Actual source code: ex15.c

petsc-dev 2014-02-02
Report Typos and Errors
  2: static char help[] = "Time-dependent PDE in 2d. Modified from ex13.c for illustrating how to solve DAEs. \n";
  3: /*
  4:    u_t = uxx + uyy
  5:    0 < x < 1, 0 < y < 1;
  6:    At t=0: u(x,y) = exp(c*r*r*r), if r=PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5)) < .125
  7:            u(x,y) = 0.0           if r >= .125


 10:    Boundary conditions:
 11:    Drichlet BC:
 12:    At x=0, x=1, y=0, y=1: u = 0.0

 14:    Neumann BC:
 15:    At x=0, x=1: du(x,y,t)/dx = 0
 16:    At y=0, y=1: du(x,y,t)/dy = 0

 18:    mpiexec -n 2 ./ex15 -da_grid_x 40 -da_grid_y 40 -ts_max_steps 2 -snes_monitor -ksp_monitor
 19:          ./ex15 -da_grid_x 40 -da_grid_y 40  -draw_pause .1 -boundary 1 -ts_monitor_draw_solution
 20:          ./ex15 -da_grid_x 40 -da_grid_y 40  -draw_pause .1 -boundary 1 -Jtype 2 -nstencilpts 9

 22: */

 24: #include <petscdmda.h>
 25: #include <petscts.h>

 27: /*
 28:    User-defined data structures and routines
 29: */

 31: /* AppCtx: used by FormIFunction() and FormIJacobian() */
 32: typedef struct {
 33:   DM        da;
 34:   PetscInt  nstencilpts;         /* number of stencil points: 5 or 9 */
 35:   PetscReal c;
 36:   PetscInt  boundary;            /* Type of boundary condition */
 37:   PetscBool viewJacobian;
 38: } AppCtx;

 40: extern PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*);
 41: extern PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat*,Mat*,MatStructure*,void*);
 42: extern PetscErrorCode FormInitialSolution(Vec,void*);

 46: int main(int argc,char **argv)
 47: {
 48:   TS             ts;                   /* nonlinear solver */
 49:   Vec            u,r;                  /* solution, residual vectors */
 50:   Mat            J,Jmf = NULL;   /* Jacobian matrices */
 51:   PetscInt       maxsteps = 1000;      /* iterations for convergence */
 53:   DM             da;
 54:   PetscReal      dt;
 55:   AppCtx         user;              /* user-defined work context */
 56:   SNES           snes;
 57:   PetscInt       Jtype; /* Jacobian type
 58:                             0: user provide Jacobian;
 59:                             1: slow finite difference;
 60:                             2: fd with coloring; */

 62:   PetscInitialize(&argc,&argv,(char*)0,help);
 63:   /* Initialize user application context */
 64:   user.da           = NULL;
 65:   user.nstencilpts  = 5;
 66:   user.c            = -30.0;
 67:   user.boundary     = 0;  /* 0: Drichlet BC; 1: Neumann BC */
 68:   user.viewJacobian = PETSC_FALSE;

 70:   PetscOptionsGetInt(NULL,"-nstencilpts",&user.nstencilpts,NULL);
 71:   PetscOptionsGetInt(NULL,"-boundary",&user.boundary,NULL);
 72:   PetscOptionsHasName(NULL,"-viewJacobian",&user.viewJacobian);

 74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 75:      Create distributed array (DMDA) to manage parallel grid and vectors
 76:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 77:   if (user.nstencilpts == 5) {
 78:     DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-11,-11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
 79:   } else if (user.nstencilpts == 9) {
 80:     DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_BOX,-11,-11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
 81:   } else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"nstencilpts %d is not supported",user.nstencilpts);
 82:   user.da = da;

 84:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 85:      Extract global vectors from DMDA;
 86:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 87:   DMCreateGlobalVector(da,&u);
 88:   VecDuplicate(u,&r);

 90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 91:      Create timestepping solver context
 92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 93:   TSCreate(PETSC_COMM_WORLD,&ts);
 94:   TSSetProblemType(ts,TS_NONLINEAR);
 95:   TSSetType(ts,TSBEULER);
 96:   TSSetDM(ts,da);
 97:   TSSetIFunction(ts,r,FormIFunction,&user);
 98:   TSSetDuration(ts,maxsteps,1.0);

100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101:      Set initial conditions
102:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
103:   FormInitialSolution(u,&user);
104:   TSSetSolution(ts,u);
105:   dt   = .01;
106:   TSSetInitialTimeStep(ts,0.0,dt);

108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109:    Set Jacobian evaluation routine
110:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
111:   DMSetMatType(da,MATAIJ);
112:   DMCreateMatrix(da,&J);
113:   Jtype = 0;
114:   PetscOptionsGetInt(NULL, "-Jtype",&Jtype,NULL);
115:   if (Jtype == 0) { /* use user provided Jacobian evaluation routine */
116:     if (user.nstencilpts != 5) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"user Jacobian routine FormIJacobian() does not support nstencilpts=%D",user.nstencilpts);
117:     TSSetIJacobian(ts,J,J,FormIJacobian,&user);
118:   } else { /* use finite difference Jacobian J as preconditioner and '-snes_mf_operator' for Mat*vec */
119:     TSGetSNES(ts,&snes);
120:     MatCreateSNESMF(snes,&Jmf);
121:     if (Jtype == 1) { /* slow finite difference J; */
122:       SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefault,NULL);
123:     } else if (Jtype == 2) { /* Use coloring to compute  finite difference J efficiently */
124:       SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefaultColor,0);
125:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Jtype is not supported");
126:   }

128:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129:    Sets various TS parameters from user options
130:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131:   TSSetFromOptions(ts);

133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134:      Solve nonlinear system
135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
136:   TSSolve(ts,u);

138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139:      Free work space.
140:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
141:   MatDestroy(&J);
142:   MatDestroy(&Jmf);
143:   VecDestroy(&u);
144:   VecDestroy(&r);
145:   TSDestroy(&ts);
146:   DMDestroy(&da);

148:   PetscFinalize();
149:   return(0);
150: }

152: /* --------------------------------------------------------------------- */
153: /*
154:   FormIFunction = Udot - RHSFunction
155: */
158: PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
159: {
161:   AppCtx         *user=(AppCtx*)ctx;
162:   DM             da   = (DM)user->da;
163:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
164:   PetscReal      hx,hy,sx,sy;
165:   PetscScalar    u,uxx,uyy,**uarray,**f,**udot;
166:   Vec            localU;

169:   DMGetLocalVector(da,&localU);
170:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
171:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

173:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
174:   hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
175:   if (user->nstencilpts == 9 && hx != hy) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"hx must equal hy when nstencilpts = 9 for this example");

177:   /*
178:      Scatter ghost points to local vector,using the 2-step process
179:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
180:      By placing code between these two statements, computations can be
181:      done while messages are in transition.
182:   */
183:   DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
184:   DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);

186:   /* Get pointers to vector data */
187:   DMDAVecGetArray(da,localU,&uarray);
188:   DMDAVecGetArray(da,F,&f);
189:   DMDAVecGetArray(da,Udot,&udot);

191:   /* Get local grid boundaries */
192:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

194:   /* Compute function over the locally owned part of the grid */
195:   for (j=ys; j<ys+ym; j++) {
196:     for (i=xs; i<xs+xm; i++) {
197:       /* Boundary conditions */
198:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
199:         if (user->boundary == 0) { /* Drichlet BC */
200:           f[j][i] = uarray[j][i]; /* F = U */
201:         } else {                  /* Neumann BC */
202:           if (i == 0 && j == 0) {              /* SW corner */
203:             f[j][i] = uarray[j][i] - uarray[j+1][i+1];
204:           } else if (i == Mx-1 && j == 0) {    /* SE corner */
205:             f[j][i] = uarray[j][i] - uarray[j+1][i-1];
206:           } else if (i == 0 && j == My-1) {    /* NW corner */
207:             f[j][i] = uarray[j][i] - uarray[j-1][i+1];
208:           } else if (i == Mx-1 && j == My-1) { /* NE corner */
209:             f[j][i] = uarray[j][i] - uarray[j-1][i-1];
210:           } else if (i == 0) {                  /* Left */
211:             f[j][i] = uarray[j][i] - uarray[j][i+1];
212:           } else if (i == Mx-1) {               /* Right */
213:             f[j][i] = uarray[j][i] - uarray[j][i-1];
214:           } else if (j == 0) {                 /* Bottom */
215:             f[j][i] = uarray[j][i] - uarray[j+1][i];
216:           } else if (j == My-1) {               /* Top */
217:             f[j][i] = uarray[j][i] - uarray[j-1][i];
218:           }
219:         }
220:       } else { /* Interior */
221:         u = uarray[j][i];
222:         /* 5-point stencil */
223:         uxx = (-2.0*u + uarray[j][i-1] + uarray[j][i+1]);
224:         uyy = (-2.0*u + uarray[j-1][i] + uarray[j+1][i]);
225:         if (user->nstencilpts == 9) {
226:           /* 9-point stencil: assume hx=hy */
227:           uxx = 2.0*uxx/3.0 + (0.5*(uarray[j-1][i-1]+uarray[j-1][i+1]+uarray[j+1][i-1]+uarray[j+1][i+1]) - 2.0*u)/6.0;
228:           uyy = 2.0*uyy/3.0 + (0.5*(uarray[j-1][i-1]+uarray[j-1][i+1]+uarray[j+1][i-1]+uarray[j+1][i+1]) - 2.0*u)/6.0;
229:         }
230:         f[j][i] = udot[j][i] - (uxx*sx + uyy*sy);
231:       }
232:     }
233:   }

235:   /* Restore vectors */
236:   DMDAVecRestoreArray(da,localU,&uarray);
237:   DMDAVecRestoreArray(da,F,&f);
238:   DMDAVecRestoreArray(da,Udot,&udot);
239:   DMRestoreLocalVector(da,&localU);
240:   PetscLogFlops(11.0*ym*xm);
241:   return(0);
242: }

244: /* --------------------------------------------------------------------- */
245: /*
246:   FormIJacobian() - Compute IJacobian = dF/dU + a dF/dUdot
247:   This routine is not used with option '-use_coloring'
248: */
251: PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat *J,Mat *Jpre,MatStructure *str,void *ctx)
252: {
254:   PetscInt       i,j,Mx,My,xs,ys,xm,ym,nc;
255:   AppCtx         *user = (AppCtx*)ctx;
256:   DM             da    = (DM)user->da;
257:   MatStencil     col[5],row;
258:   PetscScalar    vals[5],hx,hy,sx,sy;

261:   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);
262:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

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

267:   for (j=ys; j<ys+ym; j++) {
268:     for (i=xs; i<xs+xm; i++) {
269:       nc    = 0;
270:       row.j = j; row.i = i;
271:       if (user->boundary == 0 && (i == 0 || i == Mx-1 || j == 0 || j == My-1)) {
272:         col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;

274:       } else if (user->boundary > 0 && i == 0) {  /* Left Neumann */
275:         col[nc].j = j; col[nc].i = i;   vals[nc++] = 1.0;
276:         col[nc].j = j; col[nc].i = i+1; vals[nc++] = -1.0;
277:       } else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */
278:         col[nc].j = j; col[nc].i = i;   vals[nc++] = 1.0;
279:         col[nc].j = j; col[nc].i = i-1; vals[nc++] = -1.0;
280:       } else if (user->boundary > 0 && j == 0) {  /* Bottom Neumann */
281:         col[nc].j = j;   col[nc].i = i; vals[nc++] = 1.0;
282:         col[nc].j = j+1; col[nc].i = i; vals[nc++] = -1.0;
283:       } else if (user->boundary > 0 && j == My-1) { /* Top Neumann */
284:         col[nc].j = j;   col[nc].i = i;  vals[nc++] = 1.0;
285:         col[nc].j = j-1; col[nc].i = i;  vals[nc++] = -1.0;
286:       } else {   /* Interior */
287:         col[nc].j = j-1; col[nc].i = i;   vals[nc++] = -sy;
288:         col[nc].j = j;   col[nc].i = i-1; vals[nc++] = -sx;
289:         col[nc].j = j;   col[nc].i = i;   vals[nc++] = 2.0*(sx + sy) + a;
290:         col[nc].j = j;   col[nc].i = i+1; vals[nc++] = -sx;
291:         col[nc].j = j+1; col[nc].i = i;   vals[nc++] = -sy;
292:       }
293:       MatSetValuesStencil(*Jpre,1,&row,nc,col,vals,INSERT_VALUES);
294:     }
295:   }
296:   MatAssemblyBegin(*Jpre,MAT_FINAL_ASSEMBLY);
297:   MatAssemblyEnd(*Jpre,MAT_FINAL_ASSEMBLY);
298:   if (*J != *Jpre) {
299:     MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
300:     MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
301:   }

303:   if (user->viewJacobian) {
304:     PetscPrintf(PetscObjectComm((PetscObject)*Jpre),"Jpre:\n");
305:     MatView(*Jpre,PETSC_VIEWER_STDOUT_WORLD);
306:   }
307:   return(0);
308: }

310: /* ------------------------------------------------------------------- */
313: PetscErrorCode FormInitialSolution(Vec U,void *ptr)
314: {
315:   AppCtx         *user=(AppCtx*)ptr;
316:   DM             da   =user->da;
317:   PetscReal      c    =user->c;
319:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
320:   PetscScalar    **u;
321:   PetscReal      hx,hy,x,y,r;

324:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
325:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

327:   hx = 1.0/(PetscReal)(Mx-1);
328:   hy = 1.0/(PetscReal)(My-1);

330:   /* Get pointers to vector data */
331:   DMDAVecGetArray(da,U,&u);

333:   /* Get local grid boundaries */
334:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

336:   /* Compute function over the locally owned part of the grid */
337:   for (j=ys; j<ys+ym; j++) {
338:     y = j*hy;
339:     for (i=xs; i<xs+xm; i++) {
340:       x = i*hx;
341:       r = PetscSqrtReal((x-.3)*(x-.5) + (y-.5)*(y-.5));
342:       if (r < .125) u[j][i] = PetscExpReal(c*r*r*r);
343:       else u[j][i] = 0.0;
344:     }
345:   }

347:   /* Restore vectors */
348:   DMDAVecRestoreArray(da,U,&u);
349:   return(0);
350: }