Actual source code: ex30.c

petsc-master 2017-11-16
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  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 <petscdm.h>
 57:  #include <petscdmda.h>

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

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

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

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

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

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

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

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

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

125: /*-----------------------------------------------------------------------*/
126: int main(int argc,char **argv)
127: /*-----------------------------------------------------------------------*/
128: {
129:   SNES           snes;
130:   AppCtx         *user;               /* user-defined work context */
131:   Parameter      param;
132:   GridInfo       grid;
133:   PetscInt       nits;
135:   MPI_Comm       comm;
136:   DM             da;

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

146:   comm = PETSC_COMM_WORLD;

148:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149:      Set up the problem parameters.
150:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
151:   SetParams(&param,&grid);
152:   ReportParams(&param,&grid);

154:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
156:   SNESCreate(comm,&snes);
157:   DMDACreate2d(comm,grid.bx,grid.by,grid.stencil,grid.ni,grid.nj,PETSC_DECIDE,PETSC_DECIDE,grid.dof,grid.stencil_width,0,0,&da);
158:   DMSetFromOptions(da);
159:   DMSetUp(da);
160:   SNESSetDM(snes,da);
161:   DMDASetFieldName(da,0,"x-velocity");
162:   DMDASetFieldName(da,1,"y-velocity");
163:   DMDASetFieldName(da,2,"pressure");
164:   DMDASetFieldName(da,3,"temperature");


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


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


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

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

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

198:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199:      Free work space.
200:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201:   VecDestroy(&user->Xguess);
202:   VecDestroy(&user->x);
203:   PetscFree(user);
204:   SNESDestroy(&snes);
205:   DMDestroy(&da);
206:   PetscPopSignalHandler();
207:   PetscFinalize();
208:   return ierr;
209: }

211: /*=====================================================================
212:   PETSc INTERACTION FUNCTIONS (initialize & call SNESSolve)
213:   =====================================================================*/

215: /*---------------------------------------------------------------------*/
216: /*  manages solve: adaptive continuation method  */
217: PetscErrorCode UpdateSolution(SNES snes, AppCtx *user, PetscInt *nits)
218: {
219:   KSP                 ksp;
220:   PC                  pc;
221:   SNESConvergedReason reason = SNES_CONVERGED_ITERATING;
222:   Parameter           *param   = user->param;
223:   PetscReal           cont_incr=0.3;
224:   PetscInt            its;
225:   PetscErrorCode      ierr;
226:   PetscBool           q = PETSC_FALSE;
227:   DM                  dm;

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

236:   *nits=0;

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

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

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

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

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

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

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

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


291: /*=====================================================================
292:   PHYSICS FUNCTIONS (compute the discrete residual)
293:   =====================================================================*/


296: /*---------------------------------------------------------------------*/
297: PETSC_STATIC_INLINE PetscScalar UInterp(Field **x, PetscInt i, PetscInt j)
298: /*---------------------------------------------------------------------*/
299: {
300:   return 0.25*(x[j][i].u+x[j+1][i].u+x[j][i+1].u+x[j+1][i+1].u);
301: }

303: /*---------------------------------------------------------------------*/
304: PETSC_STATIC_INLINE PetscScalar WInterp(Field **x, PetscInt i, PetscInt j)
305: /*---------------------------------------------------------------------*/
306: {
307:   return 0.25*(x[j][i].w+x[j+1][i].w+x[j][i+1].w+x[j+1][i+1].w);
308: }

310: /*---------------------------------------------------------------------*/
311: PETSC_STATIC_INLINE PetscScalar PInterp(Field **x, PetscInt i, PetscInt j)
312: /*---------------------------------------------------------------------*/
313: {
314:   return 0.25*(x[j][i].p+x[j+1][i].p+x[j][i+1].p+x[j+1][i+1].p);
315: }

317: /*---------------------------------------------------------------------*/
318: PETSC_STATIC_INLINE PetscScalar TInterp(Field **x, PetscInt i, PetscInt j)
319: /*---------------------------------------------------------------------*/
320: {
321:   return 0.25*(x[j][i].T+x[j+1][i].T+x[j][i+1].T+x[j+1][i+1].T);
322: }

324: /*---------------------------------------------------------------------*/
325: /*  isoviscous analytic solution for IC */
326: PETSC_STATIC_INLINE PetscScalar HorizVelocity(PetscInt i, PetscInt j, AppCtx *user)
327: /*---------------------------------------------------------------------*/
328: {
329:   Parameter   *param = user->param;
330:   GridInfo    *grid  = user->grid;
331:   PetscScalar st, ct, th, c=param->c, d=param->d;
332:   PetscReal   x, z,r;

334:   x  = (i - grid->jlid)*grid->dx;  z = (j - grid->jlid - 0.5)*grid->dz;
335:   r  = PetscSqrtReal(x*x+z*z);
336:   st = z/r;
337:   ct = x/r;
338:   th = PetscAtanReal(z/x);
339:   return ct*(c*th*st+d*(st+th*ct)) + st*(c*(st-th*ct)+d*th*st);
340: }

342: /*---------------------------------------------------------------------*/
343: /*  isoviscous analytic solution for IC */
344: PETSC_STATIC_INLINE PetscScalar VertVelocity(PetscInt i, PetscInt j, AppCtx *user)
345: /*---------------------------------------------------------------------*/
346: {
347:   Parameter   *param = user->param;
348:   GridInfo    *grid  = user->grid;
349:   PetscScalar st, ct, th, c=param->c, d=param->d;
350:   PetscReal   x, z, r;

352:   x = (i - grid->jlid - 0.5)*grid->dx;  z = (j - grid->jlid)*grid->dz;
353:   r = PetscSqrtReal(x*x+z*z); st = z/r;  ct = x/r;  th = PetscAtanReal(z/x);
354:   return st*(c*th*st+d*(st+th*ct)) - ct*(c*(st-th*ct)+d*th*st);
355: }

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

366:   x = (i - grid->jlid - 0.5)*grid->dx;  z = (j - grid->jlid - 0.5)*grid->dz;
367:   r = PetscSqrtReal(x*x+z*z);  st = z/r;  ct = x/r;
368:   return (-2.0*(c*ct-d*st)/r);
369: }

371: /*  computes the second invariant of the strain rate tensor */
372: PETSC_STATIC_INLINE PetscScalar CalcSecInv(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
373: /*---------------------------------------------------------------------*/
374: {
375:   Parameter   *param = user->param;
376:   GridInfo    *grid  = user->grid;
377:   PetscInt    ilim   =grid->ni-1, jlim=grid->nj-1;
378:   PetscScalar uN,uS,uE,uW,wN,wS,wE,wW;
379:   PetscScalar eps11, eps12, eps22;

381:   if (i<j) return EPS_ZERO;
382:   if (i==ilim) i--;
383:   if (j==jlim) j--;

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

388:     uE = x[j][i].u; uW = x[j][i-1].u;
389:     wN = x[j][i].w; wS = x[j-1][i].w;
390:     wE = WInterp(x,i,j-1);
391:     if (i==j) {
392:       uN = param->cb; wW = param->sb;
393:     } else {
394:       uN = UInterp(x,i-1,j); wW = WInterp(x,i-1,j-1);
395:     }

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

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

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

413:     if (j==grid->jlid) {
414:       uE = 0.0;  uW = 0.0;
415:       uS = -uN;
416:       wS = -wN;
417:     } else {
418:       uE = UInterp(x,i,j);
419:       wS = WInterp(x,i,j-1);
420:     }
421:   }

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

426:   return PetscSqrtReal(0.5*(eps11*eps11 + 2.0*eps12*eps12 + eps22*eps22));
427: }

429: /*---------------------------------------------------------------------*/
430: /*  computes the shear viscosity */
431: PETSC_STATIC_INLINE PetscScalar Viscosity(PetscScalar T, PetscScalar eps, PetscScalar z, Parameter *param)
432: /*---------------------------------------------------------------------*/
433: {
434:   PetscReal   result   =0.0;
435:   ViscParam   difn     =param->diffusion, disl=param->dislocation;
436:   PetscInt    iVisc    =param->ivisc;
437:   PetscScalar eps_scale=param->V/(param->L*1000.0);
438:   PetscScalar strain_power, v1, v2, P;
439:   PetscScalar rho_g = 32340.0, R=8.3144;

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

443:   if (iVisc==VISC_CONST) {
444:     /* constant viscosity */
445:     return 1.0;
446:   } else if (iVisc==VISC_DIFN) {
447:     /* diffusion creep rheology */
448:     result = PetscRealPart((difn.A*PetscExpScalar((difn.Estar + P*difn.Vstar)/R/(T+273.0))/param->eta0));
449:   } else if (iVisc==VISC_DISL) {
450:     /* dislocation creep rheology */
451:     strain_power = PetscPowScalar(eps*eps_scale, (1.0-disl.n)/disl.n);

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

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

461:     result = PetscRealPart(1.0/(1.0/v1 + 1.0/v2));
462:   }

464:   /* max viscosity is param->eta0 */
465:   result = PetscMin(result, 1.0);
466:   /* min viscosity is param->visc_cutoff */
467:   result = PetscMax(result, param->visc_cutoff);
468:   /* continuation method */
469:   result = PetscPowReal(result,param->continuation);
470:   return result;
471: }

473: /*---------------------------------------------------------------------*/
474: /*  computes the residual of the x-component of eqn (1) above */
475: PETSC_STATIC_INLINE PetscScalar XMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
476: /*---------------------------------------------------------------------*/
477: {
478:   Parameter   *param=user->param;
479:   GridInfo    *grid =user->grid;
480:   PetscScalar dx    = grid->dx, dz=grid->dz;
481:   PetscScalar etaN,etaS,etaE,etaW,epsN=0.0,epsS=0.0,epsE=0.0,epsW=0.0;
482:   PetscScalar TE=0.0,TN=0.0,TS=0.0,TW=0.0, dPdx, residual, z_scale;
483:   PetscScalar dudxW,dudxE,dudzN,dudzS,dwdxN,dwdxS;
484:   PetscInt    jlim = grid->nj-1;

486:   z_scale = param->z_scale;

488:   if (param->ivisc==VISC_DIFN || param->ivisc>=VISC_DISL) { /* viscosity is T-dependent */
489:     TS = param->potentialT * TInterp(x,i,j-1) * PetscExpScalar((j-1.0)*dz*z_scale);
490:     if (j==jlim) TN = TS;
491:     else         TN = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
492:     TW = param->potentialT * x[j][i].T        * PetscExpScalar((j-0.5)*dz*z_scale);
493:     TE = param->potentialT * x[j][i+1].T      * PetscExpScalar((j-0.5)*dz*z_scale);
494:     if (param->ivisc>=VISC_DISL) { /* olivine dislocation creep */
495:       epsN = CalcSecInv(x,i,j,  CELL_CORNER,user);
496:       epsS = CalcSecInv(x,i,j-1,CELL_CORNER,user);
497:       epsE = CalcSecInv(x,i+1,j,CELL_CENTER,user);
498:       epsW = CalcSecInv(x,i,j,  CELL_CENTER,user);
499:     }
500:   }
501:   etaN = Viscosity(TN,epsN,dz*(j+0.5),param);
502:   etaS = Viscosity(TS,epsS,dz*(j-0.5),param);
503:   etaW = Viscosity(TW,epsW,dz*j,param);
504:   etaE = Viscosity(TE,epsE,dz*j,param);

506:   dPdx = (x[j][i+1].p - x[j][i].p)/dx;
507:   if (j==jlim) dudzN = etaN * (x[j][i].w   - x[j][i+1].w)/dx;
508:   else         dudzN = etaN * (x[j+1][i].u - x[j][i].u)  /dz;
509:   dudzS = etaS * (x[j][i].u    - x[j-1][i].u)/dz;
510:   dudxE = etaE * (x[j][i+1].u  - x[j][i].u)  /dx;
511:   dudxW = etaW * (x[j][i].u    - x[j][i-1].u)/dx;

513:   residual = -dPdx                          /* X-MOMENTUM EQUATION*/
514:              +(dudxE - dudxW)/dx
515:              +(dudzN - dudzS)/dz;

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

521:     residual += (dudxE - dudxW)/dx + (dwdxN - dwdxS)/dz;
522:   }

524:   return residual;
525: }

527: /*---------------------------------------------------------------------*/
528: /*  computes the residual of the z-component of eqn (1) above */
529: PETSC_STATIC_INLINE PetscScalar ZMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
530: /*---------------------------------------------------------------------*/
531: {
532:   Parameter   *param=user->param;
533:   GridInfo    *grid =user->grid;
534:   PetscScalar dx    = grid->dx, dz=grid->dz;
535:   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;
536:   PetscScalar TE    =0.0,TN=0.0,TS=0.0,TW=0.0, dPdz, residual,z_scale;
537:   PetscScalar dudzE,dudzW,dwdxW,dwdxE,dwdzN,dwdzS;
538:   PetscInt    ilim = grid->ni-1;

540:   /* geometric and other parameters */
541:   z_scale = param->z_scale;

543:   /* viscosity */
544:   if (param->ivisc==VISC_DIFN || param->ivisc>=VISC_DISL) { /* viscosity is T-dependent */
545:     TN = param->potentialT * x[j+1][i].T      * PetscExpScalar((j+0.5)*dz*z_scale);
546:     TS = param->potentialT * x[j][i].T        * PetscExpScalar((j-0.5)*dz*z_scale);
547:     TW = param->potentialT * TInterp(x,i-1,j) * PetscExpScalar(j*dz*z_scale);
548:     if (i==ilim) TE = TW;
549:     else         TE = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
550:     if (param->ivisc>=VISC_DISL) { /* olivine dislocation creep */
551:       epsN = CalcSecInv(x,i,j+1,CELL_CENTER,user);
552:       epsS = CalcSecInv(x,i,j,  CELL_CENTER,user);
553:       epsE = CalcSecInv(x,i,j,  CELL_CORNER,user);
554:       epsW = CalcSecInv(x,i-1,j,CELL_CORNER,user);
555:     }
556:   }
557:   etaN = Viscosity(TN,epsN,dz*(j+1.0),param);
558:   etaS = Viscosity(TS,epsS,dz*(j+0.0),param);
559:   etaW = Viscosity(TW,epsW,dz*(j+0.5),param);
560:   etaE = Viscosity(TE,epsE,dz*(j+0.5),param);

562:   dPdz  = (x[j+1][i].p - x[j][i].p)/dz;
563:   dwdzN = etaN * (x[j+1][i].w - x[j][i].w)/dz;
564:   dwdzS = etaS * (x[j][i].w - x[j-1][i].w)/dz;
565:   if (i==ilim) dwdxE = etaE * (x[j][i].u   - x[j+1][i].u)/dz;
566:   else         dwdxE = etaE * (x[j][i+1].w - x[j][i].w)  /dx;
567:   dwdxW = 2.0*etaW * (x[j][i].w - x[j][i-1].w)/dx;

569:   /* Z-MOMENTUM */
570:   residual = -dPdz                 /* constant viscosity terms */
571:              +(dwdzN - dwdzS)/dz
572:              +(dwdxE - dwdxW)/dx;

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

578:     residual += (dwdzN - dwdzS)/dz + (dudzE - dudzW)/dx;
579:   }

581:   return residual;
582: }

584: /*---------------------------------------------------------------------*/
585: /*  computes the residual of eqn (2) above */
586: PETSC_STATIC_INLINE PetscScalar ContinuityResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
587: /*---------------------------------------------------------------------*/
588: {
589:   GridInfo    *grid =user->grid;
590:   PetscScalar uE,uW,wN,wS,dudx,dwdz;

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

595:   return dudx + dwdz;
596: }

598: /*---------------------------------------------------------------------*/
599: /*  computes the residual of eqn (3) above */
600: PETSC_STATIC_INLINE PetscScalar EnergyResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
601: /*---------------------------------------------------------------------*/
602: {
603:   Parameter   *param=user->param;
604:   GridInfo    *grid =user->grid;
605:   PetscScalar dx    = grid->dx, dz=grid->dz;
606:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, jlid=grid->jlid;
607:   PetscScalar TE, TN, TS, TW, residual;
608:   PetscScalar uE,uW,wN,wS;
609:   PetscScalar fN,fS,fE,fW,dTdxW,dTdxE,dTdzN,dTdzS;

611:   dTdzN = (x[j+1][i].T - x[j][i].T)  /dz;
612:   dTdzS = (x[j][i].T   - x[j-1][i].T)/dz;
613:   dTdxE = (x[j][i+1].T - x[j][i].T)  /dx;
614:   dTdxW = (x[j][i].T   - x[j][i-1].T)/dx;

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

619:   if (j<=jlid && i>=j) {
620:     /* don't advect in the lid */
621:     return residual;
622:   } else if (i<j) {
623:     /* beneath the slab sfc */
624:     uW = uE = param->cb;
625:     wS = wN = param->sb;
626:   } else {
627:     /* advect in the slab and wedge */
628:     uW = x[j][i-1].u; uE = x[j][i].u;
629:     wS = x[j-1][i].w; wN = x[j][i].w;
630:   }

632:   if (param->adv_scheme==ADVECT_FV || i==ilim-1 || j==jlim-1 || i==1 || j==1) {
633:     /* finite volume advection */
634:     TS = (x[j][i].T + x[j-1][i].T)/2.0;
635:     TN = (x[j][i].T + x[j+1][i].T)/2.0;
636:     TE = (x[j][i].T + x[j][i+1].T)/2.0;
637:     TW = (x[j][i].T + x[j][i-1].T)/2.0;
638:     fN = wN*TN*dx; fS = wS*TS*dx;
639:     fE = uE*TE*dz; fW = uW*TW*dz;

641:   } else {
642:     /* Fromm advection scheme */
643:     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
644:               - 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;
645:     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
646:               - 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;
647:     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
648:               - 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;
649:     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
650:               - 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;
651:   }

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

655:   return residual;
656: }

658: /*---------------------------------------------------------------------*/
659: /*  computes the shear stress---used on the boundaries */
660: PETSC_STATIC_INLINE PetscScalar ShearStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
661: /*---------------------------------------------------------------------*/
662: {
663:   Parameter   *param=user->param;
664:   GridInfo    *grid =user->grid;
665:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1;
666:   PetscScalar uN, uS, wE, wW;

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

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

672:     wE = WInterp(x,i,j-1);
673:     if (i==j) {
674:       wW = param->sb;
675:       uN = param->cb;
676:     } else {
677:       wW = WInterp(x,i-1,j-1);
678:       uN = UInterp(x,i-1,j);
679:     }
680:     if (j==grid->jlid+1) uS = 0.0;
681:     else                 uS = UInterp(x,i-1,j-1);

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

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

688:   }

690:   return (uN-uS)/grid->dz + (wE-wW)/grid->dx;
691: }

693: /*---------------------------------------------------------------------*/
694: /*  computes the normal stress---used on the boundaries */
695: PETSC_STATIC_INLINE PetscScalar XNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
696: /*---------------------------------------------------------------------*/
697: {
698:   Parameter   *param=user->param;
699:   GridInfo    *grid =user->grid;
700:   PetscScalar dx    = grid->dx, dz=grid->dz;
701:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, ivisc;
702:   PetscScalar epsC  =0.0, etaC, TC, uE, uW, pC, z_scale;
703:   if (i<j || j<=grid->jlid) return EPS_ZERO;

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

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

709:     TC = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
710:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CENTER,user);
711:     etaC = Viscosity(TC,epsC,dz*j,param);

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

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

719:     TC = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
720:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
721:     etaC = Viscosity(TC,epsC,dz*(j+0.5),param);

723:     if (i==j) uW = param->sb;
724:     else      uW = UInterp(x,i-1,j);
725:     uE = UInterp(x,i,j); pC = PInterp(x,i,j);
726:   }

728:   return 2.0*etaC*(uE-uW)/dx - pC;
729: }

731: /*---------------------------------------------------------------------*/
732: /*  computes the normal stress---used on the boundaries */
733: PETSC_STATIC_INLINE PetscScalar ZNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
734: /*---------------------------------------------------------------------*/
735: {
736:   Parameter   *param=user->param;
737:   GridInfo    *grid =user->grid;
738:   PetscScalar dz    =grid->dz;
739:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, ivisc;
740:   PetscScalar epsC  =0.0, etaC, TC;
741:   PetscScalar pC, wN, wS, z_scale;
742:   if (i<j || j<=grid->jlid) return EPS_ZERO;

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

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

748:     TC = param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*z_scale);
749:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CENTER,user);
750:     etaC = Viscosity(TC,epsC,dz*j,param);
751:     wN   = x[j][i].w; wS = x[j-1][i].w; pC = x[j][i].p;

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

756:     TC = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
757:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
758:     etaC = Viscosity(TC,epsC,dz*(j+0.5),param);
759:     if (i==j) wN = param->sb;
760:     else      wN = WInterp(x,i,j);
761:     wS = WInterp(x,i,j-1); pC = PInterp(x,i,j);
762:   }

764:   return 2.0*etaC*(wN-wS)/dz - pC;
765: }

767: /*---------------------------------------------------------------------*/

769: /*=====================================================================
770:   INITIALIZATION, POST-PROCESSING AND OUTPUT FUNCTIONS
771:   =====================================================================*/

773: /*---------------------------------------------------------------------*/
774: /* initializes the problem parameters and checks for
775:    command line changes */
776: PetscErrorCode SetParams(Parameter *param, GridInfo *grid)
777: /*---------------------------------------------------------------------*/
778: {
779:   PetscErrorCode ierr, ierr_out=0;
780:   PetscReal      SEC_PER_YR                    = 3600.00*24.00*365.2500;
781:   PetscReal      alpha_g_on_cp_units_inverse_km=4.0e-5*9.8;

783:   /* domain geometry */
784:   param->slab_dip    = 45.0;
785:   param->width       = 320.0;                                              /* km */
786:   param->depth       = 300.0;                                              /* km */
787:   param->lid_depth   = 35.0;                                               /* km */
788:   param->fault_depth = 35.0;                                               /* km */

790:   PetscOptionsGetReal(NULL,NULL,"-slab_dip",&(param->slab_dip),NULL);
791:   PetscOptionsGetReal(NULL,NULL,"-width",&(param->width),NULL);
792:   PetscOptionsGetReal(NULL,NULL,"-depth",&(param->depth),NULL);
793:   PetscOptionsGetReal(NULL,NULL,"-lid_depth",&(param->lid_depth),NULL);
794:   PetscOptionsGetReal(NULL,NULL,"-fault_depth",&(param->fault_depth),NULL);

796:   param->slab_dip = param->slab_dip*PETSC_PI/180.0;                    /* radians */

798:   /* grid information */
799:   PetscOptionsGetInt(NULL,NULL, "-jfault",&(grid->jfault),NULL);
800:   grid->ni = 82;
801:   PetscOptionsGetInt(NULL,NULL, "-ni",&(grid->ni),NULL);

803:   grid->dx            = param->width/((PetscReal)(grid->ni-2));               /* km */
804:   grid->dz            = grid->dx*PetscTanReal(param->slab_dip);               /* km */
805:   grid->nj            = (PetscInt)(param->depth/grid->dz + 3.0);         /* gridpoints*/
806:   param->depth        = grid->dz*(grid->nj-2);                             /* km */
807:   grid->inose         = 0;                                          /* gridpoints*/
808:   PetscOptionsGetInt(NULL,NULL,"-inose",&(grid->inose),NULL);
809:   grid->bx            = DM_BOUNDARY_NONE;
810:   grid->by            = DM_BOUNDARY_NONE;
811:   grid->stencil       = DMDA_STENCIL_BOX;
812:   grid->dof           = 4;
813:   grid->stencil_width = 2;
814:   grid->mglevels      = 1;

816:   /* boundary conditions */
817:   param->pv_analytic = PETSC_FALSE;
818:   param->ibound      = BC_NOSTRESS;
819:   PetscOptionsGetInt(NULL,NULL,"-ibound",&(param->ibound),NULL);

821:   /* physical constants */
822:   param->slab_velocity = 5.0;               /* cm/yr */
823:   param->slab_age      = 50.0;              /* Ma */
824:   param->lid_age       = 50.0;              /* Ma */
825:   param->kappa         = 0.7272e-6;         /* m^2/sec */
826:   param->potentialT    = 1300.0;            /* degrees C */

828:   PetscOptionsGetReal(NULL,NULL,"-slab_velocity",&(param->slab_velocity),NULL);
829:   PetscOptionsGetReal(NULL,NULL,"-slab_age",&(param->slab_age),NULL);
830:   PetscOptionsGetReal(NULL,NULL,"-lid_age",&(param->lid_age),NULL);
831:   PetscOptionsGetReal(NULL,NULL,"-kappa",&(param->kappa),NULL);
832:   PetscOptionsGetReal(NULL,NULL,"-potentialT",&(param->potentialT),NULL);

834:   /* viscosity */
835:   param->ivisc        = 3;                  /* 0=isovisc, 1=difn creep, 2=disl creep, 3=full */
836:   param->eta0         = 1e24;               /* Pa-s */
837:   param->visc_cutoff  = 0.0;                /* factor of eta_0 */
838:   param->continuation = 1.0;

840:   /* constants for diffusion creep */
841:   param->diffusion.A     = 1.8e7;             /* Pa-s */
842:   param->diffusion.n     = 1.0;               /* dim'less */
843:   param->diffusion.Estar = 375e3;             /* J/mol */
844:   param->diffusion.Vstar = 5e-6;              /* m^3/mol */

846:   /* constants for param->dislocationocation creep */
847:   param->dislocation.A     = 2.8969e4;        /* Pa-s */
848:   param->dislocation.n     = 3.5;             /* dim'less */
849:   param->dislocation.Estar = 530e3;           /* J/mol */
850:   param->dislocation.Vstar = 14e-6;           /* m^3/mol */

852:   PetscOptionsGetInt(NULL,NULL, "-ivisc",&(param->ivisc),NULL);
853:   PetscOptionsGetReal(NULL,NULL,"-visc_cutoff",&(param->visc_cutoff),NULL);

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

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

860:   /* output options */
861:   param->quiet      = PETSC_FALSE;
862:   param->param_test = PETSC_FALSE;

864:   PetscOptionsHasName(NULL,NULL,"-quiet",&(param->quiet));
865:   PetscOptionsHasName(NULL,NULL,"-test",&(param->param_test));
866:   PetscOptionsGetString(NULL,NULL,"-file",param->filename,PETSC_MAX_PATH_LEN,&(param->output_to_file));

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

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

873:   /* misc. flags */
874:   param->stop_solve    = PETSC_FALSE;
875:   param->interrupted   = PETSC_FALSE;
876:   param->kspmon        = PETSC_FALSE;
877:   param->toggle_kspmon = PETSC_FALSE;

879:   /* derived parameters for slab angle */
880:   param->sb = PetscSinReal(param->slab_dip);
881:   param->cb = PetscCosReal(param->slab_dip);
882:   param->c  =  param->slab_dip*param->sb/(param->slab_dip*param->slab_dip-param->sb*param->sb);
883:   param->d  = (param->slab_dip*param->cb-param->sb)/(param->slab_dip*param->slab_dip-param->sb*param->sb);

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

889:   /* other unit conversions and derived parameters */
890:   param->scaled_width = param->width/param->L;                  /* dim'less */
891:   param->scaled_depth = param->depth/param->L;                  /* dim'less */
892:   param->lid_depth    = param->lid_depth/param->L;              /* dim'less */
893:   param->fault_depth  = param->fault_depth/param->L;            /* dim'less */
894:   grid->dx            = grid->dx/param->L;                      /* dim'less */
895:   grid->dz            = grid->dz/param->L;                      /* dim'less */
896:   grid->jlid          = (PetscInt)(param->lid_depth/grid->dz);       /* gridcells */
897:   grid->jfault        = (PetscInt)(param->fault_depth/grid->dz);     /* gridcells */
898:   param->lid_depth    = grid->jlid*grid->dz;                    /* dim'less */
899:   param->fault_depth  = grid->jfault*grid->dz;                  /* dim'less */
900:   grid->corner        = grid->jlid+1;                           /* gridcells */
901:   param->peclet       = param->V                                /* m/sec */
902:                         * param->L*1000.0                       /* m */
903:                         / param->kappa;                         /* m^2/sec */
904:   param->z_scale = param->L * alpha_g_on_cp_units_inverse_km;
905:   param->skt     = PetscSqrtReal(param->kappa*param->slab_age*SEC_PER_YR);
906:   PetscOptionsGetReal(NULL,NULL,"-peclet",&(param->peclet),NULL);

908:   return ierr_out;
909: }

911: /*---------------------------------------------------------------------*/
912: /*  prints a report of the problem parameters to stdout */
913: PetscErrorCode ReportParams(Parameter *param, GridInfo *grid)
914: /*---------------------------------------------------------------------*/
915: {
916:   PetscErrorCode ierr, ierr_out=0;
917:   char           date[30];

919:   PetscGetDate(date,30);

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

925:     PetscPrintf(PETSC_COMM_WORLD,"Domain: \n");
926:     PetscPrintf(PETSC_COMM_WORLD,"  Width = %g km,         Depth = %g km\n",(double)param->width,(double)param->depth);
927:     PetscPrintf(PETSC_COMM_WORLD,"  Slab dip = %g degrees,  Slab velocity = %g cm/yr\n",(double)(param->slab_dip*180.0/PETSC_PI),(double)param->slab_velocity);
928:     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);

930:     PetscPrintf(PETSC_COMM_WORLD,"\nGrid: \n");
931:     PetscPrintf(PETSC_COMM_WORLD,"  [ni,nj] = %D, %D       [dx,dz] = %g, %g km\n",grid->ni,grid->nj,(double)grid->dx*param->L,(double)(grid->dz*param->L));
932:     PetscPrintf(PETSC_COMM_WORLD,"  jlid = %3D              jfault = %3D \n",grid->jlid,grid->jfault);
933:     PetscPrintf(PETSC_COMM_WORLD,"  Pe = %g\n",(double)param->peclet);

935:     PetscPrintf(PETSC_COMM_WORLD,"\nRheology:");
936:     if (param->ivisc==VISC_CONST) {
937:       PetscPrintf(PETSC_COMM_WORLD,"                 Isoviscous \n");
938:       if (param->pv_analytic) {
939:         PetscPrintf(PETSC_COMM_WORLD,"                          Pressure and Velocity prescribed! \n");
940:       }
941:     } else if (param->ivisc==VISC_DIFN) {
942:       PetscPrintf(PETSC_COMM_WORLD,"                 Diffusion Creep (T-Dependent Newtonian) \n");
943:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
944:     } else if (param->ivisc==VISC_DISL) {
945:       PetscPrintf(PETSC_COMM_WORLD,"                 Dislocation Creep (T-Dependent Non-Newtonian) \n");
946:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
947:     } else if (param->ivisc==VISC_FULL) {
948:       PetscPrintf(PETSC_COMM_WORLD,"                 Full Rheology \n");
949:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
950:     } else {
951:       PetscPrintf(PETSC_COMM_WORLD,"                 Invalid! \n");
952:       ierr_out = 1;
953:     }

955:     PetscPrintf(PETSC_COMM_WORLD,"Boundary condition:");
956:     if (param->ibound==BC_ANALYTIC) {
957:       PetscPrintf(PETSC_COMM_WORLD,"       Isoviscous Analytic Dirichlet \n");
958:     } else if (param->ibound==BC_NOSTRESS) {
959:       PetscPrintf(PETSC_COMM_WORLD,"       Stress-Free (normal & shear stress)\n");
960:     } else if (param->ibound==BC_EXPERMNT) {
961:       PetscPrintf(PETSC_COMM_WORLD,"       Experimental boundary condition \n");
962:     } else {
963:       PetscPrintf(PETSC_COMM_WORLD,"       Invalid! \n");
964:       ierr_out = 1;
965:     }

967:     if (param->output_to_file)
968: #if defined(PETSC_HAVE_MATLAB_ENGINE)
969:       PetscPrintf(PETSC_COMM_WORLD,"Output Destination:       Mat file \"%s\"\n",param->filename);
970: #else
971:       PetscPrintf(PETSC_COMM_WORLD,"Output Destination:       PETSc binary file \"%s\"\n",param->filename);
972: #endif
973:     if (param->output_ivisc != param->ivisc) {
974:       PetscPrintf(PETSC_COMM_WORLD,"                          Output viscosity: -ivisc %D\n",param->output_ivisc);
975:     }

977:     PetscPrintf(PETSC_COMM_WORLD,"---------------------END ex30 PARAM REPORT---------------------\n");
978:   }
979:   if (param->param_test) PetscEnd();
980:   return ierr_out;
981: }

983: /* ------------------------------------------------------------------- */
984: /*  generates an inital guess using the analytic solution for isoviscous
985:     corner flow */
986: PetscErrorCode Initialize(DM da)
987: /* ------------------------------------------------------------------- */
988: {
989:   AppCtx         *user;
990:   Parameter      *param;
991:   GridInfo       *grid;
992:   PetscInt       i,j,is,js,im,jm;
994:   Field          **x;
995:   Vec            Xguess;

997:   /* Get the fine grid */
998:   DMGetApplicationContext(da,&user);
999:   Xguess = user->Xguess;
1000:   param  = user->param;
1001:   grid   = user->grid;
1002:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1003:   DMDAVecGetArray(da,Xguess,(void**)&x);

1005:   /* Compute initial guess */
1006:   for (j=js; j<js+jm; j++) {
1007:     for (i=is; i<is+im; i++) {
1008:       if (i<j)                x[j][i].u = param->cb;
1009:       else if (j<=grid->jlid) x[j][i].u = 0.0;
1010:       else                    x[j][i].u = HorizVelocity(i,j,user);

1012:       if (i<=j)               x[j][i].w = param->sb;
1013:       else if (j<=grid->jlid) x[j][i].w = 0.0;
1014:       else                    x[j][i].w = VertVelocity(i,j,user);

1016:       if (i<j || j<=grid->jlid) x[j][i].p = 0.0;
1017:       else                      x[j][i].p = Pressure(i,j,user);

1019:       x[j][i].T = PetscMin(grid->dz*(j-0.5),1.0);
1020:     }
1021:   }

1023:   /* Restore x to Xguess */
1024:   DMDAVecRestoreArray(da,Xguess,(void**)&x);

1026:   return 0;
1027: }

1029: /*---------------------------------------------------------------------*/
1030: /*  controls output to a file */
1031: PetscErrorCode DoOutput(SNES snes, PetscInt its)
1032: /*---------------------------------------------------------------------*/
1033: {
1034:   AppCtx         *user;
1035:   Parameter      *param;
1036:   GridInfo       *grid;
1037:   PetscInt       ivt;
1039:   PetscMPIInt    rank;
1040:   PetscViewer    viewer;
1041:   Vec            res, pars;
1042:   MPI_Comm       comm;
1043:   DM             da;

1045:   SNESGetDM(snes,&da);
1046:   DMGetApplicationContext(da,&user);
1047:   param = user->param;
1048:   grid  = user->grid;
1049:   ivt   = param->ivisc;

1051:   param->ivisc = param->output_ivisc;

1053:   /* compute final residual and final viscosity/strain rate fields */
1054:   SNESGetFunction(snes, &res, NULL, NULL);
1055:   ViscosityField(da, user->x, user->Xguess);

1057:   /* get the communicator and the rank of the processor */
1058:   PetscObjectGetComm((PetscObject)snes, &comm);
1059:   MPI_Comm_rank(comm, &rank);

1061:   if (param->output_to_file) { /* send output to binary file */
1062:     VecCreate(comm, &pars);
1063:     if (!rank) { /* on processor 0 */
1064:       VecSetSizes(pars, 20, PETSC_DETERMINE);
1065:       VecSetFromOptions(pars);
1066:       VecSetValue(pars,0, (PetscScalar)(grid->ni),INSERT_VALUES);
1067:       VecSetValue(pars,1, (PetscScalar)(grid->nj),INSERT_VALUES);
1068:       VecSetValue(pars,2, (PetscScalar)(grid->dx),INSERT_VALUES);
1069:       VecSetValue(pars,3, (PetscScalar)(grid->dz),INSERT_VALUES);
1070:       VecSetValue(pars,4, (PetscScalar)(param->L),INSERT_VALUES);
1071:       VecSetValue(pars,5, (PetscScalar)(param->V),INSERT_VALUES);
1072:       /* skipped 6 intentionally */
1073:       VecSetValue(pars,7, (PetscScalar)(param->slab_dip),INSERT_VALUES);
1074:       VecSetValue(pars,8, (PetscScalar)(grid->jlid),INSERT_VALUES);
1075:       VecSetValue(pars,9, (PetscScalar)(param->lid_depth),INSERT_VALUES);
1076:       VecSetValue(pars,10,(PetscScalar)(grid->jfault),INSERT_VALUES);
1077:       VecSetValue(pars,11,(PetscScalar)(param->fault_depth),INSERT_VALUES);
1078:       VecSetValue(pars,12,(PetscScalar)(param->potentialT),INSERT_VALUES);
1079:       VecSetValue(pars,13,(PetscScalar)(param->ivisc),INSERT_VALUES);
1080:       VecSetValue(pars,14,(PetscScalar)(param->visc_cutoff),INSERT_VALUES);
1081:       VecSetValue(pars,15,(PetscScalar)(param->ibound),INSERT_VALUES);
1082:       VecSetValue(pars,16,(PetscScalar)(its),INSERT_VALUES);
1083:     } else { /* on some other processor */
1084:       VecSetSizes(pars, 0, PETSC_DETERMINE);
1085:       VecSetFromOptions(pars);
1086:     }
1087:     VecAssemblyBegin(pars); VecAssemblyEnd(pars);

1089:     /* create viewer */
1090: #if defined(PETSC_HAVE_MATLAB_ENGINE)
1091:     PetscViewerMatlabOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1092: #else
1093:     PetscViewerBinaryOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1094: #endif

1096:     /* send vectors to viewer */
1097:     PetscObjectSetName((PetscObject)res,"res");
1098:     VecView(res,viewer);
1099:     PetscObjectSetName((PetscObject)user->x,"out");
1100:     VecView(user->x, viewer);
1101:     PetscObjectSetName((PetscObject)(user->Xguess),"aux");
1102:     VecView(user->Xguess, viewer);
1103:     StressField(da); /* compute stress fields */
1104:     PetscObjectSetName((PetscObject)(user->Xguess),"str");
1105:     VecView(user->Xguess, viewer);
1106:     PetscObjectSetName((PetscObject)pars,"par");
1107:     VecView(pars, viewer);

1109:     /* destroy viewer and vector */
1110:     PetscViewerDestroy(&viewer);
1111:     VecDestroy(&pars);
1112:   }

1114:   param->ivisc = ivt;
1115:   return 0;
1116: }

1118: /* ------------------------------------------------------------------- */
1119: /* Compute both the second invariant of the strain rate tensor and the viscosity, at both cell centers and cell corners */
1120: PetscErrorCode ViscosityField(DM da, Vec X, Vec V)
1121: /* ------------------------------------------------------------------- */
1122: {
1123:   AppCtx         *user;
1124:   Parameter      *param;
1125:   GridInfo       *grid;
1126:   Vec            localX;
1127:   Field          **v, **x;
1128:   PetscReal      eps, /* dx,*/ dz, T, epsC, TC;
1129:   PetscInt       i,j,is,js,im,jm,ilim,jlim,ivt;

1133:   DMGetApplicationContext(da,&user);
1134:   param        = user->param;
1135:   grid         = user->grid;
1136:   ivt          = param->ivisc;
1137:   param->ivisc = param->output_ivisc;

1139:   DMGetLocalVector(da, &localX);
1140:   DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
1141:   DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
1142:   DMDAVecGetArray(da,localX,(void**)&x);
1143:   DMDAVecGetArray(da,V,(void**)&v);

1145:   /* Parameters */
1146:   /* dx = grid->dx; */ dz = grid->dz;

1148:   ilim = grid->ni-1; jlim = grid->nj-1;

1150:   /* Compute real temperature, strain rate and viscosity */
1151:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1152:   for (j=js; j<js+jm; j++) {
1153:     for (i=is; i<is+im; i++) {
1154:       T = PetscRealPart(param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*param->z_scale));
1155:       if (i<ilim && j<jlim) {
1156:         TC = PetscRealPart(param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*param->z_scale));
1157:       } else {
1158:         TC = T;
1159:       }
1160:       eps  = PetscRealPart((CalcSecInv(x,i,j,CELL_CENTER,user)));
1161:       epsC = PetscRealPart(CalcSecInv(x,i,j,CELL_CORNER,user));

1163:       v[j][i].u = eps;
1164:       v[j][i].w = epsC;
1165:       v[j][i].p = Viscosity(T,eps,dz*(j-0.5),param);
1166:       v[j][i].T = Viscosity(TC,epsC,dz*j,param);
1167:     }
1168:   }
1169:   DMDAVecRestoreArray(da,V,(void**)&v);
1170:   DMDAVecRestoreArray(da,localX,(void**)&x);
1171:   DMRestoreLocalVector(da, &localX);

1173:   param->ivisc = ivt;
1174:   return(0);
1175: }

1177: /* ------------------------------------------------------------------- */
1178: /* post-processing: compute stress everywhere */
1179: PetscErrorCode StressField(DM da)
1180: /* ------------------------------------------------------------------- */
1181: {
1182:   AppCtx         *user;
1183:   PetscInt       i,j,is,js,im,jm;
1185:   Vec            locVec;
1186:   Field          **x, **y;

1188:   DMGetApplicationContext(da,&user);

1190:   /* Get the fine grid of Xguess and X */
1191:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1192:   DMDAVecGetArray(da,user->Xguess,(void**)&x);

1194:   DMGetLocalVector(da, &locVec);
1195:   DMGlobalToLocalBegin(da, user->x, INSERT_VALUES, locVec);
1196:   DMGlobalToLocalEnd(da, user->x, INSERT_VALUES, locVec);
1197:   DMDAVecGetArray(da,locVec,(void**)&y);

1199:   /* Compute stress on the corner points */
1200:   for (j=js; j<js+jm; j++) {
1201:     for (i=is; i<is+im; i++) {
1202:       x[j][i].u = ShearStress(y,i,j,CELL_CENTER,user);
1203:       x[j][i].w = ShearStress(y,i,j,CELL_CORNER,user);
1204:       x[j][i].p = XNormalStress(y,i,j,CELL_CENTER,user);
1205:       x[j][i].T = ZNormalStress(y,i,j,CELL_CENTER,user);
1206:     }
1207:   }

1209:   /* Restore the fine grid of Xguess and X */
1210:   DMDAVecRestoreArray(da,user->Xguess,(void**)&x);
1211:   DMDAVecRestoreArray(da,locVec,(void**)&y);
1212:   DMRestoreLocalVector(da, &locVec);
1213:   return 0;
1214: }

1216: /*=====================================================================
1217:   UTILITY FUNCTIONS
1218:   =====================================================================*/

1220: /*---------------------------------------------------------------------*/
1221: /* returns the velocity of the subducting slab and handles fault nodes
1222:    for BC */
1223: PETSC_STATIC_INLINE PetscScalar SlabVel(char c, PetscInt i, PetscInt j, AppCtx *user)
1224: /*---------------------------------------------------------------------*/
1225: {
1226:   Parameter *param = user->param;
1227:   GridInfo  *grid  = user->grid;

1229:   if (c=='U' || c=='u') {
1230:     if (i<j-1) return param->cb;
1231:     else if (j<=grid->jfault) return 0.0;
1232:     else return param->cb;

1234:   } else {
1235:     if (i<j) return param->sb;
1236:     else if (j<=grid->jfault) return 0.0;
1237:     else return param->sb;
1238:   }
1239: }

1241: /*---------------------------------------------------------------------*/
1242: /*  solution to diffusive half-space cooling model for BC */
1243: PETSC_STATIC_INLINE PetscScalar PlateModel(PetscInt j, PetscInt plate, AppCtx *user)
1244: /*---------------------------------------------------------------------*/
1245: {
1246:   Parameter     *param = user->param;
1247:   PetscScalar   z;
1248:   if (plate==PLATE_LID) z = (j-0.5)*user->grid->dz;
1249:   else z = (j-0.5)*user->grid->dz*param->cb;  /* PLATE_SLAB */
1250: #if defined(PETSC_HAVE_ERF)
1251:   return (PetscReal)(erf((double)PetscRealPart(z*param->L/2.0/param->skt)));
1252: #else
1253:   SETERRQ(PETSC_COMM_SELF,1,"erf() not available on this machine");
1254: #endif
1255: }


1258: /* ------------------------------------------------------------------- */
1259: /*  utility function */
1260: PetscBool  OptionsHasName(const char pre[],const char name[])
1261: /* ------------------------------------------------------------------- */
1262: {
1263:   PetscBool      retval;
1265:   PetscOptionsHasName(NULL,pre,name,&retval);CHKERRABORT(PETSC_COMM_WORLD,ierr);
1266:   return retval;
1267: }

1269: /*=====================================================================
1270:   INTERACTIVE SIGNAL HANDLING
1271:   =====================================================================*/

1273: /* ------------------------------------------------------------------- */
1274: PetscErrorCode SNESConverged_Interactive(SNES snes, PetscInt it,PetscReal xnorm, PetscReal snorm, PetscReal fnorm, SNESConvergedReason *reason, void *ctx)
1275: /* ------------------------------------------------------------------- */
1276: {
1277:   AppCtx         *user  = (AppCtx*) ctx;
1278:   Parameter      *param = user->param;
1279:   KSP            ksp;

1283:   if (param->interrupted) {
1284:     param->interrupted = PETSC_FALSE;
1285:     PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: exiting SNES solve. \n");
1286:     *reason = SNES_CONVERGED_FNORM_ABS;
1287:     return(0);
1288:   } else if (param->toggle_kspmon) {
1289:     param->toggle_kspmon = PETSC_FALSE;

1291:     SNESGetKSP(snes, &ksp);

1293:     if (param->kspmon) {
1294:       KSPMonitorCancel(ksp);

1296:       param->kspmon = PETSC_FALSE;
1297:       PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: deactivating ksp singular value monitor. \n");
1298:     } else {
1299:       PetscViewerAndFormat *vf;
1300:       PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
1301:       KSPMonitorSet(ksp,(PetscErrorCode (*)(KSP,PetscInt,PetscReal,void*))KSPMonitorSingularValue,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);

1303:       param->kspmon = PETSC_TRUE;
1304:       PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: activating ksp singular value monitor. \n");
1305:     }
1306:   }
1307:   PetscFunctionReturn(SNESConvergedDefault(snes,it,xnorm,snorm,fnorm,reason,ctx));
1308: }

1310: /* ------------------------------------------------------------------- */
1311: #include <signal.h>
1312: PetscErrorCode InteractiveHandler(int signum, void *ctx)
1313: /* ------------------------------------------------------------------- */
1314: {
1315:   AppCtx    *user  = (AppCtx*) ctx;
1316:   Parameter *param = user->param;

1318:   if (signum == SIGILL) {
1319:     param->toggle_kspmon = PETSC_TRUE;
1320: #if !defined(PETSC_MISSING_SIGCONT)
1321:   } else if (signum == SIGCONT) {
1322:     param->interrupted = PETSC_TRUE;
1323: #endif
1324: #if !defined(PETSC_MISSING_SIGURG)
1325:   } else if (signum == SIGURG) {
1326:     param->stop_solve = PETSC_TRUE;
1327: #endif
1328:   }
1329:   return 0;
1330: }

1332: /*---------------------------------------------------------------------*/
1333: /*  main call-back function that computes the processor-local piece
1334:     of the residual */
1335: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,Field **x,Field **f,void *ptr)
1336: /*---------------------------------------------------------------------*/
1337: {
1338:   AppCtx      *user  = (AppCtx*)ptr;
1339:   Parameter   *param = user->param;
1340:   GridInfo    *grid  = user->grid;
1341:   PetscScalar mag_w, mag_u;
1342:   PetscInt    i,j,mx,mz,ilim,jlim;
1343:   PetscInt    is,ie,js,je,ibound;    /* ,ivisc */

1346:   /* Define global and local grid parameters */
1347:   mx   = info->mx;     mz   = info->my;
1348:   ilim = mx-1;         jlim = mz-1;
1349:   is   = info->xs;     ie   = info->xs+info->xm;
1350:   js   = info->ys;     je   = info->ys+info->ym;

1352:   /* Define geometric and numeric parameters */
1353:   /* ivisc = param->ivisc; */ ibound = param->ibound;

1355:   for (j=js; j<je; j++) {
1356:     for (i=is; i<ie; i++) {

1358:       /************* X-MOMENTUM/VELOCITY *************/
1359:       if (i<j) f[j][i].u = x[j][i].u - SlabVel('U',i,j,user);
1360:       else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1361:         /* in the lithospheric lid */
1362:         f[j][i].u = x[j][i].u - 0.0;
1363:       } else if (i==ilim) {
1364:         /* on the right side boundary */
1365:         if (ibound==BC_ANALYTIC) {
1366:           f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1367:         } else {
1368:           f[j][i].u = XNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1369:         }

1371:       } else if (j==jlim) {
1372:         /* on the bottom boundary */
1373:         if (ibound==BC_ANALYTIC) {
1374:           f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1375:         } else if (ibound==BC_NOSTRESS) {
1376:           f[j][i].u = XMomentumResidual(x,i,j,user);
1377:         } else {
1378:           /* experimental boundary condition */
1379:         }

1381:       } else {
1382:         /* in the mantle wedge */
1383:         f[j][i].u = XMomentumResidual(x,i,j,user);
1384:       }

1386:       /************* Z-MOMENTUM/VELOCITY *************/
1387:       if (i<=j) {
1388:         f[j][i].w = x[j][i].w - SlabVel('W',i,j,user);

1390:       } else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1391:         /* in the lithospheric lid */
1392:         f[j][i].w = x[j][i].w - 0.0;

1394:       } else if (j==jlim) {
1395:         /* on the bottom boundary */
1396:         if (ibound==BC_ANALYTIC) {
1397:           f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1398:         } else {
1399:           f[j][i].w = ZNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1400:         }

1402:       } else if (i==ilim) {
1403:         /* on the right side boundary */
1404:         if (ibound==BC_ANALYTIC) {
1405:           f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1406:         } else if (ibound==BC_NOSTRESS) {
1407:           f[j][i].w = ZMomentumResidual(x,i,j,user);
1408:         } else {
1409:           /* experimental boundary condition */
1410:         }

1412:       } else {
1413:         /* in the mantle wedge */
1414:         f[j][i].w =  ZMomentumResidual(x,i,j,user);
1415:       }

1417:       /************* CONTINUITY/PRESSURE *************/
1418:       if (i<j || j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1419:         /* in the lid or slab */
1420:         f[j][i].p = x[j][i].p;

1422:       } else if ((i==ilim || j==jlim) && ibound==BC_ANALYTIC) {
1423:         /* on an analytic boundary */
1424:         f[j][i].p = x[j][i].p - Pressure(i,j,user);

1426:       } else {
1427:         /* in the mantle wedge */
1428:         f[j][i].p = ContinuityResidual(x,i,j,user);
1429:       }

1431:       /************* TEMPERATURE *************/
1432:       if (j==0) {
1433:         /* on the surface */
1434:         f[j][i].T = x[j][i].T + x[j+1][i].T + PetscMax(PetscRealPart(x[j][i].T),0.0);

1436:       } else if (i==0) {
1437:         /* slab inflow boundary */
1438:         f[j][i].T = x[j][i].T - PlateModel(j,PLATE_SLAB,user);

1440:       } else if (i==ilim) {
1441:         /* right side boundary */
1442:         mag_u = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j][i-1].u)/param->cb,1.0),0.0)), 5);
1443:         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);

1445:       } else if (j==jlim) {
1446:         /* bottom boundary */
1447:         mag_w = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j-1][i].w)/param->sb,1.0),0.0)), 5);
1448:         f[j][i].T = x[j][i].T - mag_w*x[j-1][i-1].T - (1.0-mag_w);

1450:       } else {
1451:         /* in the mantle wedge */
1452:         f[j][i].T = EnergyResidual(x,i,j,user);
1453:       }
1454:     }
1455:   }
1456:   return(0);
1457: }