Actual source code: ex30.c

petsc-master 2018-05-23
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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*);

124: /*-----------------------------------------------------------------------*/
125: int main(int argc,char **argv)
126: /*-----------------------------------------------------------------------*/
127: {
128:   SNES           snes;
129:   AppCtx         *user;               /* user-defined work context */
130:   Parameter      param;
131:   GridInfo       grid;
132:   PetscInt       nits;
134:   MPI_Comm       comm;
135:   DM             da;

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

145:   comm = PETSC_COMM_WORLD;

147:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148:      Set up the problem parameters.
149:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150:   SetParams(&param,&grid);
151:   ReportParams(&param,&grid);

153:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155:   SNESCreate(comm,&snes);
156:   DMDACreate2d(comm,grid.bx,grid.by,grid.stencil,grid.ni,grid.nj,PETSC_DECIDE,PETSC_DECIDE,grid.dof,grid.stencil_width,0,0,&da);
157:   DMSetFromOptions(da);
158:   DMSetUp(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:   PetscNew(&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 ierr;
208: }

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

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

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

235:   *nits=0;

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

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

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

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

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

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

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

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


290: /*=====================================================================
291:   PHYSICS FUNCTIONS (compute the discrete residual)
292:   =====================================================================*/


295: /*---------------------------------------------------------------------*/
296: PETSC_STATIC_INLINE PetscScalar UInterp(Field **x, PetscInt i, PetscInt j)
297: /*---------------------------------------------------------------------*/
298: {
299:   return 0.25*(x[j][i].u+x[j+1][i].u+x[j][i+1].u+x[j+1][i+1].u);
300: }

302: /*---------------------------------------------------------------------*/
303: PETSC_STATIC_INLINE PetscScalar WInterp(Field **x, PetscInt i, PetscInt j)
304: /*---------------------------------------------------------------------*/
305: {
306:   return 0.25*(x[j][i].w+x[j+1][i].w+x[j][i+1].w+x[j+1][i+1].w);
307: }

309: /*---------------------------------------------------------------------*/
310: PETSC_STATIC_INLINE PetscScalar PInterp(Field **x, PetscInt i, PetscInt j)
311: /*---------------------------------------------------------------------*/
312: {
313:   return 0.25*(x[j][i].p+x[j+1][i].p+x[j][i+1].p+x[j+1][i+1].p);
314: }

316: /*---------------------------------------------------------------------*/
317: PETSC_STATIC_INLINE PetscScalar TInterp(Field **x, PetscInt i, PetscInt j)
318: /*---------------------------------------------------------------------*/
319: {
320:   return 0.25*(x[j][i].T+x[j+1][i].T+x[j][i+1].T+x[j+1][i+1].T);
321: }

323: /*---------------------------------------------------------------------*/
324: /*  isoviscous analytic solution for IC */
325: PETSC_STATIC_INLINE PetscScalar HorizVelocity(PetscInt i, PetscInt j, AppCtx *user)
326: /*---------------------------------------------------------------------*/
327: {
328:   Parameter   *param = user->param;
329:   GridInfo    *grid  = user->grid;
330:   PetscScalar st, ct, th, c=param->c, d=param->d;
331:   PetscReal   x, z,r;

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

341: /*---------------------------------------------------------------------*/
342: /*  isoviscous analytic solution for IC */
343: PETSC_STATIC_INLINE PetscScalar VertVelocity(PetscInt i, PetscInt j, AppCtx *user)
344: /*---------------------------------------------------------------------*/
345: {
346:   Parameter   *param = user->param;
347:   GridInfo    *grid  = user->grid;
348:   PetscScalar st, ct, th, c=param->c, d=param->d;
349:   PetscReal   x, z, r;

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

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

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

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

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

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

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

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

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

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

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

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

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

428: /*---------------------------------------------------------------------*/
429: /*  computes the shear viscosity */
430: PETSC_STATIC_INLINE PetscScalar Viscosity(PetscScalar T, PetscScalar eps, PetscScalar z, Parameter *param)
431: /*---------------------------------------------------------------------*/
432: {
433:   PetscReal   result   =0.0;
434:   ViscParam   difn     =param->diffusion, disl=param->dislocation;
435:   PetscInt    iVisc    =param->ivisc;
436:   PetscScalar eps_scale=param->V/(param->L*1000.0);
437:   PetscScalar strain_power, v1, v2, P;
438:   PetscScalar rho_g = 32340.0, R=8.3144;

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

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

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

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

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

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

472: /*---------------------------------------------------------------------*/
473: /*  computes the residual of the x-component of eqn (1) above */
474: PETSC_STATIC_INLINE PetscScalar XMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
475: /*---------------------------------------------------------------------*/
476: {
477:   Parameter   *param=user->param;
478:   GridInfo    *grid =user->grid;
479:   PetscScalar dx    = grid->dx, dz=grid->dz;
480:   PetscScalar etaN,etaS,etaE,etaW,epsN=0.0,epsS=0.0,epsE=0.0,epsW=0.0;
481:   PetscScalar TE=0.0,TN=0.0,TS=0.0,TW=0.0, dPdx, residual, z_scale;
482:   PetscScalar dudxW,dudxE,dudzN,dudzS,dwdxN,dwdxS;
483:   PetscInt    jlim = grid->nj-1;

485:   z_scale = param->z_scale;

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

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

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

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

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

523:   return residual;
524: }

526: /*---------------------------------------------------------------------*/
527: /*  computes the residual of the z-component of eqn (1) above */
528: PETSC_STATIC_INLINE PetscScalar ZMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
529: /*---------------------------------------------------------------------*/
530: {
531:   Parameter   *param=user->param;
532:   GridInfo    *grid =user->grid;
533:   PetscScalar dx    = grid->dx, dz=grid->dz;
534:   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;
535:   PetscScalar TE    =0.0,TN=0.0,TS=0.0,TW=0.0, dPdz, residual,z_scale;
536:   PetscScalar dudzE,dudzW,dwdxW,dwdxE,dwdzN,dwdzS;
537:   PetscInt    ilim = grid->ni-1;

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

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

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

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

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

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

580:   return residual;
581: }

583: /*---------------------------------------------------------------------*/
584: /*  computes the residual of eqn (2) above */
585: PETSC_STATIC_INLINE PetscScalar ContinuityResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
586: /*---------------------------------------------------------------------*/
587: {
588:   GridInfo    *grid =user->grid;
589:   PetscScalar uE,uW,wN,wS,dudx,dwdz;

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

594:   return dudx + dwdz;
595: }

597: /*---------------------------------------------------------------------*/
598: /*  computes the residual of eqn (3) above */
599: PETSC_STATIC_INLINE PetscScalar EnergyResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
600: /*---------------------------------------------------------------------*/
601: {
602:   Parameter   *param=user->param;
603:   GridInfo    *grid =user->grid;
604:   PetscScalar dx    = grid->dx, dz=grid->dz;
605:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, jlid=grid->jlid;
606:   PetscScalar TE, TN, TS, TW, residual;
607:   PetscScalar uE,uW,wN,wS;
608:   PetscScalar fN,fS,fE,fW,dTdxW,dTdxE,dTdzN,dTdzS;

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

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

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

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

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

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

654:   return residual;
655: }

657: /*---------------------------------------------------------------------*/
658: /*  computes the shear stress---used on the boundaries */
659: PETSC_STATIC_INLINE PetscScalar ShearStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
660: /*---------------------------------------------------------------------*/
661: {
662:   Parameter   *param=user->param;
663:   GridInfo    *grid =user->grid;
664:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1;
665:   PetscScalar uN, uS, wE, wW;

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

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

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

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

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

687:   }

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

692: /*---------------------------------------------------------------------*/
693: /*  computes the normal stress---used on the boundaries */
694: PETSC_STATIC_INLINE PetscScalar XNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
695: /*---------------------------------------------------------------------*/
696: {
697:   Parameter   *param=user->param;
698:   GridInfo    *grid =user->grid;
699:   PetscScalar dx    = grid->dx, dz=grid->dz;
700:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, ivisc;
701:   PetscScalar epsC  =0.0, etaC, TC, uE, uW, pC, z_scale;
702:   if (i<j || j<=grid->jlid) return EPS_ZERO;

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

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

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

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

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

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

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

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

730: /*---------------------------------------------------------------------*/
731: /*  computes the normal stress---used on the boundaries */
732: PETSC_STATIC_INLINE PetscScalar ZNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
733: /*---------------------------------------------------------------------*/
734: {
735:   Parameter   *param=user->param;
736:   GridInfo    *grid =user->grid;
737:   PetscScalar dz    =grid->dz;
738:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, ivisc;
739:   PetscScalar epsC  =0.0, etaC, TC;
740:   PetscScalar pC, wN, wS, z_scale;
741:   if (i<j || j<=grid->jlid) return EPS_ZERO;

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

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

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

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

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

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

766: /*---------------------------------------------------------------------*/

768: /*=====================================================================
769:   INITIALIZATION, POST-PROCESSING AND OUTPUT FUNCTIONS
770:   =====================================================================*/

772: /*---------------------------------------------------------------------*/
773: /* initializes the problem parameters and checks for
774:    command line changes */
775: PetscErrorCode SetParams(Parameter *param, GridInfo *grid)
776: /*---------------------------------------------------------------------*/
777: {
778:   PetscErrorCode ierr, ierr_out=0;
779:   PetscReal      SEC_PER_YR                    = 3600.00*24.00*365.2500;
780:   PetscReal      alpha_g_on_cp_units_inverse_km=4.0e-5*9.8;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

907:   return ierr_out;
908: }

910: /*---------------------------------------------------------------------*/
911: /*  prints a report of the problem parameters to stdout */
912: PetscErrorCode ReportParams(Parameter *param, GridInfo *grid)
913: /*---------------------------------------------------------------------*/
914: {
915:   PetscErrorCode ierr, ierr_out=0;
916:   char           date[30];

918:   PetscGetDate(date,30);

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

924:     PetscPrintf(PETSC_COMM_WORLD,"Domain: \n");
925:     PetscPrintf(PETSC_COMM_WORLD,"  Width = %g km,         Depth = %g km\n",(double)param->width,(double)param->depth);
926:     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);
927:     PetscPrintf(PETSC_COMM_WORLD,"  Lid depth = %5.2f km,   Fault depth = %5.2f km\n",(double)(param->lid_depth*param->L),(double)(param->fault_depth*param->L));

929:     PetscPrintf(PETSC_COMM_WORLD,"\nGrid: \n");
930:     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));
931:     PetscPrintf(PETSC_COMM_WORLD,"  jlid = %3D              jfault = %3D \n",grid->jlid,grid->jfault);
932:     PetscPrintf(PETSC_COMM_WORLD,"  Pe = %g\n",(double)param->peclet);

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

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

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

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

982: /* ------------------------------------------------------------------- */
983: /*  generates an inital guess using the analytic solution for isoviscous
984:     corner flow */
985: PetscErrorCode Initialize(DM da)
986: /* ------------------------------------------------------------------- */
987: {
988:   AppCtx         *user;
989:   Parameter      *param;
990:   GridInfo       *grid;
991:   PetscInt       i,j,is,js,im,jm;
993:   Field          **x;
994:   Vec            Xguess;

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

1004:   /* Compute initial guess */
1005:   for (j=js; j<js+jm; j++) {
1006:     for (i=is; i<is+im; i++) {
1007:       if (i<j)                x[j][i].u = param->cb;
1008:       else if (j<=grid->jlid) x[j][i].u = 0.0;
1009:       else                    x[j][i].u = HorizVelocity(i,j,user);

1011:       if (i<=j)               x[j][i].w = param->sb;
1012:       else if (j<=grid->jlid) x[j][i].w = 0.0;
1013:       else                    x[j][i].w = VertVelocity(i,j,user);

1015:       if (i<j || j<=grid->jlid) x[j][i].p = 0.0;
1016:       else                      x[j][i].p = Pressure(i,j,user);

1018:       x[j][i].T = PetscMin(grid->dz*(j-0.5),1.0);
1019:     }
1020:   }

1022:   /* Restore x to Xguess */
1023:   DMDAVecRestoreArray(da,Xguess,(void**)&x);

1025:   return 0;
1026: }

1028: /*---------------------------------------------------------------------*/
1029: /*  controls output to a file */
1030: PetscErrorCode DoOutput(SNES snes, PetscInt its)
1031: /*---------------------------------------------------------------------*/
1032: {
1033:   AppCtx         *user;
1034:   Parameter      *param;
1035:   GridInfo       *grid;
1036:   PetscInt       ivt;
1038:   PetscMPIInt    rank;
1039:   PetscViewer    viewer;
1040:   Vec            res, pars;
1041:   MPI_Comm       comm;
1042:   DM             da;

1044:   SNESGetDM(snes,&da);
1045:   DMGetApplicationContext(da,&user);
1046:   param = user->param;
1047:   grid  = user->grid;
1048:   ivt   = param->ivisc;

1050:   param->ivisc = param->output_ivisc;

1052:   /* compute final residual and final viscosity/strain rate fields */
1053:   SNESGetFunction(snes, &res, NULL, NULL);
1054:   ViscosityField(da, user->x, user->Xguess);

1056:   /* get the communicator and the rank of the processor */
1057:   PetscObjectGetComm((PetscObject)snes, &comm);
1058:   MPI_Comm_rank(comm, &rank);

1060:   if (param->output_to_file) { /* send output to binary file */
1061:     VecCreate(comm, &pars);
1062:     if (!rank) { /* on processor 0 */
1063:       VecSetSizes(pars, 20, PETSC_DETERMINE);
1064:       VecSetFromOptions(pars);
1065:       VecSetValue(pars,0, (PetscScalar)(grid->ni),INSERT_VALUES);
1066:       VecSetValue(pars,1, (PetscScalar)(grid->nj),INSERT_VALUES);
1067:       VecSetValue(pars,2, (PetscScalar)(grid->dx),INSERT_VALUES);
1068:       VecSetValue(pars,3, (PetscScalar)(grid->dz),INSERT_VALUES);
1069:       VecSetValue(pars,4, (PetscScalar)(param->L),INSERT_VALUES);
1070:       VecSetValue(pars,5, (PetscScalar)(param->V),INSERT_VALUES);
1071:       /* skipped 6 intentionally */
1072:       VecSetValue(pars,7, (PetscScalar)(param->slab_dip),INSERT_VALUES);
1073:       VecSetValue(pars,8, (PetscScalar)(grid->jlid),INSERT_VALUES);
1074:       VecSetValue(pars,9, (PetscScalar)(param->lid_depth),INSERT_VALUES);
1075:       VecSetValue(pars,10,(PetscScalar)(grid->jfault),INSERT_VALUES);
1076:       VecSetValue(pars,11,(PetscScalar)(param->fault_depth),INSERT_VALUES);
1077:       VecSetValue(pars,12,(PetscScalar)(param->potentialT),INSERT_VALUES);
1078:       VecSetValue(pars,13,(PetscScalar)(param->ivisc),INSERT_VALUES);
1079:       VecSetValue(pars,14,(PetscScalar)(param->visc_cutoff),INSERT_VALUES);
1080:       VecSetValue(pars,15,(PetscScalar)(param->ibound),INSERT_VALUES);
1081:       VecSetValue(pars,16,(PetscScalar)(its),INSERT_VALUES);
1082:     } else { /* on some other processor */
1083:       VecSetSizes(pars, 0, PETSC_DETERMINE);
1084:       VecSetFromOptions(pars);
1085:     }
1086:     VecAssemblyBegin(pars); VecAssemblyEnd(pars);

1088:     /* create viewer */
1089: #if defined(PETSC_HAVE_MATLAB_ENGINE)
1090:     PetscViewerMatlabOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1091: #else
1092:     PetscViewerBinaryOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
1093: #endif

1095:     /* send vectors to viewer */
1096:     PetscObjectSetName((PetscObject)res,"res");
1097:     VecView(res,viewer);
1098:     PetscObjectSetName((PetscObject)user->x,"out");
1099:     VecView(user->x, viewer);
1100:     PetscObjectSetName((PetscObject)(user->Xguess),"aux");
1101:     VecView(user->Xguess, viewer);
1102:     StressField(da); /* compute stress fields */
1103:     PetscObjectSetName((PetscObject)(user->Xguess),"str");
1104:     VecView(user->Xguess, viewer);
1105:     PetscObjectSetName((PetscObject)pars,"par");
1106:     VecView(pars, viewer);

1108:     /* destroy viewer and vector */
1109:     PetscViewerDestroy(&viewer);
1110:     VecDestroy(&pars);
1111:   }

1113:   param->ivisc = ivt;
1114:   return 0;
1115: }

1117: /* ------------------------------------------------------------------- */
1118: /* Compute both the second invariant of the strain rate tensor and the viscosity, at both cell centers and cell corners */
1119: PetscErrorCode ViscosityField(DM da, Vec X, Vec V)
1120: /* ------------------------------------------------------------------- */
1121: {
1122:   AppCtx         *user;
1123:   Parameter      *param;
1124:   GridInfo       *grid;
1125:   Vec            localX;
1126:   Field          **v, **x;
1127:   PetscReal      eps, /* dx,*/ dz, T, epsC, TC;
1128:   PetscInt       i,j,is,js,im,jm,ilim,jlim,ivt;

1132:   DMGetApplicationContext(da,&user);
1133:   param        = user->param;
1134:   grid         = user->grid;
1135:   ivt          = param->ivisc;
1136:   param->ivisc = param->output_ivisc;

1138:   DMGetLocalVector(da, &localX);
1139:   DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
1140:   DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
1141:   DMDAVecGetArray(da,localX,(void**)&x);
1142:   DMDAVecGetArray(da,V,(void**)&v);

1144:   /* Parameters */
1145:   /* dx = grid->dx; */ dz = grid->dz;

1147:   ilim = grid->ni-1; jlim = grid->nj-1;

1149:   /* Compute real temperature, strain rate and viscosity */
1150:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1151:   for (j=js; j<js+jm; j++) {
1152:     for (i=is; i<is+im; i++) {
1153:       T = PetscRealPart(param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*param->z_scale));
1154:       if (i<ilim && j<jlim) {
1155:         TC = PetscRealPart(param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*param->z_scale));
1156:       } else {
1157:         TC = T;
1158:       }
1159:       eps  = PetscRealPart((CalcSecInv(x,i,j,CELL_CENTER,user)));
1160:       epsC = PetscRealPart(CalcSecInv(x,i,j,CELL_CORNER,user));

1162:       v[j][i].u = eps;
1163:       v[j][i].w = epsC;
1164:       v[j][i].p = Viscosity(T,eps,dz*(j-0.5),param);
1165:       v[j][i].T = Viscosity(TC,epsC,dz*j,param);
1166:     }
1167:   }
1168:   DMDAVecRestoreArray(da,V,(void**)&v);
1169:   DMDAVecRestoreArray(da,localX,(void**)&x);
1170:   DMRestoreLocalVector(da, &localX);

1172:   param->ivisc = ivt;
1173:   return(0);
1174: }

1176: /* ------------------------------------------------------------------- */
1177: /* post-processing: compute stress everywhere */
1178: PetscErrorCode StressField(DM da)
1179: /* ------------------------------------------------------------------- */
1180: {
1181:   AppCtx         *user;
1182:   PetscInt       i,j,is,js,im,jm;
1184:   Vec            locVec;
1185:   Field          **x, **y;

1187:   DMGetApplicationContext(da,&user);

1189:   /* Get the fine grid of Xguess and X */
1190:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
1191:   DMDAVecGetArray(da,user->Xguess,(void**)&x);

1193:   DMGetLocalVector(da, &locVec);
1194:   DMGlobalToLocalBegin(da, user->x, INSERT_VALUES, locVec);
1195:   DMGlobalToLocalEnd(da, user->x, INSERT_VALUES, locVec);
1196:   DMDAVecGetArray(da,locVec,(void**)&y);

1198:   /* Compute stress on the corner points */
1199:   for (j=js; j<js+jm; j++) {
1200:     for (i=is; i<is+im; i++) {
1201:       x[j][i].u = ShearStress(y,i,j,CELL_CENTER,user);
1202:       x[j][i].w = ShearStress(y,i,j,CELL_CORNER,user);
1203:       x[j][i].p = XNormalStress(y,i,j,CELL_CENTER,user);
1204:       x[j][i].T = ZNormalStress(y,i,j,CELL_CENTER,user);
1205:     }
1206:   }

1208:   /* Restore the fine grid of Xguess and X */
1209:   DMDAVecRestoreArray(da,user->Xguess,(void**)&x);
1210:   DMDAVecRestoreArray(da,locVec,(void**)&y);
1211:   DMRestoreLocalVector(da, &locVec);
1212:   return 0;
1213: }

1215: /*=====================================================================
1216:   UTILITY FUNCTIONS
1217:   =====================================================================*/

1219: /*---------------------------------------------------------------------*/
1220: /* returns the velocity of the subducting slab and handles fault nodes
1221:    for BC */
1222: PETSC_STATIC_INLINE PetscScalar SlabVel(char c, PetscInt i, PetscInt j, AppCtx *user)
1223: /*---------------------------------------------------------------------*/
1224: {
1225:   Parameter *param = user->param;
1226:   GridInfo  *grid  = user->grid;

1228:   if (c=='U' || c=='u') {
1229:     if (i<j-1) return param->cb;
1230:     else if (j<=grid->jfault) return 0.0;
1231:     else return param->cb;

1233:   } else {
1234:     if (i<j) return param->sb;
1235:     else if (j<=grid->jfault) return 0.0;
1236:     else return param->sb;
1237:   }
1238: }

1240: /*---------------------------------------------------------------------*/
1241: /*  solution to diffusive half-space cooling model for BC */
1242: PETSC_STATIC_INLINE PetscScalar PlateModel(PetscInt j, PetscInt plate, AppCtx *user)
1243: /*---------------------------------------------------------------------*/
1244: {
1245:   Parameter     *param = user->param;
1246:   PetscScalar   z;
1247:   if (plate==PLATE_LID) z = (j-0.5)*user->grid->dz;
1248:   else z = (j-0.5)*user->grid->dz*param->cb;  /* PLATE_SLAB */
1249: #if defined(PETSC_HAVE_ERF)
1250:   return (PetscReal)(erf((double)PetscRealPart(z*param->L/2.0/param->skt)));
1251: #else
1252:   (*PetscErrorPrintf)("erf() not available on this machine\n");
1253:   MPI_Abort(PETSC_COMM_SELF,1);
1254: #endif
1255: }

1257: /*=====================================================================
1258:   INTERACTIVE SIGNAL HANDLING
1259:   =====================================================================*/

1261: /* ------------------------------------------------------------------- */
1262: PetscErrorCode SNESConverged_Interactive(SNES snes, PetscInt it,PetscReal xnorm, PetscReal snorm, PetscReal fnorm, SNESConvergedReason *reason, void *ctx)
1263: /* ------------------------------------------------------------------- */
1264: {
1265:   AppCtx         *user  = (AppCtx*) ctx;
1266:   Parameter      *param = user->param;
1267:   KSP            ksp;

1271:   if (param->interrupted) {
1272:     param->interrupted = PETSC_FALSE;
1273:     PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: exiting SNES solve. \n");
1274:     *reason = SNES_CONVERGED_FNORM_ABS;
1275:     return(0);
1276:   } else if (param->toggle_kspmon) {
1277:     param->toggle_kspmon = PETSC_FALSE;

1279:     SNESGetKSP(snes, &ksp);

1281:     if (param->kspmon) {
1282:       KSPMonitorCancel(ksp);

1284:       param->kspmon = PETSC_FALSE;
1285:       PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: deactivating ksp singular value monitor. \n");
1286:     } else {
1287:       PetscViewerAndFormat *vf;
1288:       PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
1289:       KSPMonitorSet(ksp,(PetscErrorCode (*)(KSP,PetscInt,PetscReal,void*))KSPMonitorSingularValue,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);

1291:       param->kspmon = PETSC_TRUE;
1292:       PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: activating ksp singular value monitor. \n");
1293:     }
1294:   }
1295:   PetscFunctionReturn(SNESConvergedDefault(snes,it,xnorm,snorm,fnorm,reason,ctx));
1296: }

1298: /* ------------------------------------------------------------------- */
1299: #include <signal.h>
1300: PetscErrorCode InteractiveHandler(int signum, void *ctx)
1301: /* ------------------------------------------------------------------- */
1302: {
1303:   AppCtx    *user  = (AppCtx*) ctx;
1304:   Parameter *param = user->param;

1306:   if (signum == SIGILL) {
1307:     param->toggle_kspmon = PETSC_TRUE;
1308: #if !defined(PETSC_MISSING_SIGCONT)
1309:   } else if (signum == SIGCONT) {
1310:     param->interrupted = PETSC_TRUE;
1311: #endif
1312: #if !defined(PETSC_MISSING_SIGURG)
1313:   } else if (signum == SIGURG) {
1314:     param->stop_solve = PETSC_TRUE;
1315: #endif
1316:   }
1317:   return 0;
1318: }

1320: /*---------------------------------------------------------------------*/
1321: /*  main call-back function that computes the processor-local piece
1322:     of the residual */
1323: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,Field **x,Field **f,void *ptr)
1324: /*---------------------------------------------------------------------*/
1325: {
1326:   AppCtx      *user  = (AppCtx*)ptr;
1327:   Parameter   *param = user->param;
1328:   GridInfo    *grid  = user->grid;
1329:   PetscScalar mag_w, mag_u;
1330:   PetscInt    i,j,mx,mz,ilim,jlim;
1331:   PetscInt    is,ie,js,je,ibound;    /* ,ivisc */

1334:   /* Define global and local grid parameters */
1335:   mx   = info->mx;     mz   = info->my;
1336:   ilim = mx-1;         jlim = mz-1;
1337:   is   = info->xs;     ie   = info->xs+info->xm;
1338:   js   = info->ys;     je   = info->ys+info->ym;

1340:   /* Define geometric and numeric parameters */
1341:   /* ivisc = param->ivisc; */ ibound = param->ibound;

1343:   for (j=js; j<je; j++) {
1344:     for (i=is; i<ie; i++) {

1346:       /************* X-MOMENTUM/VELOCITY *************/
1347:       if (i<j) f[j][i].u = x[j][i].u - SlabVel('U',i,j,user);
1348:       else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1349:         /* in the lithospheric lid */
1350:         f[j][i].u = x[j][i].u - 0.0;
1351:       } else if (i==ilim) {
1352:         /* on the right side boundary */
1353:         if (ibound==BC_ANALYTIC) {
1354:           f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1355:         } else {
1356:           f[j][i].u = XNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1357:         }

1359:       } else if (j==jlim) {
1360:         /* on the bottom boundary */
1361:         if (ibound==BC_ANALYTIC) {
1362:           f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
1363:         } else if (ibound==BC_NOSTRESS) {
1364:           f[j][i].u = XMomentumResidual(x,i,j,user);
1365:         } else {
1366:           /* experimental boundary condition */
1367:         }

1369:       } else {
1370:         /* in the mantle wedge */
1371:         f[j][i].u = XMomentumResidual(x,i,j,user);
1372:       }

1374:       /************* Z-MOMENTUM/VELOCITY *************/
1375:       if (i<=j) {
1376:         f[j][i].w = x[j][i].w - SlabVel('W',i,j,user);

1378:       } else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1379:         /* in the lithospheric lid */
1380:         f[j][i].w = x[j][i].w - 0.0;

1382:       } else if (j==jlim) {
1383:         /* on the bottom boundary */
1384:         if (ibound==BC_ANALYTIC) {
1385:           f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1386:         } else {
1387:           f[j][i].w = ZNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
1388:         }

1390:       } else if (i==ilim) {
1391:         /* on the right side boundary */
1392:         if (ibound==BC_ANALYTIC) {
1393:           f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
1394:         } else if (ibound==BC_NOSTRESS) {
1395:           f[j][i].w = ZMomentumResidual(x,i,j,user);
1396:         } else {
1397:           /* experimental boundary condition */
1398:         }

1400:       } else {
1401:         /* in the mantle wedge */
1402:         f[j][i].w =  ZMomentumResidual(x,i,j,user);
1403:       }

1405:       /************* CONTINUITY/PRESSURE *************/
1406:       if (i<j || j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
1407:         /* in the lid or slab */
1408:         f[j][i].p = x[j][i].p;

1410:       } else if ((i==ilim || j==jlim) && ibound==BC_ANALYTIC) {
1411:         /* on an analytic boundary */
1412:         f[j][i].p = x[j][i].p - Pressure(i,j,user);

1414:       } else {
1415:         /* in the mantle wedge */
1416:         f[j][i].p = ContinuityResidual(x,i,j,user);
1417:       }

1419:       /************* TEMPERATURE *************/
1420:       if (j==0) {
1421:         /* on the surface */
1422:         f[j][i].T = x[j][i].T + x[j+1][i].T + PetscMax(PetscRealPart(x[j][i].T),0.0);

1424:       } else if (i==0) {
1425:         /* slab inflow boundary */
1426:         f[j][i].T = x[j][i].T - PlateModel(j,PLATE_SLAB,user);

1428:       } else if (i==ilim) {
1429:         /* right side boundary */
1430:         mag_u = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j][i-1].u)/param->cb,1.0),0.0)), 5);
1431:         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);

1433:       } else if (j==jlim) {
1434:         /* bottom boundary */
1435:         mag_w = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j-1][i].w)/param->sb,1.0),0.0)), 5);
1436:         f[j][i].T = x[j][i].T - mag_w*x[j-1][i-1].T - (1.0-mag_w);

1438:       } else {
1439:         /* in the mantle wedge */
1440:         f[j][i].T = EnergyResidual(x,i,j,user);
1441:       }
1442:     }
1443:   }
1444:   return(0);
1445: }


1448: /*TEST

1450:    build:
1451:       requires: !complex erf

1453:    test:
1454:       args: -ni 18
1455:       filter: grep -v Destination
1456:       requires: !single

1458: TEST*/