Actual source code: ex46.c

petsc-master 2019-05-22
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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: T*/




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

 17: /*
 18:    User-defined application context - contains data needed by the
 19:    application-provided call-back routines, FormJacobianLocal() and
 20:    FormFunctionLocal().
 21: */
 22: typedef struct {
 23:   PetscReal   D;  /* The diffusion coefficient */
 24:   PetscReal   K;  /* The advection coefficient */
 25:   PetscInt    m;  /* Exponent for A */
 26: } AppCtx;

 28: /*
 29:    User-defined routines
 30: */
 31: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
 32: extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,AppCtx*);

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

 42:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 43:      Initialize program
 44:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 48:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 49:      Initialize problem parameters
 50:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 51:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Surface Process Problem Options", "SNES");
 52:   user.D = 1.0;
 53:   PetscOptionsReal("-D", "The diffusion coefficient D", __FILE__, user.D, &user.D, NULL);
 54:   user.K = 1.0;
 55:   PetscOptionsReal("-K", "The advection coefficient K", __FILE__, user.K, &user.K, NULL);
 56:   user.m = 1;
 57:   PetscOptionsInt("-m", "The exponent for A", __FILE__, user.m, &user.m, NULL);
 58:   PetscOptionsEnd();

 60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 61:      Create distributed array (DMDA) to manage parallel grid and vectors
 62:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 63:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
 64:   DMSetFromOptions(da);
 65:   DMSetUp(da);
 66:   DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);
 67:   DMSetApplicationContext(da,&user);
 68:   SNESCreate(PETSC_COMM_WORLD, &snes);
 69:   SNESSetDM(snes, da);

 71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 72:      Set local function evaluation routine
 73:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 74:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);

 76:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 77:      Customize solver; set runtime options
 78:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 79:   SNESSetFromOptions(snes);


 82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 83:      Solve nonlinear system
 84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 85:   SNESSolve(snes,0,0);
 86:   SNESGetIterationNumber(snes,&its);

 88:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 89:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 90:   PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);

 92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 93:      Free work space.  All PETSc objects should be destroyed when they
 94:      are no longer needed.
 95:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

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

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

127: /*
128:    FormFunctionLocal - Evaluates nonlinear function, F(x).
129: */
130: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
131: {
132:   DM             coordDA;
133:   Vec            coordinates;
134:   DMDACoor2d     **coords;
135:   PetscScalar    u, ux, uy, uxx, uyy;
136:   PetscReal      D, K, hx, hy, hxdhy, hydhx;
137:   PetscInt       i,j;

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

172: /*
173:    FormJacobianLocal - Evaluates Jacobian matrix.
174: */
175: PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
176: {
177:   MatStencil     col[5], row;
178:   PetscScalar    D, K, A, v[5], hx, hy, hxdhy, hydhx, ux, uy;
179:   PetscReal      normGradZ;
180:   PetscInt       i, j,k;

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

191:   /*
192:      Compute entries for the locally owned part of the Jacobian.
193:       - Currently, all PETSc parallel matrix formats are partitioned by
194:         contiguous chunks of rows across the processors.
195:       - Each processor needs to insert only elements that it owns
196:         locally (but any non-local elements will be sent to the
197:         appropriate processor during matrix assembly).
198:       - Here, we set all entries for a particular row at once.
199:       - We can set matrix entries either using either
200:         MatSetValuesLocal() or MatSetValues(), as discussed above.
201:   */
202:   for (j=info->ys; j<info->ys+info->ym; j++) {
203:     for (i=info->xs; i<info->xs+info->xm; i++) {
204:       row.j = j; row.i = i;
205:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
206:         /* boundary points */
207:         v[0] = 1.0;
208:         MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
209:       } else {
210:         /* interior grid points */
211:         ux        = (x[j][i+1] - x[j][i])/hx;
212:         uy        = (x[j+1][i] - x[j][i])/hy;
213:         normGradZ = PetscRealPart(PetscSqrtScalar(ux*ux + uy*uy));
214:         /* PetscPrintf(PETSC_COMM_SELF, "i: %d j: %d normGradZ: %g\n", i, j, normGradZ); */
215:         if (normGradZ < 1.0e-8) normGradZ = 1.0e-8;
216:         A = funcA(x[j][i], user);

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

231:   /*
232:      Assemble matrix, using the 2-step process:
233:        MatAssemblyBegin(), MatAssemblyEnd().
234:   */
235:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
236:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
237:   /*
238:      Tell the matrix we will never add a new nonzero location to the
239:      matrix. If we do, it will generate an error.
240:   */
241:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
242:   return(0);
243: }


246: /*TEST

248:    test:
249:       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

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

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

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

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

270:    test:
271:       suffix: fm_rise_4
272:       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

274: TEST*/