Actual source code: ex7.c

petsc-master 2017-11-20
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  2: static char help[] = "Nonlinear, time-dependent PDE in 2d.\n";


  5: /*
  6:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
  7:    Include "petscts.h" so that we can use SNES solvers.  Note that this
  8:    file automatically includes:
  9:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 10:      petscmat.h - matrices
 11:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 12:      petscviewer.h - viewers               petscpc.h  - preconditioners
 13:      petscksp.h   - linear solvers
 14: */
 15:  #include <petscdm.h>
 16:  #include <petscdmda.h>
 17:  #include <petscts.h>


 20: /*
 21:    User-defined routines
 22: */
 23: extern PetscErrorCode FormFunction(TS,PetscReal,Vec,Vec,void*),FormInitialSolution(DM,Vec);
 24: extern PetscErrorCode MyTSMonitor(TS,PetscInt,PetscReal,Vec,void*);
 25: extern PetscErrorCode MySNESMonitor(SNES,PetscInt,PetscReal,PetscViewerAndFormat*);

 27: int main(int argc,char **argv)
 28: {
 29:   TS                   ts;                         /* time integrator */
 30:   SNES                 snes;
 31:   Vec                  x,r;                        /* solution, residual vectors */
 32:   PetscErrorCode       ierr;
 33:   DM                   da;
 34:   PetscViewerAndFormat *vf;

 36:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 37:      Initialize program
 38:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 39:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 40:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 41:      Create distributed array (DMDA) to manage parallel grid and vectors
 42:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 43:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,8,8,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
 44:   DMSetFromOptions(da);
 45:   DMSetUp(da);

 47:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 48:      Extract global vectors from DMDA; then duplicate for remaining
 49:      vectors that are the same types
 50:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 51:   DMCreateGlobalVector(da,&x);
 52:   VecDuplicate(x,&r);

 54:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 55:      Create timestepping solver context
 56:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 57:   TSCreate(PETSC_COMM_WORLD,&ts);
 58:   TSSetProblemType(ts,TS_NONLINEAR);
 59:   TSSetRHSFunction(ts,NULL,FormFunction,da);

 61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 62:      Create matrix data structure; set Jacobian evaluation routine

 64:      Set Jacobian matrix data structure and default Jacobian evaluation
 65:      routine. User can override with:
 66:      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
 67:                 (unless user explicitly sets preconditioner)
 68:      -snes_mf_operator : form preconditioning matrix as set by the user,
 69:                          but use matrix-free approx for Jacobian-vector
 70:                          products within Newton-Krylov method

 72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 74:   TSSetMaxTime(ts,1.0);
 75:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
 76:   TSMonitorSet(ts,MyTSMonitor,PETSC_VIEWER_STDOUT_WORLD,NULL);
 77:   TSSetDM(ts,da);
 78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 79:      Customize nonlinear solver
 80:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 81:   TSSetType(ts,TSBEULER);
 82:   TSGetSNES(ts,&snes);
 83:   PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
 84:   SNESMonitorSet(snes,(PetscErrorCode (*)(SNES,PetscInt,PetscReal,void*))MySNESMonitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);

 86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 87:      Set initial conditions
 88:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 89:   FormInitialSolution(da,x);
 90:   TSSetTimeStep(ts,.0001);
 91:   TSSetSolution(ts,x);

 93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 94:      Set runtime options
 95:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 96:   TSSetFromOptions(ts);

 98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 99:      Solve nonlinear system
100:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101:   TSSolve(ts,x);

103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104:      Free work space.  All PETSc objects should be destroyed when they
105:      are no longer needed.
106:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
107:   VecDestroy(&x);
108:   VecDestroy(&r);
109:   TSDestroy(&ts);
110:   DMDestroy(&da);

112:   PetscFinalize();
113:   return ierr;
114: }
115: /* ------------------------------------------------------------------- */
116: /*
117:    FormFunction - Evaluates nonlinear function, F(x).

119:    Input Parameters:
120: .  ts - the TS context
121: .  X - input vector
122: .  ptr - optional user-defined context, as set by SNESSetFunction()

124:    Output Parameter:
125: .  F - function vector
126:  */
127: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
128: {
129:   DM             da;
131:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
132:   PetscReal      two = 2.0,hx,hy,sx,sy;
133:   PetscScalar    u,uxx,uyy,**x,**f;
134:   Vec            localX;

137:   TSGetDM(ts,&da);
138:   DMGetLocalVector(da,&localX);
139:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

141:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
142:   hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);

144:   /*
145:      Scatter ghost points to local vector,using the 2-step process
146:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
147:      By placing code between these two statements, computations can be
148:      done while messages are in transition.
149:   */
150:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
151:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

153:   /*
154:      Get pointers to vector data
155:   */
156:   DMDAVecGetArrayRead(da,localX,&x);
157:   DMDAVecGetArray(da,F,&f);

159:   /*
160:      Get local grid boundaries
161:   */
162:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

164:   /*
165:      Compute function over the locally owned part of the grid
166:   */
167:   for (j=ys; j<ys+ym; j++) {
168:     for (i=xs; i<xs+xm; i++) {
169:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
170:         f[j][i] = x[j][i];
171:         continue;
172:       }
173:       u   = x[j][i];
174:       uxx = (two*u - x[j][i-1] - x[j][i+1])*sx;
175:       uyy = (two*u - x[j-1][i] - x[j+1][i])*sy;
176:       /*      f[j][i] = -(uxx + uyy); */
177:       f[j][i] = -u*(uxx + uyy) - (4.0 - 1.0)*((x[j][i+1] - x[j][i-1])*(x[j][i+1] - x[j][i-1])*.25*sx +
178:                                               (x[j+1][i] - x[j-1][i])*(x[j+1][i] - x[j-1][i])*.25*sy);
179:     }
180:   }

182:   /*
183:      Restore vectors
184:   */
185:   DMDAVecRestoreArrayRead(da,localX,&x);
186:   DMDAVecRestoreArray(da,F,&f);
187:   DMRestoreLocalVector(da,&localX);
188:   PetscLogFlops(11.0*ym*xm);
189:   return(0);
190: }

192: /* ------------------------------------------------------------------- */
193: PetscErrorCode FormInitialSolution(DM da,Vec U)
194: {
196:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
197:   PetscScalar    **u;
198:   PetscReal      hx,hy,x,y,r;

201:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

203:   hx = 1.0/(PetscReal)(Mx-1);
204:   hy = 1.0/(PetscReal)(My-1);

206:   /*
207:      Get pointers to vector data
208:   */
209:   DMDAVecGetArray(da,U,&u);

211:   /*
212:      Get local grid boundaries
213:   */
214:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

216:   /*
217:      Compute function over the locally owned part of the grid
218:   */
219:   for (j=ys; j<ys+ym; j++) {
220:     y = j*hy;
221:     for (i=xs; i<xs+xm; i++) {
222:       x = i*hx;
223:       r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
224:       if (r < .125) u[j][i] = PetscExpReal(-30.0*r*r*r);
225:       else          u[j][i] = 0.0;
226:     }
227:   }

229:   /*
230:      Restore vectors
231:   */
232:   DMDAVecRestoreArray(da,U,&u);
233:   return(0);
234: }

236: PetscErrorCode MyTSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec v,void *ctx)
237: {
239:   PetscReal      norm;
240:   MPI_Comm       comm;

243:   if (step < 0) return(0); /* step of -1 indicates an interpolated solution */
244:   VecNorm(v,NORM_2,&norm);
245:   PetscObjectGetComm((PetscObject)ts,&comm);
246:   PetscPrintf(comm,"timestep %D time %g norm %g\n",step,(double)ptime,(double)norm);
247:   return(0);
248: }

250: /*
251:    MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
252:    Input Parameters:
253:      snes - the SNES context
254:      its - iteration number
255:      fnorm - 2-norm function value (may be estimated)
256:      ctx - optional user-defined context for private data for the
257:          monitor routine, as set by SNESMonitorSet()
258:  */
259: PetscErrorCode MySNESMonitor(SNES snes,PetscInt its,PetscReal fnorm,PetscViewerAndFormat *vf)
260: {

264:   SNESMonitorDefaultShort(snes,its,fnorm,vf);
265:   return(0);
266: }