Actual source code: ex7.c
2: static char help[] = "Nonlinear, time-dependent PDE in 2d.\n";
4: /*
5: Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
6: Include "petscts.h" so that we can use SNES solvers. Note that this
7: file automatically includes:
8: petscsys.h - base PETSc routines petscvec.h - vectors
9: petscmat.h - matrices
10: petscis.h - index sets petscksp.h - Krylov subspace methods
11: petscviewer.h - viewers petscpc.h - preconditioners
12: petscksp.h - linear solvers
13: */
14: #include <petscdm.h>
15: #include <petscdmda.h>
16: #include <petscts.h>
18: /*
19: User-defined routines
20: */
21: extern PetscErrorCode FormFunction(TS,PetscReal,Vec,Vec,void*),FormInitialSolution(DM,Vec);
22: extern PetscErrorCode MyTSMonitor(TS,PetscInt,PetscReal,Vec,void*);
23: extern PetscErrorCode MySNESMonitor(SNES,PetscInt,PetscReal,PetscViewerAndFormat*);
25: int main(int argc,char **argv)
26: {
27: TS ts; /* time integrator */
28: SNES snes;
29: Vec x,r; /* solution, residual vectors */
30: PetscErrorCode ierr;
31: DM da;
32: PetscViewerAndFormat *vf;
34: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
35: Initialize program
36: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
37: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
38: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
39: Create distributed array (DMDA) to manage parallel grid and vectors
40: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
41: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,8,8,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
42: DMSetFromOptions(da);
43: DMSetUp(da);
45: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
46: Extract global vectors from DMDA; then duplicate for remaining
47: vectors that are the same types
48: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
49: DMCreateGlobalVector(da,&x);
50: VecDuplicate(x,&r);
52: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
53: Create timestepping solver context
54: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
55: TSCreate(PETSC_COMM_WORLD,&ts);
56: TSSetProblemType(ts,TS_NONLINEAR);
57: TSSetRHSFunction(ts,NULL,FormFunction,da);
59: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60: Create matrix data structure; set Jacobian evaluation routine
62: Set Jacobian matrix data structure and default Jacobian evaluation
63: routine. User can override with:
64: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
65: (unless user explicitly sets preconditioner)
66: -snes_mf_operator : form preconditioning matrix as set by the user,
67: but use matrix-free approx for Jacobian-vector
68: products within Newton-Krylov method
70: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
72: TSSetMaxTime(ts,1.0);
73: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
74: TSMonitorSet(ts,MyTSMonitor,PETSC_VIEWER_STDOUT_WORLD,NULL);
75: TSSetDM(ts,da);
76: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
77: Customize nonlinear solver
78: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
79: TSSetType(ts,TSBEULER);
80: TSGetSNES(ts,&snes);
81: PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
82: SNESMonitorSet(snes,(PetscErrorCode (*)(SNES,PetscInt,PetscReal,void*))MySNESMonitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: Set initial conditions
86: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
87: FormInitialSolution(da,x);
88: TSSetTimeStep(ts,.0001);
89: TSSetSolution(ts,x);
91: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92: Set runtime options
93: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94: TSSetFromOptions(ts);
96: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: Solve nonlinear system
98: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
99: TSSolve(ts,x);
101: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102: Free work space. All PETSc objects should be destroyed when they
103: are no longer needed.
104: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105: VecDestroy(&x);
106: VecDestroy(&r);
107: TSDestroy(&ts);
108: DMDestroy(&da);
110: PetscFinalize();
111: return ierr;
112: }
113: /* ------------------------------------------------------------------- */
114: /*
115: FormFunction - Evaluates nonlinear function, F(x).
117: Input Parameters:
118: . ts - the TS context
119: . X - input vector
120: . ptr - optional user-defined context, as set by SNESSetFunction()
122: Output Parameter:
123: . F - function vector
124: */
125: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
126: {
127: DM da;
129: PetscInt i,j,Mx,My,xs,ys,xm,ym;
130: PetscReal two = 2.0,hx,hy,sx,sy;
131: PetscScalar u,uxx,uyy,**x,**f;
132: Vec localX;
135: TSGetDM(ts,&da);
136: DMGetLocalVector(da,&localX);
137: 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);
139: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
140: hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
142: /*
143: Scatter ghost points to local vector,using the 2-step process
144: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
145: By placing code between these two statements, computations can be
146: done while messages are in transition.
147: */
148: DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
149: DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
151: /*
152: Get pointers to vector data
153: */
154: DMDAVecGetArrayRead(da,localX,&x);
155: DMDAVecGetArray(da,F,&f);
157: /*
158: Get local grid boundaries
159: */
160: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
162: /*
163: Compute function over the locally owned part of the grid
164: */
165: for (j=ys; j<ys+ym; j++) {
166: for (i=xs; i<xs+xm; i++) {
167: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
168: f[j][i] = x[j][i];
169: continue;
170: }
171: u = x[j][i];
172: uxx = (two*u - x[j][i-1] - x[j][i+1])*sx;
173: uyy = (two*u - x[j-1][i] - x[j+1][i])*sy;
174: /* f[j][i] = -(uxx + uyy); */
175: 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 +
176: (x[j+1][i] - x[j-1][i])*(x[j+1][i] - x[j-1][i])*.25*sy);
177: }
178: }
180: /*
181: Restore vectors
182: */
183: DMDAVecRestoreArrayRead(da,localX,&x);
184: DMDAVecRestoreArray(da,F,&f);
185: DMRestoreLocalVector(da,&localX);
186: PetscLogFlops(11.0*ym*xm);
187: return(0);
188: }
190: /* ------------------------------------------------------------------- */
191: PetscErrorCode FormInitialSolution(DM da,Vec U)
192: {
194: PetscInt i,j,xs,ys,xm,ym,Mx,My;
195: PetscScalar **u;
196: PetscReal hx,hy,x,y,r;
199: 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);
201: hx = 1.0/(PetscReal)(Mx-1);
202: hy = 1.0/(PetscReal)(My-1);
204: /*
205: Get pointers to vector data
206: */
207: DMDAVecGetArray(da,U,&u);
209: /*
210: Get local grid boundaries
211: */
212: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
214: /*
215: Compute function over the locally owned part of the grid
216: */
217: for (j=ys; j<ys+ym; j++) {
218: y = j*hy;
219: for (i=xs; i<xs+xm; i++) {
220: x = i*hx;
221: r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
222: if (r < .125) u[j][i] = PetscExpReal(-30.0*r*r*r);
223: else u[j][i] = 0.0;
224: }
225: }
227: /*
228: Restore vectors
229: */
230: DMDAVecRestoreArray(da,U,&u);
231: return(0);
232: }
234: PetscErrorCode MyTSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec v,void *ctx)
235: {
237: PetscReal norm;
238: MPI_Comm comm;
241: if (step < 0) return(0); /* step of -1 indicates an interpolated solution */
242: VecNorm(v,NORM_2,&norm);
243: PetscObjectGetComm((PetscObject)ts,&comm);
244: PetscPrintf(comm,"timestep %D time %g norm %g\n",step,(double)ptime,(double)norm);
245: return(0);
246: }
248: /*
249: MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
250: Input Parameters:
251: snes - the SNES context
252: its - iteration number
253: fnorm - 2-norm function value (may be estimated)
254: ctx - optional user-defined context for private data for the
255: monitor routine, as set by SNESMonitorSet()
256: */
257: PetscErrorCode MySNESMonitor(SNES snes,PetscInt its,PetscReal fnorm,PetscViewerAndFormat *vf)
258: {
262: SNESMonitorDefaultShort(snes,its,fnorm,vf);
263: return(0);
264: }
266: /*TEST
268: test:
269: args: -ts_max_steps 5
271: test:
272: suffix: 2
273: args: -ts_max_steps 5 -snes_mf_operator
275: test:
276: suffix: 3
277: args: -ts_max_steps 5 -snes_mf -pc_type none
279: TEST*/