Actual source code: ex46.c

petsc-master 2018-04-22
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  1: static char help[] = "Surface processes in geophysics.\n\n";

  3: /*T
  4:    Concepts: SNES^parallel Surface process example
  5:    Concepts: DMDA^using distributed arrays;
  6:    Concepts: IS coloirng types;
  7:    Processors: n
  8:    requires: !single
  9: T*/




 14:  #include <petscsnes.h>
 15:  #include <petscdm.h>
 16:  #include <petscdmda.h>

 18: /*
 19:    User-defined application context - contains data needed by the
 20:    application-provided call-back routines, FormJacobianLocal() and
 21:    FormFunctionLocal().
 22: */
 23: typedef struct {
 24:   PetscReal   D;  /* The diffusion coefficient */
 25:   PetscReal   K;  /* The advection coefficient */
 26:   PetscInt    m;  /* Exponent for A */
 27: } AppCtx;

 29: /*
 30:    User-defined routines
 31: */
 32: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
 33: extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,AppCtx*);

 35: int main(int argc,char **argv)
 36: {
 37:   SNES           snes;                         /* nonlinear solver */
 38:   AppCtx         user;                         /* user-defined work context */
 39:   PetscInt       its;                          /* iterations for convergence */
 41:   DM             da;

 43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 44:      Initialize program
 45:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 47:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

 49:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 50:      Initialize problem parameters
 51:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 52:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Surface Process Problem Options", "SNES");
 53:   user.D = 1.0;
 54:   PetscOptionsReal("-D", "The diffusion coefficient D", __FILE__, user.D, &user.D, NULL);
 55:   user.K = 1.0;
 56:   PetscOptionsReal("-K", "The advection coefficient K", __FILE__, user.K, &user.K, NULL);
 57:   user.m = 1;
 58:   PetscOptionsInt("-m", "The exponent for A", __FILE__, user.m, &user.m, NULL);
 59:   PetscOptionsEnd();

 61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 62:      Create distributed array (DMDA) to manage parallel grid and vectors
 63:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 64:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
 65:   DMSetFromOptions(da);
 66:   DMSetUp(da);
 67:   DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
 68:   DMSetApplicationContext(da,&user);
 69:   SNESCreate(PETSC_COMM_WORLD, &snes);
 70:   SNESSetDM(snes, da);

 72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 73:      Set local function evaluation routine
 74:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 75:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);

 77:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 78:      Customize solver; set runtime options
 79:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 80:   SNESSetFromOptions(snes);


 83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 84:      Solve nonlinear system
 85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 86:   SNESSolve(snes,0,0);
 87:   SNESGetIterationNumber(snes,&its);

 89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 91:   PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);

 93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 94:      Free work space.  All PETSc objects should be destroyed when they
 95:      are no longer needed.
 96:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 98:   SNESDestroy(&snes);
 99:   DMDestroy(&da);

101:   PetscFinalize();
102:   return ierr;
103: }

105: PetscScalar funcU(DMDACoor2d *coords)
106: {
107:   return coords->x + coords->y;
108: }

110: PetscScalar funcA(PetscScalar z, AppCtx *user)
111: {
112:   PetscScalar v = 1.0;
113:   PetscInt    i;

115:   for (i = 0; i < user->m; ++i) v *= z;
116:   return v;
117: }

119: PetscScalar funcADer(PetscScalar z, AppCtx *user)
120: {
121:   PetscScalar v = 1.0;
122:   PetscInt    i;

124:   for (i = 0; i < user->m-1; ++i) v *= z;
125:   return (PetscScalar)user->m*v;
126: }

128: /*
129:    FormFunctionLocal - Evaluates nonlinear function, F(x).
130: */
131: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
132: {
133:   DM             coordDA;
134:   Vec            coordinates;
135:   DMDACoor2d     **coords;
136:   PetscScalar    u, ux, uy, uxx, uyy;
137:   PetscReal      D, K, hx, hy, hxdhy, hydhx;
138:   PetscInt       i,j;

142:   D     = user->D;
143:   K     = user->K;
144:   hx    = 1.0/(PetscReal)(info->mx-1);
145:   hy    = 1.0/(PetscReal)(info->my-1);
146:   hxdhy = hx/hy;
147:   hydhx = hy/hx;
148:   /*
149:      Compute function over the locally owned part of the grid
150:   */
151:   DMGetCoordinateDM(info->da, &coordDA);
152:   DMGetCoordinates(info->da, &coordinates);
153:   DMDAVecGetArray(coordDA, coordinates, &coords);
154:   for (j=info->ys; j<info->ys+info->ym; j++) {
155:     for (i=info->xs; i<info->xs+info->xm; i++) {
156:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) f[j][i] = x[j][i];
157:       else {
158:         u       = x[j][i];
159:         ux      = (x[j][i+1] - x[j][i])/hx;
160:         uy      = (x[j+1][i] - x[j][i])/hy;
161:         uxx     = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
162:         uyy     = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
163:         f[j][i] = D*(uxx + uyy) - (K*funcA(x[j][i], user)*PetscSqrtScalar(ux*ux + uy*uy) + funcU(&coords[j][i]))*hx*hy;
164:         if (PetscIsInfOrNanScalar(f[j][i])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", PetscRealPart(f[j][i]));
165:       }
166:     }
167:   }
168:   DMDAVecRestoreArray(coordDA, coordinates, &coords);
169:   PetscLogFlops(11*info->ym*info->xm);
170:   return(0);
171: }

173: /*
174:    FormJacobianLocal - Evaluates Jacobian matrix.
175: */
176: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
177: {
178:   MatStencil     col[5], row;
179:   PetscScalar    D, K, A, v[5], hx, hy, hxdhy, hydhx, ux, uy;
180:   PetscReal      normGradZ;
181:   PetscInt       i, j,k;

185:   D     = user->D;
186:   K     = user->K;
187:   hx    = 1.0/(PetscReal)(info->mx-1);
188:   hy    = 1.0/(PetscReal)(info->my-1);
189:   hxdhy = hx/hy;
190:   hydhx = hy/hx;

192:   /*
193:      Compute entries for the locally owned part of the Jacobian.
194:       - Currently, all PETSc parallel matrix formats are partitioned by
195:         contiguous chunks of rows across the processors.
196:       - Each processor needs to insert only elements that it owns
197:         locally (but any non-local elements will be sent to the
198:         appropriate processor during matrix assembly).
199:       - Here, we set all entries for a particular row at once.
200:       - We can set matrix entries either using either
201:         MatSetValuesLocal() or MatSetValues(), as discussed above.
202:   */
203:   for (j=info->ys; j<info->ys+info->ym; j++) {
204:     for (i=info->xs; i<info->xs+info->xm; i++) {
205:       row.j = j; row.i = i;
206:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
207:         /* boundary points */
208:         v[0] = 1.0;
209:         MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
210:       } else {
211:         /* interior grid points */
212:         ux        = (x[j][i+1] - x[j][i])/hx;
213:         uy        = (x[j+1][i] - x[j][i])/hy;
214:         normGradZ = PetscRealPart(PetscSqrtScalar(ux*ux + uy*uy));
215:         /* PetscPrintf(PETSC_COMM_SELF, "i: %d j: %d normGradZ: %g\n", i, j, normGradZ); */
216:         if (normGradZ < 1.0e-8) normGradZ = 1.0e-8;
217:         A = funcA(x[j][i], user);

219:         v[0] = -D*hxdhy;                                                                          col[0].j = j - 1; col[0].i = i;
220:         v[1] = -D*hydhx;                                                                          col[1].j = j;     col[1].i = i-1;
221:         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;
222:         v[3] = -D*hydhx + K*A*hx*hy/(2.0*normGradZ);                                              col[3].j = j;     col[3].i = i+1;
223:         v[4] = -D*hxdhy + K*A*hx*hy/(2.0*normGradZ);                                              col[4].j = j + 1; col[4].i = i;
224:         for (k = 0; k < 5; ++k) {
225:           if (PetscIsInfOrNanScalar(v[k])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", PetscRealPart(v[k]));
226:         }
227:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
228:       }
229:     }
230:   }

232:   /*
233:      Assemble matrix, using the 2-step process:
234:        MatAssemblyBegin(), MatAssemblyEnd().
235:   */
236:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
237:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
238:   /*
239:      Tell the matrix we will never add a new nonzero location to the
240:      matrix. If we do, it will generate an error.
241:   */
242:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
243:   return(0);
244: }


247: /*TEST

249:    test:
250:       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

252:    test:
253:       suffix: ew_1
254:       args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 1
255:       requires: !single

257:    test:
258:       suffix: ew_2
259:       args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 2

261:    test:
262:       suffix: ew_3
263:       args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 3
264:       requires: !single

266:    test:
267:       suffix: fm_rise_2
268:       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
269:       requires: !single

271:    test:
272:       suffix: fm_rise_4
273:       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

275: TEST*/