Actual source code: ex13.c
petsc-3.7.5 2017-01-01
3: static char help[] = "Time-dependent PDE in 2d. Simplified from ex7.c for illustrating how to use TS on a structured domain. \n";
4: /*
5: u_t = uxx + uyy
6: 0 < x < 1, 0 < y < 1;
7: At t=0: u(x,y) = exp(c*r*r*r), if r=PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5)) < .125
8: u(x,y) = 0.0 if r >= .125
10: mpiexec -n 2 ./ex13 -da_grid_x 40 -da_grid_y 40 -ts_max_steps 2 -snes_monitor -ksp_monitor
11: mpiexec -n 1 ./ex13 -snes_fd_color -ts_monitor_draw_solution
12: mpiexec -n 2 ./ex13 -ts_type sundials -ts_monitor
13: */
15: #include <petscdm.h>
16: #include <petscdmda.h>
17: #include <petscts.h>
19: /*
20: User-defined data structures and routines
21: */
22: typedef struct {
23: PetscReal c;
24: } AppCtx;
26: extern PetscErrorCode RHSFunction(TS,PetscReal,Vec,Vec,void*);
27: extern PetscErrorCode RHSJacobian(TS,PetscReal,Vec,Mat,Mat,void*);
28: extern PetscErrorCode FormInitialSolution(DM,Vec,void*);
32: int main(int argc,char **argv)
33: {
34: TS ts; /* nonlinear solver */
35: Vec u,r; /* solution, residual vector */
36: Mat J; /* Jacobian matrix */
37: PetscInt steps,maxsteps = 1000; /* iterations for convergence */
39: DM da;
40: PetscReal ftime,dt;
41: AppCtx user; /* user-defined work context */
43: PetscInitialize(&argc,&argv,(char*)0,help);
44: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
45: Create distributed array (DMDA) to manage parallel grid and vectors
46: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
47: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-8,-8,PETSC_DECIDE,PETSC_DECIDE,
48: 1,1,NULL,NULL,&da);
50: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: Extract global vectors from DMDA;
52: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
53: DMCreateGlobalVector(da,&u);
54: VecDuplicate(u,&r);
56: /* Initialize user application context */
57: user.c = -30.0;
59: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60: Create timestepping solver context
61: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
62: TSCreate(PETSC_COMM_WORLD,&ts);
63: TSSetDM(ts,da);
64: TSSetType(ts,TSBEULER);
65: TSSetRHSFunction(ts,r,RHSFunction,&user);
67: /* Set Jacobian */
68: DMSetMatType(da,MATAIJ);
69: DMCreateMatrix(da,&J);
70: TSSetRHSJacobian(ts,J,J,RHSJacobian,NULL);
72: ftime = 1.0;
73: TSSetDuration(ts,maxsteps,ftime);
74: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
76: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
77: Set initial conditions
78: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
79: FormInitialSolution(da,u,&user);
80: dt = .01;
81: TSSetInitialTimeStep(ts,0.0,dt);
83: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
84: Set runtime options
85: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: TSSetFromOptions(ts);
88: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
89: Solve nonlinear system
90: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
91: TSSolve(ts,u);
92: TSGetSolveTime(ts,&ftime);
93: TSGetTimeStepNumber(ts,&steps);
95: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
96: Free work space.
97: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
98: MatDestroy(&J);
99: VecDestroy(&u);
100: VecDestroy(&r);
101: TSDestroy(&ts);
102: DMDestroy(&da);
104: PetscFinalize();
105: return(0);
106: }
107: /* ------------------------------------------------------------------- */
110: /*
111: RHSFunction - Evaluates nonlinear function, F(u).
113: Input Parameters:
114: . ts - the TS context
115: . U - input vector
116: . ptr - optional user-defined context, as set by TSSetFunction()
118: Output Parameter:
119: . F - function vector
120: */
121: PetscErrorCode RHSFunction(TS ts,PetscReal ftime,Vec U,Vec F,void *ptr)
122: {
123: /* PETSC_UNUSED AppCtx *user=(AppCtx*)ptr; */
124: DM da;
126: PetscInt i,j,Mx,My,xs,ys,xm,ym;
127: PetscReal two = 2.0,hx,hy,sx,sy;
128: PetscScalar u,uxx,uyy,**uarray,**f;
129: Vec localU;
132: TSGetDM(ts,&da);
133: DMGetLocalVector(da,&localU);
134: 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);
136: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
137: hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
139: /*
140: Scatter ghost points to local vector,using the 2-step process
141: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
142: By placing code between these two statements, computations can be
143: done while messages are in transition.
144: */
145: DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
146: DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);
148: /* Get pointers to vector data */
149: DMDAVecGetArrayRead(da,localU,&uarray);
150: DMDAVecGetArray(da,F,&f);
152: /* Get local grid boundaries */
153: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
155: /* Compute function over the locally owned part of the grid */
156: for (j=ys; j<ys+ym; j++) {
157: for (i=xs; i<xs+xm; i++) {
158: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
159: f[j][i] = uarray[j][i];
160: continue;
161: }
162: u = uarray[j][i];
163: uxx = (-two*u + uarray[j][i-1] + uarray[j][i+1])*sx;
164: uyy = (-two*u + uarray[j-1][i] + uarray[j+1][i])*sy;
165: f[j][i] = uxx + uyy;
166: }
167: }
169: /* Restore vectors */
170: DMDAVecRestoreArrayRead(da,localU,&uarray);
171: DMDAVecRestoreArray(da,F,&f);
172: DMRestoreLocalVector(da,&localU);
173: PetscLogFlops(11.0*ym*xm);
174: return(0);
175: }
177: /* --------------------------------------------------------------------- */
180: /*
181: RHSJacobian - User-provided routine to compute the Jacobian of
182: the nonlinear right-hand-side function of the ODE.
184: Input Parameters:
185: ts - the TS context
186: t - current time
187: U - global input vector
188: dummy - optional user-defined context, as set by TSetRHSJacobian()
190: Output Parameters:
191: J - Jacobian matrix
192: Jpre - optionally different preconditioning matrix
193: str - flag indicating matrix structure
194: */
195: PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat J,Mat Jpre,void *ctx)
196: {
198: DM da;
199: DMDALocalInfo info;
200: PetscInt i,j;
201: PetscReal hx,hy,sx,sy;
204: TSGetDM(ts,&da);
205: DMDAGetLocalInfo(da,&info);
206: hx = 1.0/(PetscReal)(info.mx-1); sx = 1.0/(hx*hx);
207: hy = 1.0/(PetscReal)(info.my-1); sy = 1.0/(hy*hy);
208: for (j=info.ys; j<info.ys+info.ym; j++) {
209: for (i=info.xs; i<info.xs+info.xm; i++) {
210: PetscInt nc = 0;
211: MatStencil row,col[5];
212: PetscScalar val[5];
213: row.i = i; row.j = j;
214: if (i == 0 || j == 0 || i == info.mx-1 || j == info.my-1) {
215: col[nc].i = i; col[nc].j = j; val[nc++] = 1.0;
216: } else {
217: col[nc].i = i-1; col[nc].j = j; val[nc++] = sx;
218: col[nc].i = i+1; col[nc].j = j; val[nc++] = sx;
219: col[nc].i = i; col[nc].j = j-1; val[nc++] = sy;
220: col[nc].i = i; col[nc].j = j+1; val[nc++] = sy;
221: col[nc].i = i; col[nc].j = j; val[nc++] = -2*sx - 2*sy;
222: }
223: MatSetValuesStencil(Jpre,1,&row,nc,col,val,INSERT_VALUES);
224: }
225: }
226: MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
227: MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
228: if (J != Jpre) {
229: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
230: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
231: }
232: return(0);
233: }
235: /* ------------------------------------------------------------------- */
238: PetscErrorCode FormInitialSolution(DM da,Vec U,void* ptr)
239: {
240: AppCtx *user=(AppCtx*)ptr;
241: PetscReal c=user->c;
243: PetscInt i,j,xs,ys,xm,ym,Mx,My;
244: PetscScalar **u;
245: PetscReal hx,hy,x,y,r;
248: DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
249: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
251: hx = 1.0/(PetscReal)(Mx-1);
252: hy = 1.0/(PetscReal)(My-1);
254: /* Get pointers to vector data */
255: DMDAVecGetArray(da,U,&u);
257: /* Get local grid boundaries */
258: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
260: /* Compute function over the locally owned part of the grid */
261: for (j=ys; j<ys+ym; j++) {
262: y = j*hy;
263: for (i=xs; i<xs+xm; i++) {
264: x = i*hx;
265: r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
266: if (r < .125) u[j][i] = PetscExpReal(c*r*r*r);
267: else u[j][i] = 0.0;
268: }
269: }
271: /* Restore vectors */
272: DMDAVecRestoreArray(da,U,&u);
273: return(0);
274: }