Actual source code: biharmonic2.c

petsc-3.4.2 2013-07-02
  2: static char help[] = "Solves biharmonic equation in 1d.\n";

  4: /*
  5:   Solves the equation biharmonic equation in split form

  7:     w = -kappa \Delta u
  8:     u_t =  \Delta w
  9:     -1  <= u <= 1
 10:     Periodic boundary conditions

 12: Evolve the biharmonic heat equation with bounds:  (same as biharmonic)
 13: ---------------
 14: ./biharmonic2 -ts_monitor -snes_monitor -ts_monitor_draw_solution  -pc_type lu  -draw_pause .1 -snes_converged_reason --wait   -ts_type beuler  -da_refine 5 -draw_fields 1 -ts_dt 9.53674e-9

 16:     w = -kappa \Delta u  + u^3  - u
 17:     u_t =  \Delta w
 18:     -1  <= u <= 1
 19:     Periodic boundary conditions

 21: Evolve the Cahn-Hillard equations:
 22: ---------------
 23: ./biharmonic2 -ts_monitor -snes_monitor -ts_monitor_draw_solution  -pc_type lu  -draw_pause .1 -snes_converged_reason  --wait   -ts_type beuler    -da_refine 6 -vi  -draw_fields 1  -kappa .00001 -ts_dt 5.96046e-06 -cahn-hillard


 26: */
 27: #include <petscdmda.h>
 28: #include <petscts.h>
 29: #include <petscdraw.h>

 31: /*
 32:    User-defined routines
 33: */
 34: extern PetscErrorCode FormFunction(TS,PetscReal,Vec,Vec,Vec,void*),FormInitialSolution(DM,Vec,PetscReal);
 35: typedef struct {PetscBool cahnhillard;PetscReal kappa;PetscInt energy;PetscReal tol;PetscReal theta;PetscReal theta_c;} UserCtx;

 39: int main(int argc,char **argv)
 40: {
 41:   TS             ts;                           /* nonlinear solver */
 42:   Vec            x,r;                          /* solution, residual vectors */
 43:   Mat            J;                            /* Jacobian matrix */
 44:   PetscInt       steps,Mx,maxsteps = 10000000;
 46:   DM             da;
 47:   MatFDColoring  matfdcoloring;
 48:   ISColoring     iscoloring;
 49:   PetscReal      dt;
 50:   PetscReal      vbounds[] = {-100000,100000,-1.1,1.1};
 51:   PetscBool      wait;
 52:   Vec            ul,uh;
 53:   SNES           snes;
 54:   UserCtx        ctx;

 56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 57:      Initialize program
 58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 59:   PetscInitialize(&argc,&argv,(char*)0,help);
 60:   ctx.kappa = 1.0;
 61:   PetscOptionsGetReal(NULL,"-kappa",&ctx.kappa,NULL);
 62:   ctx.cahnhillard = PETSC_FALSE;

 64:   PetscOptionsGetBool(NULL,"-cahn-hillard",&ctx.cahnhillard,NULL);
 65:   PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),2,vbounds);
 66:   PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),600,600);
 67:   ctx.energy = 1;
 68:   /*PetscOptionsGetInt(NULL,"-energy",&ctx.energy,NULL);*/
 69:   PetscOptionsInt("-energy","type of energy (1=double well, 2=double obstacle, 3=logarithmic)","",ctx.energy,&ctx.energy,NULL);
 70:   ctx.tol     = 1.0e-8;
 71:   PetscOptionsGetReal(NULL,"-tol",&ctx.tol,NULL);
 72:   ctx.theta   = .001;
 73:   ctx.theta_c = 1.0;
 74:   PetscOptionsGetReal(NULL,"-theta",&ctx.theta,NULL);
 75:   PetscOptionsGetReal(NULL,"-theta_c",&ctx.theta_c,NULL);

 77:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 78:      Create distributed array (DMDA) to manage parallel grid and vectors
 79:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 80:   DMDACreate1d(PETSC_COMM_WORLD, DMDA_BOUNDARY_PERIODIC, -10,2,2,NULL,&da);
 81:   DMDASetFieldName(da,0,"Biharmonic heat equation: w = -kappa*u_xx");
 82:   DMDASetFieldName(da,1,"Biharmonic heat equation: u");
 83:   DMDAGetInfo(da,0,&Mx,0,0,0,0,0,0,0,0,0,0,0);
 84:   dt   = 1.0/(10.*ctx.kappa*Mx*Mx*Mx*Mx);

 86:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 87:      Extract global vectors from DMDA; then duplicate for remaining
 88:      vectors that are the same types
 89:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 90:   DMCreateGlobalVector(da,&x);
 91:   VecDuplicate(x,&r);

 93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 94:      Create timestepping solver context
 95:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 96:   TSCreate(PETSC_COMM_WORLD,&ts);
 97:   TSSetDM(ts,da);
 98:   TSSetProblemType(ts,TS_NONLINEAR);
 99:   TSSetIFunction(ts,NULL,FormFunction,&ctx);
100:   TSSetDuration(ts,maxsteps,.02);
101:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_INTERPOLATE);

103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104:      Create matrix data structure; set Jacobian evaluation routine

106: <     Set Jacobian matrix data structure and default Jacobian evaluation
107:      routine. User can override with:
108:      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
109:                 (unless user explicitly sets preconditioner)
110:      -snes_mf_operator : form preconditioning matrix as set by the user,
111:                          but use matrix-free approx for Jacobian-vector
112:                          products within Newton-Krylov method

114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
115:   TSGetSNES(ts,&snes);
116:   DMCreateColoring(da,IS_COLORING_GLOBAL,MATAIJ,&iscoloring);
117:   DMCreateMatrix(da,MATAIJ,&J);
118:   MatFDColoringCreate(J,iscoloring,&matfdcoloring);
119:   ISColoringDestroy(&iscoloring);
120:   MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);
121:   MatFDColoringSetFromOptions(matfdcoloring);
122:   SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);

124:   {
125:     VecDuplicate(x,&ul);
126:     VecDuplicate(x,&uh);
127:     VecStrideSet(ul,0,SNES_VI_NINF);
128:     VecStrideSet(ul,1,-1.0);
129:     VecStrideSet(uh,0,SNES_VI_INF);
130:     VecStrideSet(uh,1,1.0);
131:     TSVISetVariableBounds(ts,ul,uh);
132:   }

134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135:      Customize nonlinear solver
136:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137:   TSSetType(ts,TSBEULER);

139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140:      Set initial conditions
141:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
142:   FormInitialSolution(da,x,ctx.kappa);
143:   TSSetInitialTimeStep(ts,0.0,dt);
144:   TSSetSolution(ts,x);

146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147:      Set runtime options
148:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149:   TSSetFromOptions(ts);

151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152:      Solve nonlinear system
153:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
154:   TSSolve(ts,x);
155:   wait = PETSC_FALSE;
156:   PetscOptionsGetBool(NULL,"-wait",&wait,NULL);
157:   if (wait) {
158:     PetscSleep(-1);
159:   }
160:   TSGetTimeStepNumber(ts,&steps);

162:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163:      Free work space.  All PETSc objects should be destroyed when they
164:      are no longer needed.
165:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
166:   {
167:     VecDestroy(&ul);
168:     VecDestroy(&uh);
169:   }
170:   MatDestroy(&J);
171:   MatFDColoringDestroy(&matfdcoloring);
172:   VecDestroy(&x);
173:   VecDestroy(&r);
174:   TSDestroy(&ts);
175:   DMDestroy(&da);

177:   PetscFinalize();
178:   return(0);
179: }

181: typedef struct {PetscScalar w,u;} Field;
182: /* ------------------------------------------------------------------- */
185: /*
186:    FormFunction - Evaluates nonlinear function, F(x).

188:    Input Parameters:
189: .  ts - the TS context
190: .  X - input vector
191: .  ptr - optional user-defined context, as set by SNESSetFunction()

193:    Output Parameter:
194: .  F - function vector
195:  */
196: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec Xdot,Vec F,void *ptr)
197: {
198:   DM             da;
200:   PetscInt       i,Mx,xs,xm;
201:   PetscReal      hx,sx;
202:   Field          *x,*xdot,*f;
203:   Vec            localX,localXdot;
204:   UserCtx        *ctx = (UserCtx*)ptr;

207:   TSGetDM(ts,&da);
208:   DMGetLocalVector(da,&localX);
209:   DMGetLocalVector(da,&localXdot);
210:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
211:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

213:   hx = 1.0/(PetscReal)Mx; sx = 1.0/(hx*hx);

215:   /*
216:      Scatter ghost points to local vector,using the 2-step process
217:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
218:      By placing code between these two statements, computations can be
219:      done while messages are in transition.
220:   */
221:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
222:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
223:   DMGlobalToLocalBegin(da,Xdot,INSERT_VALUES,localXdot);
224:   DMGlobalToLocalEnd(da,Xdot,INSERT_VALUES,localXdot);

226:   /*
227:      Get pointers to vector data
228:   */
229:   DMDAVecGetArray(da,localX,&x);
230:   DMDAVecGetArray(da,localXdot,&xdot);
231:   DMDAVecGetArray(da,F,&f);

233:   /*
234:      Get local grid boundaries
235:   */
236:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

238:   /*
239:      Compute function over the locally owned part of the grid
240:   */
241:   for (i=xs; i<xs+xm; i++) {
242:     f[i].w =  x[i].w + ctx->kappa*(x[i-1].u + x[i+1].u - 2.0*x[i].u)*sx;
243:     if (ctx->cahnhillard) {
244:       switch (ctx->energy) {
245:       case 1: /* double well */
246:         f[i].w += -x[i].u*x[i].u*x[i].u + x[i].u;
247:         break;
248:       case 2: /* double obstacle */
249:         f[i].w += x[i].u;
250:         break;
251:       case 3: /* logarithmic */
252:         if (PetscRealPart(x[i].u) < -1.0 + 2.0*ctx->tol)     f[i].w += .5*ctx->theta*(-log(ctx->tol) + log((1.0-x[i].u)/2.0)) + ctx->theta_c*x[i].u;
253:         else if (PetscRealPart(x[i].u) > 1.0 - 2.0*ctx->tol) f[i].w += .5*ctx->theta*(-log((1.0+x[i].u)/2.0) + log(ctx->tol)) + ctx->theta_c*x[i].u;
254:         else                                                 f[i].w += .5*ctx->theta*(-log((1.0+x[i].u)/2.0) + log((1.0-x[i].u)/2.0)) + ctx->theta_c*x[i].u;
255:         break;
256:       }
257:     }
258:     f[i].u = xdot[i].u - (x[i-1].w + x[i+1].w - 2.0*x[i].w)*sx;
259:   }

261:   /*
262:      Restore vectors
263:   */
264:   DMDAVecRestoreArray(da,localXdot,&xdot);
265:   DMDAVecRestoreArray(da,localX,&x);
266:   DMDAVecRestoreArray(da,F,&f);
267:   DMRestoreLocalVector(da,&localX);
268:   DMRestoreLocalVector(da,&localXdot);
269:   return(0);
270: }

272: /* ------------------------------------------------------------------- */
275: PetscErrorCode FormInitialSolution(DM da,Vec X,PetscReal kappa)
276: {
278:   PetscInt       i,xs,xm,Mx;
279:   Field          *x;
280:   PetscReal      hx,xx,r,sx;

283:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
284:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

286:   hx = 1.0/(PetscReal)Mx;
287:   sx = 1.0/(hx*hx);

289:   /*
290:      Get pointers to vector data
291:   */
292:   DMDAVecGetArray(da,X,&x);

294:   /*
295:      Get local grid boundaries
296:   */
297:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

299:   /*
300:      Compute function over the locally owned part of the grid
301:   */
302:   for (i=xs; i<xs+xm; i++) {
303:     xx = i*hx;
304:     r = PetscSqrtScalar((xx-.5)*(xx-.5));
305:     if (r < .125) x[i].u = 1.0;
306:     else          x[i].u = -.50;
307:     /*  u[i] = PetscPowScalar(x - .5,4.0); */
308:   }
309:   for (i=xs; i<xs+xm; i++) x[i].w = -kappa*(x[i-1].u + x[i+1].u - 2.0*x[i].u)*sx;

311:   /*
312:      Restore vectors
313:   */
314:   DMDAVecRestoreArray(da,X,&x);
315:   return(0);
316: }