Actual source code: ex17.c

petsc-3.5.0 2014-06-30
Report Typos and Errors
  1: static const char help[] = "Time-dependent PDE in 1d. Simplified from ex15.c for illustrating how to solve DAEs. \n";
  2: /*
  3:    u_t = uxx
  4:    0 < x < 1;
  5:    At t=0: u(x) = exp(c*r*r*r), if r=PetscSqrtReal((x-.5)*(x-.5)) < .125
  6:            u(x) = 0.0           if r >= .125


  9:    Boundary conditions:
 10:    Dirichlet BC:
 11:    At x=0, x=1, u = 0.0

 13:    Neumann BC:
 14:    At x=0, x=1: du(x,t)/dx = 0

 16:    mpiexec -n 2 ./ex17 -da_grid_x 40 -ts_max_steps 2 -snes_monitor -ksp_monitor
 17:          ./ex17 -da_grid_x 40 -monitor_solution
 18:          ./ex17 -da_grid_x 100  -ts_type theta -ts_theta_theta 0.5 # Midpoint is not L-stable
 19:          ./ex17 -jac_type fd_coloring  -da_grid_x 500 -boundary 1
 20:          ./ex17 -da_grid_x 100  -ts_type gl -ts_adapt_type none -ts_max_steps 2
 21: */

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

 27: typedef enum {JACOBIAN_ANALYTIC,JACOBIAN_FD_COLORING,JACOBIAN_FD_FULL} JacobianType;
 28: static const char *const JacobianTypes[] = {"analytic","fd_coloring","fd_full","JacobianType","fd_",0};

 30: /*
 31:    User-defined data structures and routines
 32: */
 33: typedef struct {
 34:   PetscReal c;
 35:   PetscInt  boundary;            /* Type of boundary condition */
 36:   PetscBool viewJacobian;
 37: } AppCtx;

 39: static PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*);
 40: static PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);
 41: static PetscErrorCode FormInitialSolution(TS,Vec,void*);

 45: int main(int argc,char **argv)
 46: {
 47:   TS             ts;                   /* nonlinear solver */
 48:   Vec            u;                    /* solution, residual vectors */
 49:   Mat            J;                    /* Jacobian matrix */
 50:   PetscInt       maxsteps = 1000;     /* iterations for convergence */
 51:   PetscInt       nsteps;
 52:   PetscReal      vmin,vmax,norm;
 54:   DM             da;
 55:   PetscReal      ftime,dt;
 56:   AppCtx         user;              /* user-defined work context */
 57:   JacobianType   jacType;

 59:   PetscInitialize(&argc,&argv,(char*)0,help);

 61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 62:      Create distributed array (DMDA) to manage parallel grid and vectors
 63:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 64:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,-11,1,1,NULL,&da);

 66:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 67:      Extract global vectors from DMDA;
 68:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 69:   DMCreateGlobalVector(da,&u);

 71:   /* Initialize user application context */
 72:   user.c            = -30.0;
 73:   user.boundary     = 0;  /* 0: Dirichlet BC; 1: Neumann BC */
 74:   user.viewJacobian = PETSC_FALSE;

 76:   PetscOptionsGetInt(NULL,"-boundary",&user.boundary,NULL);
 77:   PetscOptionsHasName(NULL,"-viewJacobian",&user.viewJacobian);

 79:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 80:      Create timestepping solver context
 81:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 82:   TSCreate(PETSC_COMM_WORLD,&ts);
 83:   TSSetProblemType(ts,TS_NONLINEAR);
 84:   TSSetType(ts,TSTHETA);
 85:   TSThetaSetTheta(ts,1.0); /* Make the Theta method behave like backward Euler */
 86:   TSSetIFunction(ts,NULL,FormIFunction,&user);

 88:   DMSetMatType(da,MATAIJ);
 89:   DMCreateMatrix(da,&J);
 90:   jacType = JACOBIAN_ANALYTIC; /* use user-provide Jacobian */

 92:   TSSetDM(ts,da); /* Use TSGetDM() to access. Setting here allows easy use of geometric multigrid. */

 94:   ftime = 1.0;
 95:   TSSetDuration(ts,maxsteps,ftime);

 97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 98:      Set initial conditions
 99:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100:   FormInitialSolution(ts,u,&user);
101:   TSSetSolution(ts,u);
102:   dt   = .01;
103:   TSSetInitialTimeStep(ts,0.0,dt);


106:   /* Use slow fd Jacobian or fast fd Jacobian with colorings.
107:      Note: this requirs snes which is not created until TSSetUp()/TSSetFromOptions() is called */
108:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Options for Jacobian evaluation",NULL);
109:   PetscOptionsEnum("-jac_type","Type of Jacobian","",JacobianTypes,(PetscEnum)jacType,(PetscEnum*)&jacType,0);
110:   PetscOptionsEnd();
111:   if (jacType == JACOBIAN_ANALYTIC) {
112:     TSSetIJacobian(ts,J,J,FormIJacobian,&user);
113:   } else if (jacType == JACOBIAN_FD_COLORING) {
114:     SNES snes;
115:     TSGetSNES(ts,&snes);
116:     SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,0);
117:   } else if (jacType == JACOBIAN_FD_FULL) {
118:     SNES snes;
119:     TSGetSNES(ts,&snes);
120:     SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,&user);
121:   }

123:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
124:      Set runtime options
125:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
126:   TSSetFromOptions(ts);

128:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129:      Integrate ODE system
130:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131:   TSSolve(ts,u);

133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134:    Compute diagnostics of the solution
135:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
136:   VecNorm(u,NORM_1,&norm);
137:   VecMax(u,NULL,&vmax);
138:   VecMin(u,NULL,&vmin);
139:   TSGetTimeStepNumber(ts,&nsteps);
140:   TSGetTime(ts,&ftime);
141:   PetscPrintf(PETSC_COMM_WORLD,"timestep %D: time %g, solution norm %g, max %g, min %g\n",nsteps,(double)ftime,(double)norm,(double)vmax,(double)vmin);

143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144:      Free work space.
145:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
146:   MatDestroy(&J);
147:   VecDestroy(&u);
148:   TSDestroy(&ts);
149:   DMDestroy(&da);
150:   PetscFinalize();
151:   return(0);
152: }
153: /* ------------------------------------------------------------------- */
156: static PetscErrorCode FormIFunction(TS ts,PetscReal ftime,Vec U,Vec Udot,Vec F,void *ptr)
157: {
158:   AppCtx         *user=(AppCtx*)ptr;
159:   DM             da;
161:   PetscInt       i,Mx,xs,xm;
162:   PetscReal      hx,sx;
163:   PetscScalar    *u,*udot,*f;
164:   Vec            localU;

167:   TSGetDM(ts,&da);
168:   DMGetLocalVector(da,&localU);
169:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
170:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

172:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);

174:   /*
175:      Scatter ghost points to local vector,using the 2-step process
176:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
177:      By placing code between these two statements, computations can be
178:      done while messages are in transition.
179:   */
180:   DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
181:   DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);

183:   /* Get pointers to vector data */
184:   DMDAVecGetArray(da,localU,&u);
185:   DMDAVecGetArray(da,Udot,&udot);
186:   DMDAVecGetArray(da,F,&f);

188:   /* Get local grid boundaries */
189:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

191:   /* Compute function over the locally owned part of the grid */
192:   for (i=xs; i<xs+xm; i++) {
193:     if (user->boundary == 0) { /* Dirichlet BC */
194:       if (i == 0 || i == Mx-1) f[i] = u[i]; /* F = U */
195:       else                     f[i] = udot[i] + (2.*u[i] - u[i-1] - u[i+1])*sx;
196:     } else { /* Neumann BC */
197:       if (i == 0)         f[i] = u[0] - u[1];
198:       else if (i == Mx-1) f[i] = u[i] - u[i-1];
199:       else                f[i] = udot[i] + (2.*u[i] - u[i-1] - u[i+1])*sx;
200:     }
201:   }

203:   /* Restore vectors */
204:   DMDAVecRestoreArray(da,localU,&u);
205:   DMDAVecRestoreArray(da,Udot,&udot);
206:   DMDAVecRestoreArray(da,F,&f);
207:   DMRestoreLocalVector(da,&localU);
208:   return(0);
209: }

211: /* --------------------------------------------------------------------- */
212: /*
213:   IJacobian - Compute IJacobian = dF/dU + a dF/dUdot
214: */
217: PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx)
218: {
220:   PetscInt       i,rstart,rend,Mx;
221:   PetscReal      hx,sx;
222:   AppCtx         *user = (AppCtx*)ctx;
223:   DM             da;
224:   MatStencil     col[3],row;
225:   PetscInt       nc;
226:   PetscScalar    vals[3];

229:   TSGetDM(ts,&da);
230:   MatGetOwnershipRange(Jpre,&rstart,&rend);
231:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
232:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
233:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
234:   for (i=rstart; i<rend; i++) {
235:     nc    = 0;
236:     row.i = i;
237:     if (user->boundary == 0 && (i == 0 || i == Mx-1)) {
238:       col[nc].i = i; vals[nc++] = 1.0;
239:     } else if (user->boundary > 0 && i == 0) { /* Left Neumann */
240:       col[nc].i = i;   vals[nc++] = 1.0;
241:       col[nc].i = i+1; vals[nc++] = -1.0;
242:     } else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */
243:       col[nc].i = i-1; vals[nc++] = -1.0;
244:       col[nc].i = i;   vals[nc++] = 1.0;
245:     } else {                    /* Interior */
246:       col[nc].i = i-1; vals[nc++] = -1.0*sx;
247:       col[nc].i = i;   vals[nc++] = 2.0*sx + a;
248:       col[nc].i = i+1; vals[nc++] = -1.0*sx;
249:     }
250:     MatSetValuesStencil(Jpre,1,&row,nc,col,vals,INSERT_VALUES);
251:   }

253:   MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
254:   MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
255:   if (J != Jpre) {
256:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
257:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
258:   }
259:   if (user->viewJacobian) {
260:     PetscPrintf(PETSC_COMM_WORLD,"Jpre:\n");
261:     MatView(Jpre,PETSC_VIEWER_STDOUT_WORLD);
262:   }
263:   return(0);
264: }

266: /* ------------------------------------------------------------------- */
269: PetscErrorCode FormInitialSolution(TS ts,Vec U,void *ptr)
270: {
271:   AppCtx         *user=(AppCtx*)ptr;
272:   PetscReal      c    =user->c;
273:   DM             da;
275:   PetscInt       i,xs,xm,Mx;
276:   PetscScalar    *u;
277:   PetscReal      hx,x,r;

280:   TSGetDM(ts,&da);
281:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
282:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

284:   hx = 1.0/(PetscReal)(Mx-1);

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

289:   /* Get local grid boundaries */
290:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

292:   /* Compute function over the locally owned part of the grid */
293:   for (i=xs; i<xs+xm; i++) {
294:     x = i*hx;
295:     r = PetscSqrtReal((x-.5)*(x-.5));
296:     if (r < .125) u[i] = PetscExpReal(c*r*r*r);
297:     else          u[i] = 0.0;
298:   }

300:   /* Restore vectors */
301:   DMDAVecRestoreArray(da,U,&u);
302:   return(0);
303: }