Actual source code: ex15.c
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
9: Boundary conditions:
10: Drichlet BC:
11: At x=0, x=1, y=0, y=1: u = 0.0
13: Neumann BC:
14: At x=0, x=1: du(x,y,t)/dx = 0
15: At y=0, y=1: du(x,y,t)/dy = 0
17: mpiexec -n 2 ./ex15 -da_grid_x 40 -da_grid_y 40 -ts_max_steps 2 -snes_monitor -ksp_monitor
18: ./ex15 -da_grid_x 40 -da_grid_y 40 -draw_pause .1 -boundary 1 -ts_monitor_draw_solution
19: ./ex15 -da_grid_x 40 -da_grid_y 40 -draw_pause .1 -boundary 1 -Jtype 2 -nstencilpts 9
21: */
23: #include <petscdm.h>
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,void*);
42: extern PetscErrorCode FormInitialSolution(Vec,void*);
44: int main(int argc,char **argv)
45: {
46: TS ts; /* nonlinear solver */
47: Vec u,r; /* solution, residual vectors */
48: Mat J,Jmf = NULL; /* Jacobian matrices */
50: DM da;
51: PetscReal dt;
52: AppCtx user; /* user-defined work context */
53: SNES snes;
54: PetscInt Jtype; /* Jacobian type
55: 0: user provide Jacobian;
56: 1: slow finite difference;
57: 2: fd with coloring; */
59: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
60: /* Initialize user application context */
61: user.da = NULL;
62: user.nstencilpts = 5;
63: user.c = -30.0;
64: user.boundary = 0; /* 0: Drichlet BC; 1: Neumann BC */
65: user.viewJacobian = PETSC_FALSE;
67: PetscOptionsGetInt(NULL,NULL,"-nstencilpts",&user.nstencilpts,NULL);
68: PetscOptionsGetInt(NULL,NULL,"-boundary",&user.boundary,NULL);
69: PetscOptionsHasName(NULL,NULL,"-viewJacobian",&user.viewJacobian);
71: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
72: Create distributed array (DMDA) to manage parallel grid and vectors
73: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
74: if (user.nstencilpts == 5) {
75: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
76: } else if (user.nstencilpts == 9) {
77: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
78: } else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"nstencilpts %d is not supported",user.nstencilpts);
79: DMSetFromOptions(da);
80: DMSetUp(da);
81: user.da = da;
83: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
84: Extract global vectors from DMDA;
85: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: DMCreateGlobalVector(da,&u);
87: VecDuplicate(u,&r);
89: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
90: Create timestepping solver context
91: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
92: TSCreate(PETSC_COMM_WORLD,&ts);
93: TSSetProblemType(ts,TS_NONLINEAR);
94: TSSetType(ts,TSBEULER);
95: TSSetDM(ts,da);
96: TSSetIFunction(ts,r,FormIFunction,&user);
97: TSSetMaxTime(ts,1.0);
98: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
100: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101: Set initial conditions
102: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
103: FormInitialSolution(u,&user);
104: TSSetSolution(ts,u);
105: dt = .01;
106: TSSetTimeStep(ts,dt);
108: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109: Set Jacobian evaluation routine
110: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
111: DMSetMatType(da,MATAIJ);
112: DMCreateMatrix(da,&J);
113: Jtype = 0;
114: PetscOptionsGetInt(NULL,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 ierr;
150: }
152: /* --------------------------------------------------------------------- */
153: /*
154: FormIFunction = Udot - RHSFunction
155: */
156: PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
157: {
159: AppCtx *user=(AppCtx*)ctx;
160: DM da = (DM)user->da;
161: PetscInt i,j,Mx,My,xs,ys,xm,ym;
162: PetscReal hx,hy,sx,sy;
163: PetscScalar u,uxx,uyy,**uarray,**f,**udot;
164: Vec localU;
167: DMGetLocalVector(da,&localU);
168: 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);
170: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
171: hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
172: if (user->nstencilpts == 9 && hx != hy) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"hx must equal hy when nstencilpts = 9 for this example");
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: DMDAVecGetArrayRead(da,localU,&uarray);
185: DMDAVecGetArray(da,F,&f);
186: DMDAVecGetArray(da,Udot,&udot);
188: /* Get local grid boundaries */
189: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
191: /* Compute function over the locally owned part of the grid */
192: for (j=ys; j<ys+ym; j++) {
193: for (i=xs; i<xs+xm; i++) {
194: /* Boundary conditions */
195: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
196: if (user->boundary == 0) { /* Drichlet BC */
197: f[j][i] = uarray[j][i]; /* F = U */
198: } else { /* Neumann BC */
199: if (i == 0 && j == 0) { /* SW corner */
200: f[j][i] = uarray[j][i] - uarray[j+1][i+1];
201: } else if (i == Mx-1 && j == 0) { /* SE corner */
202: f[j][i] = uarray[j][i] - uarray[j+1][i-1];
203: } else if (i == 0 && j == My-1) { /* NW corner */
204: f[j][i] = uarray[j][i] - uarray[j-1][i+1];
205: } else if (i == Mx-1 && j == My-1) { /* NE corner */
206: f[j][i] = uarray[j][i] - uarray[j-1][i-1];
207: } else if (i == 0) { /* Left */
208: f[j][i] = uarray[j][i] - uarray[j][i+1];
209: } else if (i == Mx-1) { /* Right */
210: f[j][i] = uarray[j][i] - uarray[j][i-1];
211: } else if (j == 0) { /* Bottom */
212: f[j][i] = uarray[j][i] - uarray[j+1][i];
213: } else if (j == My-1) { /* Top */
214: f[j][i] = uarray[j][i] - uarray[j-1][i];
215: }
216: }
217: } else { /* Interior */
218: u = uarray[j][i];
219: /* 5-point stencil */
220: uxx = (-2.0*u + uarray[j][i-1] + uarray[j][i+1]);
221: uyy = (-2.0*u + uarray[j-1][i] + uarray[j+1][i]);
222: if (user->nstencilpts == 9) {
223: /* 9-point stencil: assume hx=hy */
224: 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;
225: 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;
226: }
227: f[j][i] = udot[j][i] - (uxx*sx + uyy*sy);
228: }
229: }
230: }
232: /* Restore vectors */
233: DMDAVecRestoreArrayRead(da,localU,&uarray);
234: DMDAVecRestoreArray(da,F,&f);
235: DMDAVecRestoreArray(da,Udot,&udot);
236: DMRestoreLocalVector(da,&localU);
237: PetscLogFlops(11.0*ym*xm);
238: return(0);
239: }
241: /* --------------------------------------------------------------------- */
242: /*
243: FormIJacobian() - Compute IJacobian = dF/dU + a dF/dUdot
244: This routine is not used with option '-use_coloring'
245: */
246: PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx)
247: {
249: PetscInt i,j,Mx,My,xs,ys,xm,ym,nc;
250: AppCtx *user = (AppCtx*)ctx;
251: DM da = (DM)user->da;
252: MatStencil col[5],row;
253: PetscScalar vals[5],hx,hy,sx,sy;
256: 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);
257: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
259: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
260: hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
262: for (j=ys; j<ys+ym; j++) {
263: for (i=xs; i<xs+xm; i++) {
264: nc = 0;
265: row.j = j; row.i = i;
266: if (user->boundary == 0 && (i == 0 || i == Mx-1 || j == 0 || j == My-1)) {
267: col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
269: } else if (user->boundary > 0 && i == 0) { /* Left Neumann */
270: col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
271: col[nc].j = j; col[nc].i = i+1; vals[nc++] = -1.0;
272: } else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */
273: col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
274: col[nc].j = j; col[nc].i = i-1; vals[nc++] = -1.0;
275: } else if (user->boundary > 0 && j == 0) { /* Bottom Neumann */
276: col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
277: col[nc].j = j+1; col[nc].i = i; vals[nc++] = -1.0;
278: } else if (user->boundary > 0 && j == My-1) { /* Top Neumann */
279: col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
280: col[nc].j = j-1; col[nc].i = i; vals[nc++] = -1.0;
281: } else { /* Interior */
282: col[nc].j = j-1; col[nc].i = i; vals[nc++] = -sy;
283: col[nc].j = j; col[nc].i = i-1; vals[nc++] = -sx;
284: col[nc].j = j; col[nc].i = i; vals[nc++] = 2.0*(sx + sy) + a;
285: col[nc].j = j; col[nc].i = i+1; vals[nc++] = -sx;
286: col[nc].j = j+1; col[nc].i = i; vals[nc++] = -sy;
287: }
288: MatSetValuesStencil(Jpre,1,&row,nc,col,vals,INSERT_VALUES);
289: }
290: }
291: MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
292: MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
293: if (J != Jpre) {
294: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
295: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
296: }
298: if (user->viewJacobian) {
299: PetscPrintf(PetscObjectComm((PetscObject)Jpre),"Jpre:\n");
300: MatView(Jpre,PETSC_VIEWER_STDOUT_WORLD);
301: }
302: return(0);
303: }
305: /* ------------------------------------------------------------------- */
306: PetscErrorCode FormInitialSolution(Vec U,void *ptr)
307: {
308: AppCtx *user=(AppCtx*)ptr;
309: DM da =user->da;
310: PetscReal c =user->c;
312: PetscInt i,j,xs,ys,xm,ym,Mx,My;
313: PetscScalar **u;
314: PetscReal hx,hy,x,y,r;
317: 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);
319: hx = 1.0/(PetscReal)(Mx-1);
320: hy = 1.0/(PetscReal)(My-1);
322: /* Get pointers to vector data */
323: DMDAVecGetArray(da,U,&u);
325: /* Get local grid boundaries */
326: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
328: /* Compute function over the locally owned part of the grid */
329: for (j=ys; j<ys+ym; j++) {
330: y = j*hy;
331: for (i=xs; i<xs+xm; i++) {
332: x = i*hx;
333: r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
334: if (r < .125) u[j][i] = PetscExpReal(c*r*r*r);
335: else u[j][i] = 0.0;
336: }
337: }
339: /* Restore vectors */
340: DMDAVecRestoreArray(da,U,&u);
341: return(0);
342: }
344: /*TEST
346: test:
347: args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -ts_monitor
349: test:
350: suffix: 2
351: args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -Jtype 2 -ts_monitor
353: test:
354: suffix: 3
355: requires: !single
356: args: -da_grid_x 20 -da_grid_y 20 -boundary 1 -ts_max_steps 10 -ts_monitor
358: test:
359: suffix: 4
360: requires: !single
361: nsize: 2
362: args: -da_grid_x 20 -da_grid_y 20 -boundary 1 -ts_max_steps 10 -ts_monitor
364: test:
365: suffix: 5
366: nsize: 1
367: args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -Jtype 1 -ts_monitor
369: TEST*/