Actual source code: ex7.c
petsc-3.14.6 2021-03-30
2: static char help[] = "Nonlinear, time-dependent PDE in 2d.\n";
5: /*
6: Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
7: Include "petscts.h" so that we can use SNES solvers. Note that this
8: file automatically includes:
9: petscsys.h - base PETSc routines petscvec.h - vectors
10: petscmat.h - matrices
11: petscis.h - index sets petscksp.h - Krylov subspace methods
12: petscviewer.h - viewers petscpc.h - preconditioners
13: petscksp.h - linear solvers
14: */
15: #include <petscdm.h>
16: #include <petscdmda.h>
17: #include <petscts.h>
20: /*
21: User-defined routines
22: */
23: extern PetscErrorCode FormFunction(TS,PetscReal,Vec,Vec,void*),FormInitialSolution(DM,Vec);
24: extern PetscErrorCode MyTSMonitor(TS,PetscInt,PetscReal,Vec,void*);
25: extern PetscErrorCode MySNESMonitor(SNES,PetscInt,PetscReal,PetscViewerAndFormat*);
27: int main(int argc,char **argv)
28: {
29: TS ts; /* time integrator */
30: SNES snes;
31: Vec x,r; /* solution, residual vectors */
32: PetscErrorCode ierr;
33: DM da;
34: PetscViewerAndFormat *vf;
36: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
37: Initialize program
38: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
39: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
40: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
41: Create distributed array (DMDA) to manage parallel grid and vectors
42: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
43: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,8,8,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
44: DMSetFromOptions(da);
45: DMSetUp(da);
47: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
48: Extract global vectors from DMDA; then duplicate for remaining
49: vectors that are the same types
50: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
51: DMCreateGlobalVector(da,&x);
52: VecDuplicate(x,&r);
54: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: Create timestepping solver context
56: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
57: TSCreate(PETSC_COMM_WORLD,&ts);
58: TSSetProblemType(ts,TS_NONLINEAR);
59: TSSetRHSFunction(ts,NULL,FormFunction,da);
61: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
62: Create matrix data structure; set Jacobian evaluation routine
64: Set Jacobian matrix data structure and default Jacobian evaluation
65: routine. User can override with:
66: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
67: (unless user explicitly sets preconditioner)
68: -snes_mf_operator : form preconditioning matrix as set by the user,
69: but use matrix-free approx for Jacobian-vector
70: products within Newton-Krylov method
72: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
74: TSSetMaxTime(ts,1.0);
75: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
76: TSMonitorSet(ts,MyTSMonitor,PETSC_VIEWER_STDOUT_WORLD,NULL);
77: TSSetDM(ts,da);
78: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
79: Customize nonlinear solver
80: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
81: TSSetType(ts,TSBEULER);
82: TSGetSNES(ts,&snes);
83: PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,&vf);
84: SNESMonitorSet(snes,(PetscErrorCode (*)(SNES,PetscInt,PetscReal,void*))MySNESMonitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);
86: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87: Set initial conditions
88: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
89: FormInitialSolution(da,x);
90: TSSetTimeStep(ts,.0001);
91: TSSetSolution(ts,x);
93: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
94: Set runtime options
95: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
96: TSSetFromOptions(ts);
98: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
99: Solve nonlinear system
100: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101: TSSolve(ts,x);
103: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104: Free work space. All PETSc objects should be destroyed when they
105: are no longer needed.
106: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
107: VecDestroy(&x);
108: VecDestroy(&r);
109: TSDestroy(&ts);
110: DMDestroy(&da);
112: PetscFinalize();
113: return ierr;
114: }
115: /* ------------------------------------------------------------------- */
116: /*
117: FormFunction - Evaluates nonlinear function, F(x).
119: Input Parameters:
120: . ts - the TS context
121: . X - input vector
122: . ptr - optional user-defined context, as set by SNESSetFunction()
124: Output Parameter:
125: . F - function vector
126: */
127: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
128: {
129: DM da;
131: PetscInt i,j,Mx,My,xs,ys,xm,ym;
132: PetscReal two = 2.0,hx,hy,sx,sy;
133: PetscScalar u,uxx,uyy,**x,**f;
134: Vec localX;
137: TSGetDM(ts,&da);
138: DMGetLocalVector(da,&localX);
139: 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);
141: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
142: hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
144: /*
145: Scatter ghost points to local vector,using the 2-step process
146: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
147: By placing code between these two statements, computations can be
148: done while messages are in transition.
149: */
150: DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
151: DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
153: /*
154: Get pointers to vector data
155: */
156: DMDAVecGetArrayRead(da,localX,&x);
157: DMDAVecGetArray(da,F,&f);
159: /*
160: Get local grid boundaries
161: */
162: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
164: /*
165: Compute function over the locally owned part of the grid
166: */
167: for (j=ys; j<ys+ym; j++) {
168: for (i=xs; i<xs+xm; i++) {
169: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
170: f[j][i] = x[j][i];
171: continue;
172: }
173: u = x[j][i];
174: uxx = (two*u - x[j][i-1] - x[j][i+1])*sx;
175: uyy = (two*u - x[j-1][i] - x[j+1][i])*sy;
176: /* f[j][i] = -(uxx + uyy); */
177: 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 +
178: (x[j+1][i] - x[j-1][i])*(x[j+1][i] - x[j-1][i])*.25*sy);
179: }
180: }
182: /*
183: Restore vectors
184: */
185: DMDAVecRestoreArrayRead(da,localX,&x);
186: DMDAVecRestoreArray(da,F,&f);
187: DMRestoreLocalVector(da,&localX);
188: PetscLogFlops(11.0*ym*xm);
189: return(0);
190: }
192: /* ------------------------------------------------------------------- */
193: PetscErrorCode FormInitialSolution(DM da,Vec U)
194: {
196: PetscInt i,j,xs,ys,xm,ym,Mx,My;
197: PetscScalar **u;
198: PetscReal hx,hy,x,y,r;
201: 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);
203: hx = 1.0/(PetscReal)(Mx-1);
204: hy = 1.0/(PetscReal)(My-1);
206: /*
207: Get pointers to vector data
208: */
209: DMDAVecGetArray(da,U,&u);
211: /*
212: Get local grid boundaries
213: */
214: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
216: /*
217: Compute function over the locally owned part of the grid
218: */
219: for (j=ys; j<ys+ym; j++) {
220: y = j*hy;
221: for (i=xs; i<xs+xm; i++) {
222: x = i*hx;
223: r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
224: if (r < .125) u[j][i] = PetscExpReal(-30.0*r*r*r);
225: else u[j][i] = 0.0;
226: }
227: }
229: /*
230: Restore vectors
231: */
232: DMDAVecRestoreArray(da,U,&u);
233: return(0);
234: }
236: PetscErrorCode MyTSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec v,void *ctx)
237: {
239: PetscReal norm;
240: MPI_Comm comm;
243: if (step < 0) return(0); /* step of -1 indicates an interpolated solution */
244: VecNorm(v,NORM_2,&norm);
245: PetscObjectGetComm((PetscObject)ts,&comm);
246: PetscPrintf(comm,"timestep %D time %g norm %g\n",step,(double)ptime,(double)norm);
247: return(0);
248: }
250: /*
251: MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
252: Input Parameters:
253: snes - the SNES context
254: its - iteration number
255: fnorm - 2-norm function value (may be estimated)
256: ctx - optional user-defined context for private data for the
257: monitor routine, as set by SNESMonitorSet()
258: */
259: PetscErrorCode MySNESMonitor(SNES snes,PetscInt its,PetscReal fnorm,PetscViewerAndFormat *vf)
260: {
264: SNESMonitorDefaultShort(snes,its,fnorm,vf);
265: return(0);
266: }
268: /*TEST
270: test:
271: args: -ts_max_steps 5
273: test:
274: suffix: 2
275: args: -ts_max_steps 5 -snes_mf_operator
277: test:
278: suffix: 3
279: args: -ts_max_steps 5 -snes_mf -pc_type none
281: TEST*/