Date: 2022-03-04T17:39:26+00:00

Actual source code: ex30.c

      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:
-------$w_{ij}$------
$u_{i-1j}$ $P,T_{ij}$ $u_{ij}$
------$w_{ij-1}$-----

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

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

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

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

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

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

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

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

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

    117: /* Post-processing & misc */
    118: extern PetscErrorCode ViscosityField(DM,Vec,Vec);
    119: extern PetscErrorCode StressField(DM);
    120: extern PetscErrorCode SNESConverged_Interactive(SNES, PetscInt, PetscReal, PetscReal, PetscReal, SNESConvergedReason*, void*);
    121: extern PetscErrorCode InteractiveHandler(int, void*);

    123: /*-----------------------------------------------------------------------*/
    124: int main(int argc,char **argv)
    125: /*-----------------------------------------------------------------------*/
    126: {
    127:   SNES           snes;
    128:   AppCtx         *user;               /* user-defined work context */
    129:   Parameter      param;
    130:   GridInfo       grid;
    131:   PetscInt       nits;
    133:   MPI_Comm       comm;
    134:   DM             da;

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

    144:   comm = PETSC_COMM_WORLD;

    146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    147:      Set up the problem parameters.
    148:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    149:   SetParams(&param,&grid);
    150:   ReportParams(&param,&grid);

    152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    153:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    154:   SNESCreate(comm,&snes);
    155:   DMDACreate2d(comm,grid.bx,grid.by,grid.stencil,grid.ni,grid.nj,PETSC_DECIDE,PETSC_DECIDE,grid.dof,grid.stencil_width,0,0,&da);
    156:   DMSetFromOptions(da);
    157:   DMSetUp(da);
    158:   SNESSetDM(snes,da);
    159:   DMDASetFieldName(da,0,"x-velocity");
    160:   DMDASetFieldName(da,1,"y-velocity");
    161:   DMDASetFieldName(da,2,"pressure");
    162:   DMDASetFieldName(da,3,"temperature");

    164:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    165:      Create user context, set problem data, create vector data structures.
    166:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    167:   PetscNew(&user);
    168:   user->param = &param;
    169:   user->grid  = &grid;
    170:   DMSetApplicationContext(da,user);
    171:   DMCreateGlobalVector(da,&(user->Xguess));

    173:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    174:      Set up the SNES solver with callback functions.
    175:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    176:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,(void*)user);
    177:   SNESSetFromOptions(snes);

    179:   SNESSetConvergenceTest(snes,SNESConverged_Interactive,(void*)user,NULL);
    180:   PetscPushSignalHandler(InteractiveHandler,(void*)user);

    182:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    183:      Initialize and solve the nonlinear system
    184:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    185:   Initialize(da);
    186:   UpdateSolution(snes,user,&nits);

    188:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    189:      Output variables.
    190:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    191:   DoOutput(snes,nits);

    193:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    194:      Free work space.
    195:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    196:   VecDestroy(&user->Xguess);
    197:   VecDestroy(&user->x);
    198:   PetscFree(user);
    199:   SNESDestroy(&snes);
    200:   DMDestroy(&da);
    201:   PetscPopSignalHandler();
    202:   PetscFinalize();
    203:   return ierr;
    204: }

    206: /*=====================================================================
    207:   PETSc INTERACTION FUNCTIONS (initialize & call SNESSolve)
    208:   =====================================================================*/

    210: /*---------------------------------------------------------------------*/
    211: /*  manages solve: adaptive continuation method  */
    212: PetscErrorCode UpdateSolution(SNES snes, AppCtx *user, PetscInt *nits)
    213: {
    214:   KSP                 ksp;
    215:   PC                  pc;
    216:   SNESConvergedReason reason = SNES_CONVERGED_ITERATING;
    217:   Parameter           *param   = user->param;
    218:   PetscReal           cont_incr=0.3;
    219:   PetscInt            its;
    220:   PetscErrorCode      ierr;
    221:   PetscBool           q = PETSC_FALSE;
    222:   DM                  dm;

    225:   SNESGetDM(snes,&dm);
    226:   DMCreateGlobalVector(dm,&user->x);
    227:   SNESGetKSP(snes,&ksp);
    228:   KSPGetPC(ksp, &pc);
    229:   KSPSetComputeSingularValues(ksp, PETSC_TRUE);

    231:   *nits=0;

    233:   /* Isoviscous solve */
    234:   if (param->ivisc == VISC_CONST && !param->stop_solve) {
    235:     param->ivisc = VISC_CONST;

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

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

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

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

    262:       if (reason<0) {
    263:         /* NOT converged */
    264:         cont_incr = -PetscAbsReal(cont_incr)/2.0;
    265:         if (PetscAbsReal(cont_incr)<0.01) goto done;

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

    275:         if (param->continuation+cont_incr > 1.0) cont_incr = 1.0 - param->continuation;
    276:       } /* endif reason<0 */
    277:     }
    278:   }
    279: done:
    280:   if (param->stop_solve && !q) {PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: stopping solve.\n");}
    281:   if (reason<0 && !q) {PetscPrintf(PETSC_COMM_WORLD,"FAILED TO CONVERGE: stopping solve.\n");}
    282:   return(0);
    283: }

    285: /*=====================================================================
    286:   PHYSICS FUNCTIONS (compute the discrete residual)
    287:   =====================================================================*/

    289: /*---------------------------------------------------------------------*/
    290: PETSC_STATIC_INLINE PetscScalar UInterp(Field **x, PetscInt i, PetscInt j)
    291: /*---------------------------------------------------------------------*/
    292: {
    293:   return 0.25*(x[j][i].u+x[j+1][i].u+x[j][i+1].u+x[j+1][i+1].u);
    294: }

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

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

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

    317: /*---------------------------------------------------------------------*/
    318: /*  isoviscous analytic solution for IC */
    319: PETSC_STATIC_INLINE PetscScalar HorizVelocity(PetscInt i, PetscInt j, AppCtx *user)
    320: /*---------------------------------------------------------------------*/
    321: {
    322:   Parameter   *param = user->param;
    323:   GridInfo    *grid  = user->grid;
    324:   PetscScalar st, ct, th, c=param->c, d=param->d;
    325:   PetscReal   x, z,r;

    327:   x  = (i - grid->jlid)*grid->dx;  z = (j - grid->jlid - 0.5)*grid->dz;
    328:   r  = PetscSqrtReal(x*x+z*z);
    329:   st = z/r;
    330:   ct = x/r;
    331:   th = PetscAtanReal(z/x);
    332:   return ct*(c*th*st+d*(st+th*ct)) + st*(c*(st-th*ct)+d*th*st);
    333: }

    335: /*---------------------------------------------------------------------*/
    336: /*  isoviscous analytic solution for IC */
    337: PETSC_STATIC_INLINE PetscScalar VertVelocity(PetscInt i, PetscInt j, AppCtx *user)
    338: /*---------------------------------------------------------------------*/
    339: {
    340:   Parameter   *param = user->param;
    341:   GridInfo    *grid  = user->grid;
    342:   PetscScalar st, ct, th, c=param->c, d=param->d;
    343:   PetscReal   x, z, r;

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

    350: /*---------------------------------------------------------------------*/
    351: /*  isoviscous analytic solution for IC */
    352: PETSC_STATIC_INLINE PetscScalar Pressure(PetscInt i, PetscInt j, AppCtx *user)
    353: /*---------------------------------------------------------------------*/
    354: {
    355:   Parameter   *param = user->param;
    356:   GridInfo    *grid  = user->grid;
    357:   PetscScalar x, z, r, st, ct, c=param->c, d=param->d;

    359:   x = (i - grid->jlid - 0.5)*grid->dx;  z = (j - grid->jlid - 0.5)*grid->dz;
    360:   r = PetscSqrtReal(x*x+z*z);  st = z/r;  ct = x/r;
    361:   return (-2.0*(c*ct-d*st)/r);
    362: }

    364: /*  computes the second invariant of the strain rate tensor */
    365: PETSC_STATIC_INLINE PetscScalar CalcSecInv(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
    366: /*---------------------------------------------------------------------*/
    367: {
    368:   Parameter   *param = user->param;
    369:   GridInfo    *grid  = user->grid;
    370:   PetscInt    ilim   =grid->ni-1, jlim=grid->nj-1;
    371:   PetscScalar uN,uS,uE,uW,wN,wS,wE,wW;
    372:   PetscScalar eps11, eps12, eps22;

    374:   if (i<j) return EPS_ZERO;
    375:   if (i==ilim) i--;
    376:   if (j==jlim) j--;

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

    381:     uE = x[j][i].u; uW = x[j][i-1].u;
    382:     wN = x[j][i].w; wS = x[j-1][i].w;
    383:     wE = WInterp(x,i,j-1);
    384:     if (i==j) {
    385:       uN = param->cb; wW = param->sb;
    386:     } else {
    387:       uN = UInterp(x,i-1,j); wW = WInterp(x,i-1,j-1);
    388:     }

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

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

    396:     uN = x[j+1][i].u;  uS = x[j][i].u;
    397:     wE = x[j][i+1].w;  wW = x[j][i].w;
    398:     if (i==j) {
    399:       wN = param->sb;
    400:       uW = param->cb;
    401:     } else {
    402:       wN = WInterp(x,i,j);
    403:       uW = UInterp(x,i-1,j);
    404:     }

    406:     if (j==grid->jlid) {
    407:       uE = 0.0;  uW = 0.0;
    408:       uS = -uN;
    409:       wS = -wN;
    410:     } else {
    411:       uE = UInterp(x,i,j);
    412:       wS = WInterp(x,i,j-1);
    413:     }
    414:   }

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

    419:   return PetscSqrtReal(0.5*(eps11*eps11 + 2.0*eps12*eps12 + eps22*eps22));
    420: }

    422: /*---------------------------------------------------------------------*/
    423: /*  computes the shear viscosity */
    424: PETSC_STATIC_INLINE PetscScalar Viscosity(PetscScalar T, PetscScalar eps, PetscScalar z, Parameter *param)
    425: /*---------------------------------------------------------------------*/
    426: {
    427:   PetscReal   result   =0.0;
    428:   ViscParam   difn     =param->diffusion, disl=param->dislocation;
    429:   PetscInt    iVisc    =param->ivisc;
    430:   PetscScalar eps_scale=param->V/(param->L*1000.0);
    431:   PetscScalar strain_power, v1, v2, P;
    432:   PetscScalar rho_g = 32340.0, R=8.3144;

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

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

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

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

    454:     result = PetscRealPart(1.0/(1.0/v1 + 1.0/v2));
    455:   }

    457:   /* max viscosity is param->eta0 */
    458:   result = PetscMin(result, 1.0);
    459:   /* min viscosity is param->visc_cutoff */
    460:   result = PetscMax(result, param->visc_cutoff);
    461:   /* continuation method */
    462:   result = PetscPowReal(result,param->continuation);
    463:   return result;
    464: }

    466: /*---------------------------------------------------------------------*/
    467: /*  computes the residual of the x-component of eqn (1) above */
    468: PETSC_STATIC_INLINE PetscScalar XMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
    469: /*---------------------------------------------------------------------*/
    470: {
    471:   Parameter   *param=user->param;
    472:   GridInfo    *grid =user->grid;
    473:   PetscScalar dx    = grid->dx, dz=grid->dz;
    474:   PetscScalar etaN,etaS,etaE,etaW,epsN=0.0,epsS=0.0,epsE=0.0,epsW=0.0;
    475:   PetscScalar TE=0.0,TN=0.0,TS=0.0,TW=0.0, dPdx, residual, z_scale;
    476:   PetscScalar dudxW,dudxE,dudzN,dudzS,dwdxN,dwdxS;
    477:   PetscInt    jlim = grid->nj-1;

    479:   z_scale = param->z_scale;

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

    499:   dPdx = (x[j][i+1].p - x[j][i].p)/dx;
    500:   if (j==jlim) dudzN = etaN * (x[j][i].w   - x[j][i+1].w)/dx;
    501:   else         dudzN = etaN * (x[j+1][i].u - x[j][i].u)  /dz;
    502:   dudzS = etaS * (x[j][i].u    - x[j-1][i].u)/dz;
    503:   dudxE = etaE * (x[j][i+1].u  - x[j][i].u)  /dx;
    504:   dudxW = etaW * (x[j][i].u    - x[j][i-1].u)/dx;

    506:   residual = -dPdx                          /* X-MOMENTUM EQUATION*/
    507:              +(dudxE - dudxW)/dx
    508:              +(dudzN - dudzS)/dz;

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

    514:     residual += (dudxE - dudxW)/dx + (dwdxN - dwdxS)/dz;
    515:   }

    517:   return residual;
    518: }

    520: /*---------------------------------------------------------------------*/
    521: /*  computes the residual of the z-component of eqn (1) above */
    522: PETSC_STATIC_INLINE PetscScalar ZMomentumResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
    523: /*---------------------------------------------------------------------*/
    524: {
    525:   Parameter   *param=user->param;
    526:   GridInfo    *grid =user->grid;
    527:   PetscScalar dx    = grid->dx, dz=grid->dz;
    528:   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;
    529:   PetscScalar TE    =0.0,TN=0.0,TS=0.0,TW=0.0, dPdz, residual,z_scale;
    530:   PetscScalar dudzE,dudzW,dwdxW,dwdxE,dwdzN,dwdzS;
    531:   PetscInt    ilim = grid->ni-1;

    533:   /* geometric and other parameters */
    534:   z_scale = param->z_scale;

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

    555:   dPdz  = (x[j+1][i].p - x[j][i].p)/dz;
    556:   dwdzN = etaN * (x[j+1][i].w - x[j][i].w)/dz;
    557:   dwdzS = etaS * (x[j][i].w - x[j-1][i].w)/dz;
    558:   if (i==ilim) dwdxE = etaE * (x[j][i].u   - x[j+1][i].u)/dz;
    559:   else         dwdxE = etaE * (x[j][i+1].w - x[j][i].w)  /dx;
    560:   dwdxW = 2.0*etaW * (x[j][i].w - x[j][i-1].w)/dx;

    562:   /* Z-MOMENTUM */
    563:   residual = -dPdz                 /* constant viscosity terms */
    564:              +(dwdzN - dwdzS)/dz
    565:              +(dwdxE - dwdxW)/dx;

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

    571:     residual += (dwdzN - dwdzS)/dz + (dudzE - dudzW)/dx;
    572:   }

    574:   return residual;
    575: }

    577: /*---------------------------------------------------------------------*/
    578: /*  computes the residual of eqn (2) above */
    579: PETSC_STATIC_INLINE PetscScalar ContinuityResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
    580: /*---------------------------------------------------------------------*/
    581: {
    582:   GridInfo    *grid =user->grid;
    583:   PetscScalar uE,uW,wN,wS,dudx,dwdz;

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

    588:   return dudx + dwdz;
    589: }

    591: /*---------------------------------------------------------------------*/
    592: /*  computes the residual of eqn (3) above */
    593: PETSC_STATIC_INLINE PetscScalar EnergyResidual(Field **x, PetscInt i, PetscInt j, AppCtx *user)
    594: /*---------------------------------------------------------------------*/
    595: {
    596:   Parameter   *param=user->param;
    597:   GridInfo    *grid =user->grid;
    598:   PetscScalar dx    = grid->dx, dz=grid->dz;
    599:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, jlid=grid->jlid;
    600:   PetscScalar TE, TN, TS, TW, residual;
    601:   PetscScalar uE,uW,wN,wS;
    602:   PetscScalar fN,fS,fE,fW,dTdxW,dTdxE,dTdzN,dTdzS;

    604:   dTdzN = (x[j+1][i].T - x[j][i].T)  /dz;
    605:   dTdzS = (x[j][i].T   - x[j-1][i].T)/dz;
    606:   dTdxE = (x[j][i+1].T - x[j][i].T)  /dx;
    607:   dTdxW = (x[j][i].T   - x[j][i-1].T)/dx;

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

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

    625:   if (param->adv_scheme==ADVECT_FV || i==ilim-1 || j==jlim-1 || i==1 || j==1) {
    626:     /* finite volume advection */
    627:     TS = (x[j][i].T + x[j-1][i].T)/2.0;
    628:     TN = (x[j][i].T + x[j+1][i].T)/2.0;
    629:     TE = (x[j][i].T + x[j][i+1].T)/2.0;
    630:     TW = (x[j][i].T + x[j][i-1].T)/2.0;
    631:     fN = wN*TN*dx; fS = wS*TS*dx;
    632:     fE = uE*TE*dz; fW = uW*TW*dz;

    634:   } else {
    635:     /* Fromm advection scheme */
    636:     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
    637:               - 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;
    638:     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
    639:               - 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;
    640:     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
    641:               - 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;
    642:     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
    643:               - 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;
    644:   }

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

    648:   return residual;
    649: }

    651: /*---------------------------------------------------------------------*/
    652: /*  computes the shear stress---used on the boundaries */
    653: PETSC_STATIC_INLINE PetscScalar ShearStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
    654: /*---------------------------------------------------------------------*/
    655: {
    656:   Parameter   *param=user->param;
    657:   GridInfo    *grid =user->grid;
    658:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1;
    659:   PetscScalar uN, uS, wE, wW;

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

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

    665:     wE = WInterp(x,i,j-1);
    666:     if (i==j) {
    667:       wW = param->sb;
    668:       uN = param->cb;
    669:     } else {
    670:       wW = WInterp(x,i-1,j-1);
    671:       uN = UInterp(x,i-1,j);
    672:     }
    673:     if (j==grid->jlid+1) uS = 0.0;
    674:     else                 uS = UInterp(x,i-1,j-1);

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

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

    681:   }

    683:   return (uN-uS)/grid->dz + (wE-wW)/grid->dx;
    684: }

    686: /*---------------------------------------------------------------------*/
    687: /*  computes the normal stress---used on the boundaries */
    688: PETSC_STATIC_INLINE PetscScalar XNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
    689: /*---------------------------------------------------------------------*/
    690: {
    691:   Parameter   *param=user->param;
    692:   GridInfo    *grid =user->grid;
    693:   PetscScalar dx    = grid->dx, dz=grid->dz;
    694:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, ivisc;
    695:   PetscScalar epsC  =0.0, etaC, TC, uE, uW, pC, z_scale;
    696:   if (i<j || j<=grid->jlid) return EPS_ZERO;

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

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

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

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

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

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

    716:     if (i==j) uW = param->sb;
    717:     else      uW = UInterp(x,i-1,j);
    718:     uE = UInterp(x,i,j); pC = PInterp(x,i,j);
    719:   }

    721:   return 2.0*etaC*(uE-uW)/dx - pC;
    722: }

    724: /*---------------------------------------------------------------------*/
    725: /*  computes the normal stress---used on the boundaries */
    726: PETSC_STATIC_INLINE PetscScalar ZNormalStress(Field **x, PetscInt i, PetscInt j, PetscInt ipos, AppCtx *user)
    727: /*---------------------------------------------------------------------*/
    728: {
    729:   Parameter   *param=user->param;
    730:   GridInfo    *grid =user->grid;
    731:   PetscScalar dz    =grid->dz;
    732:   PetscInt    ilim  =grid->ni-1, jlim=grid->nj-1, ivisc;
    733:   PetscScalar epsC  =0.0, etaC, TC;
    734:   PetscScalar pC, wN, wS, z_scale;
    735:   if (i<j || j<=grid->jlid) return EPS_ZERO;

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

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

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

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

    749:     TC = param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*z_scale);
    750:     if (ivisc>=VISC_DISL) epsC = CalcSecInv(x,i,j,CELL_CORNER,user);
    751:     etaC = Viscosity(TC,epsC,dz*(j+0.5),param);
    752:     if (i==j) wN = param->sb;
    753:     else      wN = WInterp(x,i,j);
    754:     wS = WInterp(x,i,j-1); pC = PInterp(x,i,j);
    755:   }

    757:   return 2.0*etaC*(wN-wS)/dz - pC;
    758: }

    760: /*---------------------------------------------------------------------*/

    762: /*=====================================================================
    763:   INITIALIZATION, POST-PROCESSING AND OUTPUT FUNCTIONS
    764:   =====================================================================*/

    766: /*---------------------------------------------------------------------*/
    767: /* initializes the problem parameters and checks for
    768:    command line changes */
    769: PetscErrorCode SetParams(Parameter *param, GridInfo *grid)
    770: /*---------------------------------------------------------------------*/
    771: {
    772:   PetscErrorCode ierr, ierr_out=0;
    773:   PetscReal      SEC_PER_YR                    = 3600.00*24.00*365.2500;
    774:   PetscReal      alpha_g_on_cp_units_inverse_km=4.0e-5*9.8;

    776:   /* domain geometry */
    777:   param->slab_dip    = 45.0;
    778:   param->width       = 320.0;                                              /* km */
    779:   param->depth       = 300.0;                                              /* km */
    780:   param->lid_depth   = 35.0;                                               /* km */
    781:   param->fault_depth = 35.0;                                               /* km */

    783:   PetscOptionsGetReal(NULL,NULL,"-slab_dip",&(param->slab_dip),NULL);
    784:   PetscOptionsGetReal(NULL,NULL,"-width",&(param->width),NULL);
    785:   PetscOptionsGetReal(NULL,NULL,"-depth",&(param->depth),NULL);
    786:   PetscOptionsGetReal(NULL,NULL,"-lid_depth",&(param->lid_depth),NULL);
    787:   PetscOptionsGetReal(NULL,NULL,"-fault_depth",&(param->fault_depth),NULL);

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

    791:   /* grid information */
    792:   PetscOptionsGetInt(NULL,NULL, "-jfault",&(grid->jfault),NULL);
    793:   grid->ni = 82;
    794:   PetscOptionsGetInt(NULL,NULL, "-ni",&(grid->ni),NULL);

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

    809:   /* boundary conditions */
    810:   param->pv_analytic = PETSC_FALSE;
    811:   param->ibound      = BC_NOSTRESS;
    812:   PetscOptionsGetInt(NULL,NULL,"-ibound",&(param->ibound),NULL);

    814:   /* physical constants */
    815:   param->slab_velocity = 5.0;               /* cm/yr */
    816:   param->slab_age      = 50.0;              /* Ma */
    817:   param->lid_age       = 50.0;              /* Ma */
    818:   param->kappa         = 0.7272e-6;         /* m^2/sec */
    819:   param->potentialT    = 1300.0;            /* degrees C */

    821:   PetscOptionsGetReal(NULL,NULL,"-slab_velocity",&(param->slab_velocity),NULL);
    822:   PetscOptionsGetReal(NULL,NULL,"-slab_age",&(param->slab_age),NULL);
    823:   PetscOptionsGetReal(NULL,NULL,"-lid_age",&(param->lid_age),NULL);
    824:   PetscOptionsGetReal(NULL,NULL,"-kappa",&(param->kappa),NULL);
    825:   PetscOptionsGetReal(NULL,NULL,"-potentialT",&(param->potentialT),NULL);

    827:   /* viscosity */
    828:   param->ivisc        = 3;                  /* 0=isovisc, 1=difn creep, 2=disl creep, 3=full */
    829:   param->eta0         = 1e24;               /* Pa-s */
    830:   param->visc_cutoff  = 0.0;                /* factor of eta_0 */
    831:   param->continuation = 1.0;

    833:   /* constants for diffusion creep */
    834:   param->diffusion.A     = 1.8e7;             /* Pa-s */
    835:   param->diffusion.n     = 1.0;               /* dim'less */
    836:   param->diffusion.Estar = 375e3;             /* J/mol */
    837:   param->diffusion.Vstar = 5e-6;              /* m^3/mol */

    839:   /* constants for param->dislocationocation creep */
    840:   param->dislocation.A     = 2.8969e4;        /* Pa-s */
    841:   param->dislocation.n     = 3.5;             /* dim'less */
    842:   param->dislocation.Estar = 530e3;           /* J/mol */
    843:   param->dislocation.Vstar = 14e-6;           /* m^3/mol */

    845:   PetscOptionsGetInt(NULL,NULL, "-ivisc",&(param->ivisc),NULL);
    846:   PetscOptionsGetReal(NULL,NULL,"-visc_cutoff",&(param->visc_cutoff),NULL);

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

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

    853:   /* output options */
    854:   param->quiet      = PETSC_FALSE;
    855:   param->param_test = PETSC_FALSE;

    857:   PetscOptionsHasName(NULL,NULL,"-quiet",&(param->quiet));
    858:   PetscOptionsHasName(NULL,NULL,"-test",&(param->param_test));
    859:   PetscOptionsGetString(NULL,NULL,"-file",param->filename,sizeof(param->filename),&(param->output_to_file));

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

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

    866:   /* misc. flags */
    867:   param->stop_solve    = PETSC_FALSE;
    868:   param->interrupted   = PETSC_FALSE;
    869:   param->kspmon        = PETSC_FALSE;
    870:   param->toggle_kspmon = PETSC_FALSE;

    872:   /* derived parameters for slab angle */
    873:   param->sb = PetscSinReal(param->slab_dip);
    874:   param->cb = PetscCosReal(param->slab_dip);
    875:   param->c  =  param->slab_dip*param->sb/(param->slab_dip*param->slab_dip-param->sb*param->sb);
    876:   param->d  = (param->slab_dip*param->cb-param->sb)/(param->slab_dip*param->slab_dip-param->sb*param->sb);

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

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

    901:   return ierr_out;
    902: }

    904: /*---------------------------------------------------------------------*/
    905: /*  prints a report of the problem parameters to stdout */
    906: PetscErrorCode ReportParams(Parameter *param, GridInfo *grid)
    907: /*---------------------------------------------------------------------*/
    908: {
    909:   PetscErrorCode ierr, ierr_out=0;
    910:   char           date[30];

    912:   PetscGetDate(date,30);

    914:   if (!(param->quiet)) {
    915:     PetscPrintf(PETSC_COMM_WORLD,"---------------------BEGIN ex30 PARAM REPORT-------------------\n");
    916:     PetscPrintf(PETSC_COMM_WORLD,"Domain: \n");
    917:     PetscPrintf(PETSC_COMM_WORLD,"  Width = %g km,         Depth = %g km\n",(double)param->width,(double)param->depth);
    918:     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);
    919:     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));

    921:     PetscPrintf(PETSC_COMM_WORLD,"\nGrid: \n");
    922:     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));
    923:     PetscPrintf(PETSC_COMM_WORLD,"  jlid = %3D              jfault = %3D \n",grid->jlid,grid->jfault);
    924:     PetscPrintf(PETSC_COMM_WORLD,"  Pe = %g\n",(double)param->peclet);

    926:     PetscPrintf(PETSC_COMM_WORLD,"\nRheology:");
    927:     if (param->ivisc==VISC_CONST) {
    928:       PetscPrintf(PETSC_COMM_WORLD,"                 Isoviscous \n");
    929:       if (param->pv_analytic) {
    930:         PetscPrintf(PETSC_COMM_WORLD,"                          Pressure and Velocity prescribed! \n");
    931:       }
    932:     } else if (param->ivisc==VISC_DIFN) {
    933:       PetscPrintf(PETSC_COMM_WORLD,"                 Diffusion Creep (T-Dependent Newtonian) \n");
    934:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
    935:     } else if (param->ivisc==VISC_DISL) {
    936:       PetscPrintf(PETSC_COMM_WORLD,"                 Dislocation Creep (T-Dependent Non-Newtonian) \n");
    937:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
    938:     } else if (param->ivisc==VISC_FULL) {
    939:       PetscPrintf(PETSC_COMM_WORLD,"                 Full Rheology \n");
    940:       PetscPrintf(PETSC_COMM_WORLD,"                          Viscosity range: %g--%g Pa-sec \n",(double)param->eta0,(double)(param->visc_cutoff*param->eta0));
    941:     } else {
    942:       PetscPrintf(PETSC_COMM_WORLD,"                 Invalid! \n");
    943:       ierr_out = 1;
    944:     }

    946:     PetscPrintf(PETSC_COMM_WORLD,"Boundary condition:");
    947:     if (param->ibound==BC_ANALYTIC) {
    948:       PetscPrintf(PETSC_COMM_WORLD,"       Isoviscous Analytic Dirichlet \n");
    949:     } else if (param->ibound==BC_NOSTRESS) {
    950:       PetscPrintf(PETSC_COMM_WORLD,"       Stress-Free (normal & shear stress)\n");
    951:     } else if (param->ibound==BC_EXPERMNT) {
    952:       PetscPrintf(PETSC_COMM_WORLD,"       Experimental boundary condition \n");
    953:     } else {
    954:       PetscPrintf(PETSC_COMM_WORLD,"       Invalid! \n");
    955:       ierr_out = 1;
    956:     }

    958:     if (param->output_to_file) {
    959: #if defined(PETSC_HAVE_MATLAB_ENGINE)
    960:       PetscPrintf(PETSC_COMM_WORLD,"Output Destination:       Mat file \"%s\"\n",param->filename);
    961: #else
    962:       PetscPrintf(PETSC_COMM_WORLD,"Output Destination:       PETSc binary file \"%s\"\n",param->filename);
    963: #endif
    964:     }
    965:     if (param->output_ivisc != param->ivisc) {
    966:       PetscPrintf(PETSC_COMM_WORLD,"                          Output viscosity: -ivisc %D\n",param->output_ivisc);
    967:     }

    969:     PetscPrintf(PETSC_COMM_WORLD,"---------------------END ex30 PARAM REPORT---------------------\n");
    970:   }
    971:   if (param->param_test) PetscEnd();
    972:   return ierr_out;
    973: }

    975: /* ------------------------------------------------------------------- */
    976: /*  generates an initial guess using the analytic solution for isoviscous
    977:     corner flow */
    978: PetscErrorCode Initialize(DM da)
    979: /* ------------------------------------------------------------------- */
    980: {
    981:   AppCtx         *user;
    982:   Parameter      *param;
    983:   GridInfo       *grid;
    984:   PetscInt       i,j,is,js,im,jm;
    986:   Field          **x;
    987:   Vec            Xguess;

    989:   /* Get the fine grid */
    990:   DMGetApplicationContext(da,&user);
    991:   Xguess = user->Xguess;
    992:   param  = user->param;
    993:   grid   = user->grid;
    994:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
    995:   DMDAVecGetArray(da,Xguess,(void**)&x);

    997:   /* Compute initial guess */
    998:   for (j=js; j<js+jm; j++) {
    999:     for (i=is; i<is+im; i++) {
    1000:       if (i<j)                x[j][i].u = param->cb;
    1001:       else if (j<=grid->jlid) x[j][i].u = 0.0;
    1002:       else                    x[j][i].u = HorizVelocity(i,j,user);

    1004:       if (i<=j)               x[j][i].w = param->sb;
    1005:       else if (j<=grid->jlid) x[j][i].w = 0.0;
    1006:       else                    x[j][i].w = VertVelocity(i,j,user);

    1008:       if (i<j || j<=grid->jlid) x[j][i].p = 0.0;
    1009:       else                      x[j][i].p = Pressure(i,j,user);

    1011:       x[j][i].T = PetscMin(grid->dz*(j-0.5),1.0);
    1012:     }
    1013:   }

    1015:   /* Restore x to Xguess */
    1016:   DMDAVecRestoreArray(da,Xguess,(void**)&x);

    1018:   return 0;
    1019: }

    1021: /*---------------------------------------------------------------------*/
    1022: /*  controls output to a file */
    1023: PetscErrorCode DoOutput(SNES snes, PetscInt its)
    1024: /*---------------------------------------------------------------------*/
    1025: {
    1026:   AppCtx         *user;
    1027:   Parameter      *param;
    1028:   GridInfo       *grid;
    1029:   PetscInt       ivt;
    1031:   PetscMPIInt    rank;
    1032:   PetscViewer    viewer;
    1033:   Vec            res, pars;
    1034:   MPI_Comm       comm;
    1035:   DM             da;

    1037:   SNESGetDM(snes,&da);
    1038:   DMGetApplicationContext(da,&user);
    1039:   param = user->param;
    1040:   grid  = user->grid;
    1041:   ivt   = param->ivisc;

    1043:   param->ivisc = param->output_ivisc;

    1045:   /* compute final residual and final viscosity/strain rate fields */
    1046:   SNESGetFunction(snes, &res, NULL, NULL);
    1047:   ViscosityField(da, user->x, user->Xguess);

    1049:   /* get the communicator and the rank of the processor */
    1050:   PetscObjectGetComm((PetscObject)snes, &comm);
    1051:   MPI_Comm_rank(comm, &rank);

    1053:   if (param->output_to_file) { /* send output to binary file */
    1054:     VecCreate(comm, &pars);
    1055:     if (rank == 0) { /* on processor 0 */
    1056:       VecSetSizes(pars, 20, PETSC_DETERMINE);
    1057:       VecSetFromOptions(pars);
    1058:       VecSetValue(pars,0, (PetscScalar)(grid->ni),INSERT_VALUES);
    1059:       VecSetValue(pars,1, (PetscScalar)(grid->nj),INSERT_VALUES);
    1060:       VecSetValue(pars,2, (PetscScalar)(grid->dx),INSERT_VALUES);
    1061:       VecSetValue(pars,3, (PetscScalar)(grid->dz),INSERT_VALUES);
    1062:       VecSetValue(pars,4, (PetscScalar)(param->L),INSERT_VALUES);
    1063:       VecSetValue(pars,5, (PetscScalar)(param->V),INSERT_VALUES);
    1064:       /* skipped 6 intentionally */
    1065:       VecSetValue(pars,7, (PetscScalar)(param->slab_dip),INSERT_VALUES);
    1066:       VecSetValue(pars,8, (PetscScalar)(grid->jlid),INSERT_VALUES);
    1067:       VecSetValue(pars,9, (PetscScalar)(param->lid_depth),INSERT_VALUES);
    1068:       VecSetValue(pars,10,(PetscScalar)(grid->jfault),INSERT_VALUES);
    1069:       VecSetValue(pars,11,(PetscScalar)(param->fault_depth),INSERT_VALUES);
    1070:       VecSetValue(pars,12,(PetscScalar)(param->potentialT),INSERT_VALUES);
    1071:       VecSetValue(pars,13,(PetscScalar)(param->ivisc),INSERT_VALUES);
    1072:       VecSetValue(pars,14,(PetscScalar)(param->visc_cutoff),INSERT_VALUES);
    1073:       VecSetValue(pars,15,(PetscScalar)(param->ibound),INSERT_VALUES);
    1074:       VecSetValue(pars,16,(PetscScalar)(its),INSERT_VALUES);
    1075:     } else { /* on some other processor */
    1076:       VecSetSizes(pars, 0, PETSC_DETERMINE);
    1077:       VecSetFromOptions(pars);
    1078:     }
    1079:     VecAssemblyBegin(pars); VecAssemblyEnd(pars);

    1081:     /* create viewer */
    1082: #if defined(PETSC_HAVE_MATLAB_ENGINE)
    1083:     PetscViewerMatlabOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
    1084: #else
    1085:     PetscViewerBinaryOpen(PETSC_COMM_WORLD,param->filename,FILE_MODE_WRITE,&viewer);
    1086: #endif

    1088:     /* send vectors to viewer */
    1089:     PetscObjectSetName((PetscObject)res,"res");
    1090:     VecView(res,viewer);
    1091:     PetscObjectSetName((PetscObject)user->x,"out");
    1092:     VecView(user->x, viewer);
    1093:     PetscObjectSetName((PetscObject)(user->Xguess),"aux");
    1094:     VecView(user->Xguess, viewer);
    1095:     StressField(da); /* compute stress fields */
    1096:     PetscObjectSetName((PetscObject)(user->Xguess),"str");
    1097:     VecView(user->Xguess, viewer);
    1098:     PetscObjectSetName((PetscObject)pars,"par");
    1099:     VecView(pars, viewer);

    1101:     /* destroy viewer and vector */
    1102:     PetscViewerDestroy(&viewer);
    1103:     VecDestroy(&pars);
    1104:   }

    1106:   param->ivisc = ivt;
    1107:   return 0;
    1108: }

    1110: /* ------------------------------------------------------------------- */
    1111: /* Compute both the second invariant of the strain rate tensor and the viscosity, at both cell centers and cell corners */
    1112: PetscErrorCode ViscosityField(DM da, Vec X, Vec V)
    1113: /* ------------------------------------------------------------------- */
    1114: {
    1115:   AppCtx         *user;
    1116:   Parameter      *param;
    1117:   GridInfo       *grid;
    1118:   Vec            localX;
    1119:   Field          **v, **x;
    1120:   PetscReal      eps, /* dx,*/ dz, T, epsC, TC;
    1121:   PetscInt       i,j,is,js,im,jm,ilim,jlim,ivt;

    1125:   DMGetApplicationContext(da,&user);
    1126:   param        = user->param;
    1127:   grid         = user->grid;
    1128:   ivt          = param->ivisc;
    1129:   param->ivisc = param->output_ivisc;

    1131:   DMGetLocalVector(da, &localX);
    1132:   DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX);
    1133:   DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX);
    1134:   DMDAVecGetArray(da,localX,(void**)&x);
    1135:   DMDAVecGetArray(da,V,(void**)&v);

    1137:   /* Parameters */
    1138:   /* dx = grid->dx; */ dz = grid->dz;

    1140:   ilim = grid->ni-1; jlim = grid->nj-1;

    1142:   /* Compute real temperature, strain rate and viscosity */
    1143:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
    1144:   for (j=js; j<js+jm; j++) {
    1145:     for (i=is; i<is+im; i++) {
    1146:       T = PetscRealPart(param->potentialT * x[j][i].T * PetscExpScalar((j-0.5)*dz*param->z_scale));
    1147:       if (i<ilim && j<jlim) {
    1148:         TC = PetscRealPart(param->potentialT * TInterp(x,i,j) * PetscExpScalar(j*dz*param->z_scale));
    1149:       } else {
    1150:         TC = T;
    1151:       }
    1152:       eps  = PetscRealPart((CalcSecInv(x,i,j,CELL_CENTER,user)));
    1153:       epsC = PetscRealPart(CalcSecInv(x,i,j,CELL_CORNER,user));

    1155:       v[j][i].u = eps;
    1156:       v[j][i].w = epsC;
    1157:       v[j][i].p = Viscosity(T,eps,dz*(j-0.5),param);
    1158:       v[j][i].T = Viscosity(TC,epsC,dz*j,param);
    1159:     }
    1160:   }
    1161:   DMDAVecRestoreArray(da,V,(void**)&v);
    1162:   DMDAVecRestoreArray(da,localX,(void**)&x);
    1163:   DMRestoreLocalVector(da, &localX);

    1165:   param->ivisc = ivt;
    1166:   return(0);
    1167: }

    1169: /* ------------------------------------------------------------------- */
    1170: /* post-processing: compute stress everywhere */
    1171: PetscErrorCode StressField(DM da)
    1172: /* ------------------------------------------------------------------- */
    1173: {
    1174:   AppCtx         *user;
    1175:   PetscInt       i,j,is,js,im,jm;
    1177:   Vec            locVec;
    1178:   Field          **x, **y;

    1180:   DMGetApplicationContext(da,&user);

    1182:   /* Get the fine grid of Xguess and X */
    1183:   DMDAGetCorners(da,&is,&js,NULL,&im,&jm,NULL);
    1184:   DMDAVecGetArray(da,user->Xguess,(void**)&x);

    1186:   DMGetLocalVector(da, &locVec);
    1187:   DMGlobalToLocalBegin(da, user->x, INSERT_VALUES, locVec);
    1188:   DMGlobalToLocalEnd(da, user->x, INSERT_VALUES, locVec);
    1189:   DMDAVecGetArray(da,locVec,(void**)&y);

    1191:   /* Compute stress on the corner points */
    1192:   for (j=js; j<js+jm; j++) {
    1193:     for (i=is; i<is+im; i++) {
    1194:       x[j][i].u = ShearStress(y,i,j,CELL_CENTER,user);
    1195:       x[j][i].w = ShearStress(y,i,j,CELL_CORNER,user);
    1196:       x[j][i].p = XNormalStress(y,i,j,CELL_CENTER,user);
    1197:       x[j][i].T = ZNormalStress(y,i,j,CELL_CENTER,user);
    1198:     }
    1199:   }

    1201:   /* Restore the fine grid of Xguess and X */
    1202:   DMDAVecRestoreArray(da,user->Xguess,(void**)&x);
    1203:   DMDAVecRestoreArray(da,locVec,(void**)&y);
    1204:   DMRestoreLocalVector(da, &locVec);
    1205:   return 0;
    1206: }

    1208: /*=====================================================================
    1209:   UTILITY FUNCTIONS
    1210:   =====================================================================*/

    1212: /*---------------------------------------------------------------------*/
    1213: /* returns the velocity of the subducting slab and handles fault nodes
    1214:    for BC */
    1215: PETSC_STATIC_INLINE PetscScalar SlabVel(char c, PetscInt i, PetscInt j, AppCtx *user)
    1216: /*---------------------------------------------------------------------*/
    1217: {
    1218:   Parameter *param = user->param;
    1219:   GridInfo  *grid  = user->grid;

    1221:   if (c=='U' || c=='u') {
    1222:     if (i<j-1) return param->cb;
    1223:     else if (j<=grid->jfault) return 0.0;
    1224:     else return param->cb;

    1226:   } else {
    1227:     if (i<j) return param->sb;
    1228:     else if (j<=grid->jfault) return 0.0;
    1229:     else return param->sb;
    1230:   }
    1231: }

    1233: /*---------------------------------------------------------------------*/
    1234: /*  solution to diffusive half-space cooling model for BC */
    1235: PETSC_STATIC_INLINE PetscScalar PlateModel(PetscInt j, PetscInt plate, AppCtx *user)
    1236: /*---------------------------------------------------------------------*/
    1237: {
    1238:   Parameter     *param = user->param;
    1239:   PetscScalar   z;
    1240:   if (plate==PLATE_LID) z = (j-0.5)*user->grid->dz;
    1241:   else z = (j-0.5)*user->grid->dz*param->cb;  /* PLATE_SLAB */
    1242: #if defined(PETSC_HAVE_ERF)
    1243:   return (PetscReal)(erf((double)PetscRealPart(z*param->L/2.0/param->skt)));
    1244: #else
    1245:   (*PetscErrorPrintf)("erf() not available on this machine\n");
    1246:   MPI_Abort(PETSC_COMM_SELF,1);
    1247: #endif
    1248: }

    1250: /*=====================================================================
    1251:   INTERACTIVE SIGNAL HANDLING
    1252:   =====================================================================*/

    1254: /* ------------------------------------------------------------------- */
    1255: PetscErrorCode SNESConverged_Interactive(SNES snes, PetscInt it,PetscReal xnorm, PetscReal snorm, PetscReal fnorm, SNESConvergedReason *reason, void *ctx)
    1256: /* ------------------------------------------------------------------- */
    1257: {
    1258:   AppCtx         *user  = (AppCtx*) ctx;
    1259:   Parameter      *param = user->param;
    1260:   KSP            ksp;

    1264:   if (param->interrupted) {
    1265:     param->interrupted = PETSC_FALSE;
    1266:     PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: exiting SNES solve. \n");
    1267:     *reason = SNES_CONVERGED_FNORM_ABS;
    1268:     return(0);
    1269:   } else if (param->toggle_kspmon) {
    1270:     param->toggle_kspmon = PETSC_FALSE;

    1272:     SNESGetKSP(snes, &ksp);

    1274:     if (param->kspmon) {
    1275:       KSPMonitorCancel(ksp);

    1277:       param->kspmon = PETSC_FALSE;
    1278:       PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: deactivating ksp singular value monitor. \n");
    1279:     } else {
    1280:       PetscViewerAndFormat *vf;
    1281:       PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
    1282:       KSPMonitorSet(ksp,(PetscErrorCode (*)(KSP,PetscInt,PetscReal,void*))KSPMonitorSingularValue,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);

    1284:       param->kspmon = PETSC_TRUE;
    1285:       PetscPrintf(PETSC_COMM_WORLD,"USER SIGNAL: activating ksp singular value monitor. \n");
    1286:     }
    1287:   }
    1288:   PetscFunctionReturn(SNESConvergedDefault(snes,it,xnorm,snorm,fnorm,reason,ctx));
    1289: }

    1291: /* ------------------------------------------------------------------- */
    1292: #include <signal.h>
    1293: PetscErrorCode InteractiveHandler(int signum, void *ctx)
    1294: /* ------------------------------------------------------------------- */
    1295: {
    1296:   AppCtx    *user  = (AppCtx*) ctx;
    1297:   Parameter *param = user->param;

    1299:   if (signum == SIGILL) {
    1300:     param->toggle_kspmon = PETSC_TRUE;
    1301: #if !defined(PETSC_MISSING_SIGCONT)
    1302:   } else if (signum == SIGCONT) {
    1303:     param->interrupted = PETSC_TRUE;
    1304: #endif
    1305: #if !defined(PETSC_MISSING_SIGURG)
    1306:   } else if (signum == SIGURG) {
    1307:     param->stop_solve = PETSC_TRUE;
    1308: #endif
    1309:   }
    1310:   return 0;
    1311: }

    1313: /*---------------------------------------------------------------------*/
    1314: /*  main call-back function that computes the processor-local piece
    1315:     of the residual */
    1316: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,Field **x,Field **f,void *ptr)
    1317: /*---------------------------------------------------------------------*/
    1318: {
    1319:   AppCtx      *user  = (AppCtx*)ptr;
    1320:   Parameter   *param = user->param;
    1321:   GridInfo    *grid  = user->grid;
    1322:   PetscScalar mag_w, mag_u;
    1323:   PetscInt    i,j,mx,mz,ilim,jlim;
    1324:   PetscInt    is,ie,js,je,ibound;    /* ,ivisc */

    1327:   /* Define global and local grid parameters */
    1328:   mx   = info->mx;     mz   = info->my;
    1329:   ilim = mx-1;         jlim = mz-1;
    1330:   is   = info->xs;     ie   = info->xs+info->xm;
    1331:   js   = info->ys;     je   = info->ys+info->ym;

    1333:   /* Define geometric and numeric parameters */
    1334:   /* ivisc = param->ivisc; */ ibound = param->ibound;

    1336:   for (j=js; j<je; j++) {
    1337:     for (i=is; i<ie; i++) {

    1339:       /************* X-MOMENTUM/VELOCITY *************/
    1340:       if (i<j) f[j][i].u = x[j][i].u - SlabVel('U',i,j,user);
    1341:       else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
    1342:         /* in the lithospheric lid */
    1343:         f[j][i].u = x[j][i].u - 0.0;
    1344:       } else if (i==ilim) {
    1345:         /* on the right side boundary */
    1346:         if (ibound==BC_ANALYTIC) {
    1347:           f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
    1348:         } else {
    1349:           f[j][i].u = XNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
    1350:         }

    1352:       } else if (j==jlim) {
    1353:         /* on the bottom boundary */
    1354:         if (ibound==BC_ANALYTIC) {
    1355:           f[j][i].u = x[j][i].u - HorizVelocity(i,j,user);
    1356:         } else if (ibound==BC_NOSTRESS) {
    1357:           f[j][i].u = XMomentumResidual(x,i,j,user);
    1358:         } else {
    1359:           /* experimental boundary condition */
    1360:         }

    1362:       } else {
    1363:         /* in the mantle wedge */
    1364:         f[j][i].u = XMomentumResidual(x,i,j,user);
    1365:       }

    1367:       /************* Z-MOMENTUM/VELOCITY *************/
    1368:       if (i<=j) {
    1369:         f[j][i].w = x[j][i].w - SlabVel('W',i,j,user);

    1371:       } else if (j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
    1372:         /* in the lithospheric lid */
    1373:         f[j][i].w = x[j][i].w - 0.0;

    1375:       } else if (j==jlim) {
    1376:         /* on the bottom boundary */
    1377:         if (ibound==BC_ANALYTIC) {
    1378:           f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
    1379:         } else {
    1380:           f[j][i].w = ZNormalStress(x,i,j,CELL_CENTER,user) - EPS_ZERO;
    1381:         }

    1383:       } else if (i==ilim) {
    1384:         /* on the right side boundary */
    1385:         if (ibound==BC_ANALYTIC) {
    1386:           f[j][i].w = x[j][i].w - VertVelocity(i,j,user);
    1387:         } else if (ibound==BC_NOSTRESS) {
    1388:           f[j][i].w = ZMomentumResidual(x,i,j,user);
    1389:         } else {
    1390:           /* experimental boundary condition */
    1391:         }

    1393:       } else {
    1394:         /* in the mantle wedge */
    1395:         f[j][i].w =  ZMomentumResidual(x,i,j,user);
    1396:       }

    1398:       /************* CONTINUITY/PRESSURE *************/
    1399:       if (i<j || j<=grid->jlid || (j<grid->corner+grid->inose && i<grid->corner+grid->inose)) {
    1400:         /* in the lid or slab */
    1401:         f[j][i].p = x[j][i].p;

    1403:       } else if ((i==ilim || j==jlim) && ibound==BC_ANALYTIC) {
    1404:         /* on an analytic boundary */
    1405:         f[j][i].p = x[j][i].p - Pressure(i,j,user);

    1407:       } else {
    1408:         /* in the mantle wedge */
    1409:         f[j][i].p = ContinuityResidual(x,i,j,user);
    1410:       }

    1412:       /************* TEMPERATURE *************/
    1413:       if (j==0) {
    1414:         /* on the surface */
    1415:         f[j][i].T = x[j][i].T + x[j+1][i].T + PetscMax(PetscRealPart(x[j][i].T),0.0);

    1417:       } else if (i==0) {
    1418:         /* slab inflow boundary */
    1419:         f[j][i].T = x[j][i].T - PlateModel(j,PLATE_SLAB,user);

    1421:       } else if (i==ilim) {
    1422:         /* right side boundary */
    1423:         mag_u = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j][i-1].u)/param->cb,1.0),0.0)), 5);
    1424:         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);

    1426:       } else if (j==jlim) {
    1427:         /* bottom boundary */
    1428:         mag_w = 1.0 - PetscPowRealInt((1.0-PetscMax(PetscMin(PetscRealPart(x[j-1][i].w)/param->sb,1.0),0.0)), 5);
    1429:         f[j][i].T = x[j][i].T - mag_w*x[j-1][i-1].T - (1.0-mag_w);

    1431:       } else {
    1432:         /* in the mantle wedge */
    1433:         f[j][i].T = EnergyResidual(x,i,j,user);
    1434:       }
    1435:     }
    1436:   }
    1437:   return(0);
    1438: }

    1440: /*TEST

    1442:    build:
    1443:       requires: !complex erf

    1445:    test:
    1446:       args: -ni 18
    1447:       filter: grep -v Destination
    1448:       requires: !single

    1450: TEST*/