Date: 2022-08-02T03:14:55+00:00

Actual source code: ex46.c

      1: static char help[] = "Surface processes in geophysics.\n\n";

      3: #include <petscsnes.h>
      4: #include <petscdm.h>
      5: #include <petscdmda.h>

      7: /*
      8:    User-defined application context - contains data needed by the
      9:    application-provided call-back routines, FormJacobianLocal() and
     10:    FormFunctionLocal().
     11: */
     12: typedef struct {
     13:   PetscReal   D;  /* The diffusion coefficient */
     14:   PetscReal   K;  /* The advection coefficient */
     15:   PetscInt    m;  /* Exponent for A */
     16: } AppCtx;

     18: /*
     19:    User-defined routines
     20: */
     21: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
     22: extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,AppCtx*);

     24: int main(int argc,char **argv)
     25: {
     26:   SNES           snes;                         /* nonlinear solver */
     27:   AppCtx         user;                         /* user-defined work context */
     28:   PetscInt       its;                          /* iterations for convergence */
     30:   DM             da;

     32:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     33:      Initialize program
     34:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     36:   PetscInitialize(&argc,&argv,(char*)0,help);

     38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     39:      Initialize problem parameters
     40:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     41:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Surface Process Problem Options", "SNES");
     42:   user.D = 1.0;
     43:   PetscOptionsReal("-D", "The diffusion coefficient D", __FILE__, user.D, &user.D, NULL);
     44:   user.K = 1.0;
     45:   PetscOptionsReal("-K", "The advection coefficient K", __FILE__, user.K, &user.K, NULL);
     46:   user.m = 1;
     47:   PetscOptionsInt("-m", "The exponent for A", __FILE__, user.m, &user.m, NULL);
     48:   PetscOptionsEnd();

     50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     51:      Create distributed array (DMDA) to manage parallel grid and vectors
     52:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     53:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     54:   DMSetFromOptions(da);
     55:   DMSetUp(da);
     56:   DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
     57:   DMSetApplicationContext(da,&user);
     58:   SNESCreate(PETSC_COMM_WORLD, &snes);
     59:   SNESSetDM(snes, da);

     61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     62:      Set local function evaluation routine
     63:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     64:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);

     66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     67:      Customize solver; set runtime options
     68:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     69:   SNESSetFromOptions(snes);

     71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     72:      Solve nonlinear system
     73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     74:   SNESSolve(snes,0,0);
     75:   SNESGetIterationNumber(snes,&its);

     77:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     78:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     79:   PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);

     81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     82:      Free work space.  All PETSc objects should be destroyed when they
     83:      are no longer needed.
     84:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     86:   SNESDestroy(&snes);
     87:   DMDestroy(&da);

     89:   PetscFinalize();
     90:   return 0;
     91: }

     93: PetscScalar funcU(DMDACoor2d *coords)
     94: {
     95:   return coords->x + coords->y;
     96: }

     98: PetscScalar funcA(PetscScalar z, AppCtx *user)
     99: {
    100:   PetscScalar v = 1.0;
    101:   PetscInt    i;

    103:   for (i = 0; i < user->m; ++i) v *= z;
    104:   return v;
    105: }

    107: PetscScalar funcADer(PetscScalar z, AppCtx *user)
    108: {
    109:   PetscScalar v = 1.0;
    110:   PetscInt    i;

    112:   for (i = 0; i < user->m-1; ++i) v *= z;
    113:   return (PetscScalar)user->m*v;
    114: }

    116: /*
    117:    FormFunctionLocal - Evaluates nonlinear function, F(x).
    118: */
    119: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
    120: {
    121:   DM             coordDA;
    122:   Vec            coordinates;
    123:   DMDACoor2d     **coords;
    124:   PetscScalar    u, ux, uy, uxx, uyy;
    125:   PetscReal      D, K, hx, hy, hxdhy, hydhx;
    126:   PetscInt       i,j;

    129:   D     = user->D;
    130:   K     = user->K;
    131:   hx    = 1.0/(PetscReal)(info->mx-1);
    132:   hy    = 1.0/(PetscReal)(info->my-1);
    133:   hxdhy = hx/hy;
    134:   hydhx = hy/hx;
    135:   /*
    136:      Compute function over the locally owned part of the grid
    137:   */
    138:   DMGetCoordinateDM(info->da, &coordDA);
    139:   DMGetCoordinates(info->da, &coordinates);
    140:   DMDAVecGetArray(coordDA, coordinates, &coords);
    141:   for (j=info->ys; j<info->ys+info->ym; j++) {
    142:     for (i=info->xs; i<info->xs+info->xm; i++) {
    143:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) f[j][i] = x[j][i];
    144:       else {
    145:         u       = x[j][i];
    146:         ux      = (x[j][i+1] - x[j][i])/hx;
    147:         uy      = (x[j+1][i] - x[j][i])/hy;
    148:         uxx     = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
    149:         uyy     = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
    150:         f[j][i] = D*(uxx + uyy) - (K*funcA(x[j][i], user)*PetscSqrtScalar(ux*ux + uy*uy) + funcU(&coords[j][i]))*hx*hy;
    152:       }
    153:     }
    154:   }
    155:   DMDAVecRestoreArray(coordDA, coordinates, &coords);
    156:   PetscLogFlops(11.0*info->ym*info->xm);
    157:   return 0;
    158: }

    160: /*
    161:    FormJacobianLocal - Evaluates Jacobian matrix.
    162: */
    163: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
    164: {
    165:   MatStencil     col[5], row;
    166:   PetscScalar    D, K, A, v[5], hx, hy, hxdhy, hydhx, ux, uy;
    167:   PetscReal      normGradZ;
    168:   PetscInt       i, j,k;

    171:   D     = user->D;
    172:   K     = user->K;
    173:   hx    = 1.0/(PetscReal)(info->mx-1);
    174:   hy    = 1.0/(PetscReal)(info->my-1);
    175:   hxdhy = hx/hy;
    176:   hydhx = hy/hx;

    178:   /*
    179:      Compute entries for the locally owned part of the Jacobian.
    180:       - Currently, all PETSc parallel matrix formats are partitioned by
    181:         contiguous chunks of rows across the processors.
    182:       - Each processor needs to insert only elements that it owns
    183:         locally (but any non-local elements will be sent to the
    184:         appropriate processor during matrix assembly).
    185:       - Here, we set all entries for a particular row at once.
    186:       - We can set matrix entries either using either
    187:         MatSetValuesLocal() or MatSetValues(), as discussed above.
    188:   */
    189:   for (j=info->ys; j<info->ys+info->ym; j++) {
    190:     for (i=info->xs; i<info->xs+info->xm; i++) {
    191:       row.j = j; row.i = i;
    192:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
    193:         /* boundary points */
    194:         v[0] = 1.0;
    195:         MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
    196:       } else {
    197:         /* interior grid points */
    198:         ux        = (x[j][i+1] - x[j][i])/hx;
    199:         uy        = (x[j+1][i] - x[j][i])/hy;
    200:         normGradZ = PetscRealPart(PetscSqrtScalar(ux*ux + uy*uy));
    201:         if (normGradZ < 1.0e-8) normGradZ = 1.0e-8;
    202:         A = funcA(x[j][i], user);

    204:         v[0] = -D*hxdhy;                                                                          col[0].j = j - 1; col[0].i = i;
    205:         v[1] = -D*hydhx;                                                                          col[1].j = j;     col[1].i = i-1;
    206:         v[2] = D*2.0*(hydhx + hxdhy) + K*(funcADer(x[j][i], user)*normGradZ - A/normGradZ)*hx*hy; col[2].j = row.j; col[2].i = row.i;
    207:         v[3] = -D*hydhx + K*A*hx*hy/(2.0*normGradZ);                                              col[3].j = j;     col[3].i = i+1;
    208:         v[4] = -D*hxdhy + K*A*hx*hy/(2.0*normGradZ);                                              col[4].j = j + 1; col[4].i = i;
    209:         for (k = 0; k < 5; ++k) {
    211:         }
    212:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
    213:       }
    214:     }
    215:   }

    217:   /*
    218:      Assemble matrix, using the 2-step process:
    219:        MatAssemblyBegin(), MatAssemblyEnd().
    220:   */
    221:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    222:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    223:   /*
    224:      Tell the matrix we will never add a new nonzero location to the
    225:      matrix. If we do, it will generate an error.
    226:   */
    227:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    228:   return 0;
    229: }

    231: /*TEST

    233:    test:
    234:       args: -snes_view -snes_monitor_short -da_refine 1 -pc_type mg -ksp_type fgmres -pc_mg_type full -mg_levels_ksp_chebyshev_esteig 0.5,1.1

    236:    test:
    237:       suffix: ew_1
    238:       args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 1
    239:       requires: !single

    241:    test:
    242:       suffix: ew_2
    243:       args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 2

    245:    test:
    246:       suffix: ew_3
    247:       args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 3
    248:       requires: !single

    250:    test:
    251:       suffix: fm_rise_2
    252:       args: -K 3 -m 1 -D 0.2 -snes_monitor_short -snes_type ngmres -snes_npc_side right -npc_snes_type newtonls -npc_snes_linesearch_type basic -snes_ngmres_restart_it 1 -snes_ngmres_restart_fm_rise
    253:       requires: !single

    255:    test:
    256:       suffix: fm_rise_4
    257:       args: -K 3 -m 1 -D 0.2 -snes_monitor_short -snes_type ngmres -snes_npc_side right -npc_snes_type newtonls -npc_snes_linesearch_type basic -snes_ngmres_restart_it 2 -snes_ngmres_restart_fm_rise -snes_rtol 1.e-2 -snes_max_it 5

    259: TEST*/