Actual source code: ex7.c

petsc-3.7.0 2016-04-25
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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*);

 29: int main(int argc,char **argv)
 30: {
 31:   TS                   ts;                         /* time integrator */
 32:   SNES                 snes;
 33:   Vec                  x,r;                        /* solution, residual vectors */
 34:   PetscInt             maxsteps = 100;             /* iterations for convergence */
 35:   PetscErrorCode       ierr;
 36:   DM                   da;
 37:   PetscViewerAndFormat *vf;

 39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 40:      Initialize program
 41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 42:   PetscInitialize(&argc,&argv,(char*)0,help);

 44:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 45:      Create distributed array (DMDA) to manage parallel grid and vectors
 46:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 47:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-8,-8,PETSC_DECIDE,PETSC_DECIDE,
 48:                       1,1,NULL,NULL,&da);

 50:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 51:      Extract global vectors from DMDA; then duplicate for remaining
 52:      vectors that are the same types
 53:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 54:   DMCreateGlobalVector(da,&x);
 55:   VecDuplicate(x,&r);

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

 64:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 65:      Create matrix data structure; set Jacobian evaluation routine

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

 75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90:      Set initial conditions
 91:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 92:   FormInitialSolution(da,x);
 93:   TSSetInitialTimeStep(ts,0.0,.0001);
 94:   TSSetSolution(ts,x);

 96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 97:      Set runtime options
 98:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 99:   TSSetFromOptions(ts);

101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102:      Solve nonlinear system
103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
104:   TSSolve(ts,x);

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

115:   PetscFinalize();
116:   return(0);
117: }
118: /* ------------------------------------------------------------------- */
121: /*
122:    FormFunction - Evaluates nonlinear function, F(x).

124:    Input Parameters:
125: .  ts - the TS context
126: .  X - input vector
127: .  ptr - optional user-defined context, as set by SNESSetFunction()

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

142:   TSGetDM(ts,&da);
143:   DMGetLocalVector(da,&localX);
144:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
145:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

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

150:   /*
151:      Scatter ghost points to local vector,using the 2-step process
152:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
153:      By placing code between these two statements, computations can be
154:      done while messages are in transition.
155:   */
156:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
157:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

159:   /*
160:      Get pointers to vector data
161:   */
162:   DMDAVecGetArrayRead(da,localX,&x);
163:   DMDAVecGetArray(da,F,&f);

165:   /*
166:      Get local grid boundaries
167:   */
168:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

170:   /*
171:      Compute function over the locally owned part of the grid
172:   */
173:   for (j=ys; j<ys+ym; j++) {
174:     for (i=xs; i<xs+xm; i++) {
175:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
176:         f[j][i] = x[j][i];
177:         continue;
178:       }
179:       u   = x[j][i];
180:       uxx = (two*u - x[j][i-1] - x[j][i+1])*sx;
181:       uyy = (two*u - x[j-1][i] - x[j+1][i])*sy;
182:       /*      f[j][i] = -(uxx + uyy); */
183:       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 +
184:                                               (x[j+1][i] - x[j-1][i])*(x[j+1][i] - x[j-1][i])*.25*sy);
185:     }
186:   }

188:   /*
189:      Restore vectors
190:   */
191:   DMDAVecRestoreArrayRead(da,localX,&x);
192:   DMDAVecRestoreArray(da,F,&f);
193:   DMRestoreLocalVector(da,&localX);
194:   PetscLogFlops(11.0*ym*xm);
195:   return(0);
196: }

198: /* ------------------------------------------------------------------- */
201: PetscErrorCode FormInitialSolution(DM da,Vec U)
202: {
204:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
205:   PetscScalar    **u;
206:   PetscReal      hx,hy,x,y,r;

209:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
210:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

212:   hx = 1.0/(PetscReal)(Mx-1);
213:   hy = 1.0/(PetscReal)(My-1);

215:   /*
216:      Get pointers to vector data
217:   */
218:   DMDAVecGetArray(da,U,&u);

220:   /*
221:      Get local grid boundaries
222:   */
223:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

225:   /*
226:      Compute function over the locally owned part of the grid
227:   */
228:   for (j=ys; j<ys+ym; j++) {
229:     y = j*hy;
230:     for (i=xs; i<xs+xm; i++) {
231:       x = i*hx;
232:       r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
233:       if (r < .125) u[j][i] = PetscExpReal(-30.0*r*r*r);
234:       else          u[j][i] = 0.0;
235:     }
236:   }

238:   /*
239:      Restore vectors
240:   */
241:   DMDAVecRestoreArray(da,U,&u);
242:   return(0);
243: }

247: PetscErrorCode MyTSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec v,void *ctx)
248: {
250:   PetscReal      norm;
251:   MPI_Comm       comm;

254:   if (step < 0) return(0); /* step of -1 indicates an interpolated solution */
255:   VecNorm(v,NORM_2,&norm);
256:   PetscObjectGetComm((PetscObject)ts,&comm);
257:   PetscPrintf(comm,"timestep %D time %g norm %g\n",step,(double)ptime,(double)norm);
258:   return(0);
259: }

263: /*
264:    MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
265:    Input Parameters:
266:      snes - the SNES context
267:      its - iteration number
268:      fnorm - 2-norm function value (may be estimated)
269:      ctx - optional user-defined context for private data for the
270:          monitor routine, as set by SNESMonitorSet()
271:  */
272: PetscErrorCode MySNESMonitor(SNES snes,PetscInt its,PetscReal fnorm,PetscViewerAndFormat *vf)
273: {

277:   SNESMonitorDefaultShort(snes,its,fnorm,vf);
278:   return(0);
279: }