress-Free (normal & shear stress)\n");
999:     } else if (param->ibound==BC_EXPERMNT) {
1000:       PetscPrintf(PETSC_COMM_WORLD,"       Experimental boundary condition \n");
1001:     } else {
1002:       PetscPrintf(PETSC_COMM_WORLD,"       Invalid! \n");
1003:       ierr_out = 1;
1004:     }

1006:     if (param->output_to_file)
1007: #if defined(PETSC_HAVE_MATLAB_ENGINE)
1008:       PetscPrintf(PETSC_COMM_WORLD,"Output Destination:       Mat file \"%s\"\n",param->filename);
1009: #else
1010:       PetscPrintf(PETSC_COMM_WORLD,"Output Destination:       PETSc binary file \"%s\"\n",param->filename);
1011: #endif
1012:     if (param->output_ivisc != param->ivisc) {
1013:       PetscPrintf(PETSC_COMM_WORLD,"                          Output viscosity: -ivisc %D\n",param->output_ivisc);
1014:     }

1016:     PetscPrintf(PETSC_COMM_WORLD,"---------------------END ex30 PARAM REPORT---------------------\n");
1017:   }
1018:   if (param->param_test) PetscEnd();
1019:   return ierr_out;
1020: }

1022: /* ------------------------------------------------------------------- */
1025: /*  generates an inital guess using the analytic solution for isoviscous
1026:     corner flow */
1027: PetscErrorCode Initialize(DM da)
1028: /* ------------------------------------------------------------------- */
1029: {
1030:   AppCtx         *user;
1031:   Parameter      *param;
1032:   GridInfo       *grid;
1033:   PetscInt       i,j,is,js,im,jm;
1035:   Field          **x;
1036:   Vec            Xguess;

1038:   /* Get the fine grid */
1039:   DMGetApplicationContext(da,&user);
1040:   Xguess = user->Xguess;
1041:   param  = user->param;
1042:   grid   = user->grid;
1043:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1044:   DMDAVecGetArray(da,Xguess,(void**)&x);

1046:   /* Compute initial guess */
1047:   for (j=js; j<js+jm; j++) {
1048:     for (i=is; i<is+im; i++) {
1049:       if (i<j)                x[j][i].u = param->cb;
1050:       else if (j<=grid->jlid) x[j][i].u = 0.0;
1051:       else                    x[j][i].u = HorizVelocity(i,j,user);

1053:       if (i<=j)               x[j][i].w = param->sb;
1054:       else if (j<=grid->jlid) x[j][i].w = 0.0;
1055:       else                    x[j][i].w = VertVelocity(i,j,user);

1057:       if (i<j || j<=grid->jlid) x[j][i].p = 0.0;
1058:       else                      x[j][i].p = Pressure(i,j,user);

1060:       x[j][i].T = PetscMin(grid->dz*(j-0.5),1.0);
1061:     }
1062:   }

1064:   /* Restore x to Xguess */
1065:   DMDAVecRestoreArray(da,Xguess,(void**)&x);

1067:   return 0;
1068: }

1070: /*---------------------------------------------------------------------*/
1073: /*  controls output to a file */
1074: PetscErrorCode DoOutput(SNES snes, PetscInt its)
1075: /*---------------------------------------------------------------------*/
1076: {
1077:   AppCtx         *user;
1078:   Parameter      *param;
1079:   GridInfo       *grid;
1080:   PetscInt       ivt;
1082:   PetscMPIInt    rank;
1083:   PetscViewer    viewer;
1084:   Vec            res, pars;
1085:   MPI_Comm       comm;
1086:   DM             da;

1088:   SNESGetDM(snes,&da);
1089:   DMGetApplicationContext(da,&user);
1090:   param = user->param;
1091:   grid  = user->grid;
1092:   ivt   = param->ivisc;

1094:   param->ivisc = param->output_ivisc;

1096:   /* compute final residual and final viscosity/strain rate fields */
1097:   SNESGetFunction(snes, &res, NULL, NULL);
1098:   ViscosityField(da, user->x, user->Xguess);

1100:   /* get the communicator and the rank of the processor */
1101:   PetscObjectGetComm((PetscObject)snes, &comm);
1102:   MPI_Comm_rank(comm, &rank);

1104:   if (param->output_to_file) { /* send output to binary file */
1105:     VecCreate(comm, &pars);
1106:     if (!rank) { /* on processor 0 */
1107:       VecSetSizes(pars, 20, PETSC_DETERMINE);
1108:       VecSetFromOptions(pars);
1109:       VecSetValue(pars,0, (PetscScalar)(grid->ni),INSERT_VALUES);
1110:       VecSetValue(pars,1, (PetscScalar)(grid->nj),INSERT_VALUES);
1111:       VecSetValue(pars,2, (PetscScalar)(grid->dx),INSERT_VALUES);
1112:       VecSetValue(pars,3, (PetscScalar)(grid->dz),INSERT_VALUES);
1113:       VecSetValue(pars,4, (PetscScalar)(param->L),INSERT_VALUES);
1114:       VecSetValue(pars,5, (PetscScalar)(param->V),INSERT_VALUES);
1115:       /* skipped 6 intentionally */
1116:       VecSetValue(pars,7, (PetscScalar)(param->slab_dip),INSERT_VALUES);
1117:       VecSetValue(pars,8, (PetscScalar)(grid->jlid),INSERT_VALUES);
1118:       VecSetValue(pars,9, (PetscScalar)(param->lid_depth),INSERT_VALUES);
1119:       VecSetValue(pars,10,(PetscScalar)(grid->jfault),INSERT_VALUES);
1120:       VecSetValue(pars,11,(PetscScalar)(param->fault_depth),INSERT_VALUES);
1121:       VecSetValue(pars,12,(PetscScalar)(param->potentialT),INSERT_VALUES);
1122:       VecSetValue(pars,13,(PetscScalar)(param->ivisc),INSERT_VALUES);
1123:       VecSetValue(pars,14,(PetscScalar)(param->visc_cutoff),INSERT_VALUES);
1124:       VecSetValue(pars,15,(PetscScalar)(param->ibound),INSERT_VALUES);
1125:       VecSetValue(pars,16,(PetscScalar)(its),INSERT_VALUES);
1126:     } else { /* on some other processor */
1127:       VecSetSizes(pars, 0, PETSC_DETERMINE);
1128:       VecSetFromOptions(pars);
1129:     }
1130:     VecAssemblyBegin(pars); VecAssemblyEnd(pars);

1132:     /* create viewer */
1133: #if defined(PETSC_HAVE_MATLAB_ENGINE)
1134:     PetscViewerMatlabOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1135: #else
1136:     PetscViewerBinaryOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1137: #endif

1139:     /* send vectors to viewer */
1140:     PetscObjectSetName((PetscObject)res,"res");
1141:     VecView(res,viewer);
1142:     PetscObjectSetName((PetscObject)user->x,"out");
1143:     VecView(user->x, viewer);
1144:     PetscObjectSetName((PetscObject)(user->Xguess),"aux");
1145:     VecView(user->Xguess, viewer);
1146:     StressField(da); /* compute stress fields */
1147:     PetscObjectSetName((PetscObject)(user->Xguess),"str");
1148:     VecView(user->Xguess, viewer);
1149:     PetscObjectSetName((PetscObject)pars,"par");
1150:     VecView(pars, viewer);

1152:     /* destroy viewer and vector */
1153:     PetscViewerDestroy(&viewer);
1154:     VecDestroy(&pars);
1155:   }

1157:   param->ivisc = ivt;
1158:   return 0;
1159: }

1161: /* ------------------------------------------------------------------- */
1164: /* Compute both the second invariant of the strain rate tensor and the viscosity, at both cell centers and cell corners */
1165: PetscErrorCode ViscosityField(DM da, Vec X, Vec V)
1166: /* ------------------------------------------------------------------- */
1167: {
1168:   AppCtx         *user;
1169:   Parameter      *param;
1170:   GridInfo       *grid;
1171:   Vec            localX;
1172:   Field          **v, **x;
1173:   PassiveReal    eps, /* dx,*/ dz, T, epsC, TC;
1174:   PetscInt       i,j,is,js,im,jm,ilim,jlim,ivt;

1178:   DMGetApplicationContext(da,&user);
1179:   param        = user->param;
1180:   grid         = user->grid;
1181:   ivt          = param->ivisc;
1182:   param->ivisc = param->output_ivisc;

1184:   DMGetLocalVector(da, &localX);
1185:   DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
1186:   DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
1187:   DMDAVecGetArray(da,localX,(void**)&x);
1188:   DMDAVecGetArray(da,V,(void**)&v);

1190:   /* Parameters */
1191:   /* dx = grid->dx; */ dz = grid->dz;

1193:   ilim = grid->ni-1; jlim = grid->nj-1;

1195:   /* Compute real temperature, strain rate and viscosity */
1196:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1197:   for (j=js; j<js+jm; j++) {
1198:     for (i=is; i<is+im; i++) {
1199:       T = PetscRealPart(param->potentialT * x[j][i].T * exp((j-0.5)*dz*param->z_scale));
1200:       if (i<ilim && j<jlim) {
1201:         TC = PetscRealPart(param->potentialT * TInterp(x,i,j) * exp(j*dz*param->z_scale));
1202:       } else {
1203:         TC = T;
1204:       }
1205:       eps  = PetscRealPart((CalcSecInv(x,i,j,CELL_CENTER,user)));
1206:       epsC = PetscRealPart(CalcSecInv(x,i,j,CELL_CORNER,user));

1208:       v[j][i].u = eps;
1209:       v[j][i].w = epsC;
1210:       v[j][i].p = Viscosity(T,eps,dz*(j-0.5),param);
1211:       v[j][i].T = Viscosity(TC,epsC,dz*j,param);
1212:     }
1213:   }
1214:   DMDAVecRestoreArray(da,V,(void**)&v);
1215:   DMDAVecRestoreArray(da,localX,(void**)&x);
1216:   DMRestoreLocalVector(da, &localX);

1218:   param->ivisc = ivt;
1219:   return(0);
1220: }

1222: /* ------------------------------------------------------------------- */
1225: /* post-processing: compute stress everywhere */
1226: PetscErrorCode StressField(DM da)
1227: /* ------------------------------------------------------------------- */
1228: {
1229:   AppCtx         *user;
1230:   PetscInt       i,j,is,js,im,jm;
1232:   Vec            locVec;
1233:   Field          **x, **y;

1235:   DMGetApplicationContext(da,&user);

1237:   /* Get the fine grid of Xguess and X */
1238:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1239:   DMDAVecGetArray(da,user->Xguess,(void**)&x);

1241:   DMGetLocalVector(da, &locVec);
1242:   DMGlobalToLocalBegin(da, user->x, INSERT_VALUES, locVec);
1243:   DMGlobalToLocalEnd(da, user->x, INSERT_VALUES, locVec);
1244:   DMDAVecGetArray(da,locVec,(void**)&y);

1246:   /* Compute stress on the corner points */
1247:   for (j=js; j<js+jm; j++) {
1248:     for (i=is; i<is+im; i++) {
1249:       x[j][i].u = ShearStress(y,i,j,CELL_CENTER,user);
1250:       x[j][i].w = ShearStress(y,i,j,CELL_CORNER,user);
1251:       x[j][i].p = XNormalStress(y,i,j,CELL_CENTER,user);
1252:       x[j][i].T = ZNormalStress(y,i,j,CELL_CENTER,user);
1253:     }
1254:   }

1256:   /* Restore the fine grid of Xguess and X */
1257:   DMDAVecRestoreArray(da,user->Xguess,(void**)&x);
1258:   DMDAVecRestoreArray(da,locVec,(void**)&y);
1259:   DMRestoreLocalVector(da, &locVec);
1260:   return 0;
1261: }

1263: /*=====================================================================
1264:   UTILITY FUNCTIONS
1265:   =====================================================================*/

1267: /*---------------------------------------------------------------------*/
1270: /* returns the velocity of the subducting slab and handles fault nodes
1271:    for BC */
1272: PETSC_STATIC_INLINE PassiveScalar SlabVel(char c, PetscInt i, PetscInt j, AppCtx *user)
1273: /*---------------------------------------------------------------------*/
1274: {
1275:   Parameter *param = user->param;
1276:   GridInfo  *grid  = user->grid;

1278:   if (c=='U' || c=='u') {
1279:     if (i<j-1) return param->cb;
1280:     else if (j<=grid->jfault) return 0.0;
1281:     else return param->cb;

1283:   } else {
1284:     if (i<j) return param->sb;
1285:     else if (j<=grid->jfault) return 0.0;
1286:     else return param->sb;
1287:   }
1288: }

1290: /*---------------------------------------------------------------------*/
1293: /*  solution to diffusive half-space cooling model for BC */
1294: PETSC_STATIC_INLINE PassiveScalar PlateModel(PetscInt j, PetscInt plate, AppCtx *user)
1295: /*---------------------------------------------------------------------*/
1296: {
1297:   Parameter     *param = user->param;
1298:   PassiveScalar z;
1299:   if (plate==PLATE_LID) z = (j-0.5)*user->grid->dz;
1300:   else z = (j-0.5)*user->grid->dz*param->cb;  /* PLATE_SLAB */
1301: #if defined(PETSC_HAVE_ERF)
1302:   return (erf(PetscRealPart(z*param->L/2.0/param->skt)));
1303: #else
1304:   SETERRQ(PETSC_COMM_SELF,1,"erf() not available on this machine");
1305: #endif
1306: }


1309: /* ------------------------------------------------------------------- */
1312: /*  utility function */
1313: PetscBool  OptionsHasName(const char pre[],const char name[])
1314: /* ------------------------------------------------------------------- */
1315: {
1316:   PetscBool      retval;
1318:   PetscOptionsHasName(pre,name,&retval);CHKERRABORT(PETSC_COMM_WORLD,ierr);
1319:   return retval;
1320: }

1322: /*=====================================================================
1323:   INTERACTIVE SIGNAL HANDLING
1324:   =====================================================================*/

1326: /* ------------------------------------------------------------------- */
1329: PetscErrorCode SNESConverged_Interactive(SNES snes, PetscInt it,PetscReal xnorm, PetscReal snorm, PetscReal fnorm, SNESConvergedReason *reason, void *ctx)
1330: /* ------------------------------------------------------------------- */
1331: {
1332:   AppCtx         *user  = (AppCtx*) ctx;
1333:   Parameter      *param = user->param;
1334:   KSP            ksp;

1338:   if (param->interrupted) {
1339:     param->interrupted = PETSC_FALSE;
1340:     PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: exiting SNES solve. \n");
1341:     *reason = SNES_CONVERGED_FNORM_ABS;
1342:     return(0);
1343:   } else if (param->toggle_kspmon) {
1344:     param->toggle_kspmon = PETSC_FALSE;

1346:     SNESGetKSP(snes, &ksp);

1348:     if (param->kspmon) {
1349:       KSPMonitorCancel(ksp);

1351:       param->kspmon = PETSC_FALSE;
1352:       PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: deactivating ksp singular value monitor. \n");
1353:     } else {
1354:       KSPMonitorSet(ksp,KSPMonitorSingularValue,NULL,NULL);

1356:       param->kspmon = PETSC_TRUE;
1357:       PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: activating ksp singular value monitor. \n");
1358:     }
1359:   }
1360:   PetscFunctionReturn(SNESConvergedDefault(snes,it,xnorm,snorm,fnorm,reason,ctx));
1361: }

1363: /* ------------------------------------------------------------------- */
1364: #include <signal.h>
1367: PetscErrorCode InteractiveHandler(int signum, void *ctx)
1368: /* ------------------------------------------------------------------- */
1369: {
1370:   AppCtx    *user  = (AppCtx*) ctx;
1371:   Parameter *param = user->param;

1373:   if (signum == SIGILL) {
1374:     param->toggle_kspmon = PETSC_TRUE;
1375: #if !defined(PETSC_MISSING_SIGCONT)
1376:   } else if (signum == SIGCONT) {
1377:     param->interrupted = PETSC_TRUE;
1378: #endif
1379: #if !defined(PETSC_MISSING_SIGURG)
1380:   } else if (signum == SIGURG) {
1381:     param->stop_solve = PETSC_TRUE;
1382: #endif
1383:   }
1384:   return 0;
1385: }

1387: /*---------------------------------------------------------------------*/
1390: /*  main call-back function that computes the processor-local piece
1391:     of the residual */
1392: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,Field **x,Field **f,void *ptr)
1393: /*---------------------------------------------------------------------*/
1394: {
1395:   AppCtx      *user  = (AppCtx*)ptr;
1396:   Parameter   *param = user->param;
1397:   GridInfo    *grid  = user->grid;
1398:   PetscScalar mag_w, mag_u;
1399:   PetscInt    i,j,mx,mz,ilim,jlim;
1400:   PetscInt    is,ie,js,je,ibound;    /* ,ivisc */

1403:   /* Define global and local grid parameters */
1404:   mx   = info->mx;     mz   = info->my;
1405:   ilim = mx-1;         jlim = mz-1;
1406:   is   = info->xs;     ie   = info->xs+info->xm;
1407:   js   = info->ys;     je   = info->ys+info->ym;

1409:   /* Define geometric and numeric parameters */
1410:   /* ivisc = param->ivisc; */ ibound = param->ibound;

1412:   for (j=js; j<je; j++) {
1413:     for (i=is; i<ie; i++) {

1415:       /************* X-MOMENTUM/VELOCITY *************/
1416:       if (i<j) f[j][i].u = x[j][i].u - SlabVel('U',i,j,user);
1417:       else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1418:         /* in the lithospheric lid */
1419:         f[j][i].u = x[j][i].u - 0.0;
1420:       } else if (i==ilim) {
1421:         /* on the right side boundary */
1422:         if (ibound==BC_ANALYTIC) {
1423:           f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1424:         } else {
1425:           f[j][i].u = XNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1426:         }

1428:       } else if (j==jlim) {
1429:         /* on the bottom boundary */
1430:         if (ibound==BC_ANALYTIC) {
1431:           f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1432:         } else if (ibound==BC_NOSTRESS) {
1433:           f[j][i].u = XMomentumResidual(x,i,j,user);
1434:         } else {
1435:           /* experimental boundary condition */
1436:         }

1438:       } else {
1439:         /* in the mantle wedge */
1440:         f[j][i].u = XMomentumResidual(x,i,j,user);
1441:       }

1443:       /************* Z-MOMENTUM/VELOCITY *************/
1444:       if (i<=j) {
1445:         f[j][i].w = x[j][i].w - SlabVel('W',i,j,user);

1447:       } else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1448:         /* in the lithospheric lid */
1449:         f[j][i].w = x[j][i].w - 0.0;

1451:       } else if (j==jlim) {
1452:         /* on the bottom boundary */
1453:         if (ibound==BC_ANALYTIC) {
1454:           f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1455:         } else {
1456:           f[j][i].w = ZNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1457:         }

1459:       } else if (i==ilim) {
1460:         /* on the right side boundary */
1461:         if (ibound==BC_ANALYTIC) {
1462:           f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1463:         } else if (ibound==BC_NOSTRESS) {
1464:           f[j][i].w = ZMomentumResidual(x,i,j,user);
1465:         } else {
1466:           /* experimental boundary condition */
1467:         }

1469:       } else {
1470:         /* in the mantle wedge */
1471:         f[j][i].w =  ZMomentumResidual(x,i,j,user);
1472:       }

1474:       /************* CONTINUITY/PRESSURE *************/
1475:       if (i<j || j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1476:         /* in the lid or slab */
1477:         f[j][i].p = x[j][i].p;

1479:       } else if ((i==ilim || j==jlim) && ibound==BC_ANALYTIC) {
1480:         /* on an analytic boundary */
1481:         f[j][i].p = x[j][i].p - Pressure(i,j,user);

1483:       } else {
1484:         /* in the mantle wedge */
1485:         f[j][i].p = ContinuityResidual(x,i,j,user);
1486:       }

1488:       /************* TEMPERATURE *************/
1489:       if (j==0) {
1490:         /* on the surface */
1491:         f[j][i].T = x[j][i].T + x[j+1][i].T + PetscMax(PetscRealPart(x[j][i].T),0.0);

1493:       } else if (i==0) {
1494:         /* slab inflow boundary */
1495:         f[j][i].T = x[j][i].T - PlateModel(j,PLATE_SLAB,user);

1497:       } else if (i==ilim) {
1498:         /* right side boundary */
1499:         mag_u = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j][i-1].u)/param->cb,1.0),0.0)), 5);
1500:         f[j][i].T = x[j][i].T - mag_u*x[j-1][i-1].T - (1.0-mag_u)*PlateModel(j,PLATE_LID,user);

1502:       } else if (j==jlim) {
1503:         /* bottom boundary */
1504:         mag_w = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j-1][i].w)/param->sb,1.0),0.0)), 5);
1505:         f[j][i].T = x[j][i].T - mag_w*x[j-1][i-1].T - (1.0-mag_w);

1507:       } else {
1508:         /* in the mantle wedge */
1509:         f[j][i].T = EnergyResidual(x,i,j,user);
1510:       }
1511:     }
1512:   }
1513:   return(0);
1514: }