Actual source code: biharmonic3.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;
 63:   PetscOptionsGetBool(NULL,"-cahn-hillard",&ctx.cahnhillard,NULL);
 64:   PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),2,vbounds);
 65:   PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),600,600);
 66:   ctx.energy      = 1;
 67:   /* PetscOptionsGetInt(NULL,"-energy",&ctx.energy,NULL); */
 68:   PetscOptionsInt("-energy","type of energy (1=double well, 2=double obstacle, 3=logarithmic, 4=degenerate mobility and weird splitting)","",ctx.energy,&ctx.energy,NULL);
 69:   ctx.tol     = 1.0e-8;
 70:   PetscOptionsGetReal(NULL,"-tol",&ctx.tol,NULL);
 71:   ctx.theta   = .001;
 72:   ctx.theta_c = 1.0;
 73:   PetscOptionsGetReal(NULL,"-theta",&ctx.theta,NULL);
 74:   PetscOptionsGetReal(NULL,"-theta_c",&ctx.theta_c,NULL);

 76:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 77:      Create distributed array (DMDA) to manage parallel grid and vectors
 78:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 79:   DMDACreate1d(PETSC_COMM_WORLD, DMDA_BOUNDARY_PERIODIC, -10,2,2,NULL,&da);
 80:   DMDASetFieldName(da,0,"Biharmonic heat equation: w = -kappa*u_xx");
 81:   DMDASetFieldName(da,1,"Biharmonic heat equation: u");
 82:   DMDAGetInfo(da,0,&Mx,0,0,0,0,0,0,0,0,0,0,0);
 83:   dt   = 1.0/(10.*ctx.kappa*Mx*Mx*Mx*Mx);

 85:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 86:      Extract global vectors from DMDA; then duplicate for remaining
 87:      vectors that are the same types
 88:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 89:   DMCreateGlobalVector(da,&x);
 90:   VecDuplicate(x,&r);

 92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 93:      Create timestepping solver context
 94:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 95:   TSCreate(PETSC_COMM_WORLD,&ts);
 96:   TSSetDM(ts,da);
 97:   TSSetProblemType(ts,TS_NONLINEAR);
 98:   TSSetIFunction(ts,NULL,FormFunction,&ctx);
 99:   TSSetDuration(ts,maxsteps,.02);
100:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);

102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103:      Create matrix data structure; set Jacobian evaluation routine

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

113:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
114:   TSGetSNES(ts,&snes);
115:   DMCreateColoring(da,IS_COLORING_GLOBAL,MATAIJ,&iscoloring);
116:   DMCreateMatrix(da,MATAIJ,&J);
117:   MatFDColoringCreate(J,iscoloring,&matfdcoloring);
118:   ISColoringDestroy(&iscoloring);
119:   MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);
120:   MatFDColoringSetFromOptions(matfdcoloring);
121:   SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);

123:   {
124:     VecDuplicate(x,&ul);
125:     VecDuplicate(x,&uh);
126:     VecStrideSet(ul,0,SNES_VI_NINF);
127:     VecStrideSet(ul,1,-1.0);
128:     VecStrideSet(uh,0,SNES_VI_INF);
129:     VecStrideSet(uh,1,1.0);
130:     TSVISetVariableBounds(ts,ul,uh);
131:   }

133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134:      Customize nonlinear solver
135:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
136:   TSSetType(ts,TSBEULER);

138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139:      Set initial conditions
140:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
141:   FormInitialSolution(da,x,ctx.kappa);
142:   TSSetInitialTimeStep(ts,0.0,dt);
143:   TSSetSolution(ts,x);

145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146:      Set runtime options
147:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
148:   TSSetFromOptions(ts);

150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151:      Solve nonlinear system
152:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153:   TSSolve(ts,x);
154:   wait = PETSC_FALSE;
155:   PetscOptionsGetBool(NULL,"-wait",&wait,NULL);
156:   if (wait) {
157:     PetscSleep(-1);
158:   }
159:   TSGetTimeStepNumber(ts,&steps);

161:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162:      Free work space.  All PETSc objects should be destroyed when they
163:      are no longer needed.
164:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
165:   {
166:     VecDestroy(&ul);
167:     VecDestroy(&uh);
168:   }
169:   MatDestroy(&J);
170:   MatFDColoringDestroy(&matfdcoloring);
171:   VecDestroy(&x);
172:   VecDestroy(&r);
173:   TSDestroy(&ts);
174:   DMDestroy(&da);

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

180: typedef struct {PetscScalar w,u;} Field;
181: /* ------------------------------------------------------------------- */
184: /*
185:    FormFunction - Evaluates nonlinear function, F(x).

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

192:    Output Parameter:
193: .  F - function vector
194:  */
195: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec Xdot,Vec F,void *ptr)
196: {
197:   DM             da;
199:   PetscInt       i,Mx,xs,xm;
200:   PetscReal      hx,sx;
201:   PetscScalar    r,l;
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 (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 (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:       case 4:
257:         break;
258:       }
259:     }
260:     f[i].u = xdot[i].u - (x[i-1].w + x[i+1].w - 2.0*x[i].w)*sx;
261:     if (ctx->energy==4) {
262:       f[i].u = xdot[i].u;
263:       /* approximation of \grad (M(u) \grad w), where M(u) = (1-u^2) */
264:       r       = (1.0 - x[i+1].u*x[i+1].u)*(x[i+2].w-x[i].w)*.5/hx;
265:       l       = (1.0 - x[i-1].u*x[i-1].u)*(x[i].w-x[i-2].w)*.5/hx;
266:       f[i].u -= (r - l)*.5/hx;
267:       f[i].u += 2.0*ctx->theta_c*x[i].u*(x[i+1].u-x[i-1].u)*(x[i+1].u-x[i-1].u)*.25*sx - (ctx->theta - ctx->theta_c*(1-x[i].u*x[i].u))*(x[i+1].u + x[i-1].u - 2.0*x[i].u)*sx;
268:     }
269:   }

271:   /*
272:      Restore vectors
273:   */
274:   DMDAVecRestoreArray(da,localXdot,&xdot);
275:   DMDAVecRestoreArray(da,localX,&x);
276:   DMDAVecRestoreArray(da,F,&f);
277:   DMRestoreLocalVector(da,&localX);
278:   DMRestoreLocalVector(da,&localXdot);
279:   return(0);
280: }

282: /* ------------------------------------------------------------------- */
285: PetscErrorCode FormInitialSolution(DM da,Vec X,PetscReal kappa)
286: {
288:   PetscInt       i,xs,xm,Mx;
289:   Field          *x;
290:   PetscReal      hx,xx,r,sx;

293:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
294:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

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

299:   /*
300:      Get pointers to vector data
301:   */
302:   DMDAVecGetArray(da,X,&x);

304:   /*
305:      Get local grid boundaries
306:   */
307:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

309:   /*
310:      Compute function over the locally owned part of the grid
311:   */
312:   for (i=xs; i<xs+xm; i++) {
313:     xx = i*hx;
314:     r  = PetscSqrtScalar((xx-.5)*(xx-.5));
315:     if (r < .125) x[i].u = 1.0;
316:     else          x[i].u = -.50;
317:     /*  u[i] = PetscPowScalar(x - .5,4.0); */
318:   }
319:   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;

321:   /*
322:      Restore vectors
323:   */
324:   DMDAVecRestoreArray(da,X,&x);
325:   return(0);
326: }