Actual source code: ex15.c
petsc-3.11.4 2019-09-28
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
10: Boundary conditions:
11: Drichlet BC:
12: At x=0, x=1, y=0, y=1: u = 0.0
14: Neumann BC:
15: At x=0, x=1: du(x,y,t)/dx = 0
16: At y=0, y=1: du(x,y,t)/dy = 0
18: mpiexec -n 2 ./ex15 -da_grid_x 40 -da_grid_y 40 -ts_max_steps 2 -snes_monitor -ksp_monitor
19: ./ex15 -da_grid_x 40 -da_grid_y 40 -draw_pause .1 -boundary 1 -ts_monitor_draw_solution
20: ./ex15 -da_grid_x 40 -da_grid_y 40 -draw_pause .1 -boundary 1 -Jtype 2 -nstencilpts 9
22: */
24: #include <petscdm.h>
25: #include <petscdmda.h>
26: #include <petscts.h>
28: /*
29: User-defined data structures and routines
30: */
32: /* AppCtx: used by FormIFunction() and FormIJacobian() */
33: typedef struct {
34: DM da;
35: PetscInt nstencilpts; /* number of stencil points: 5 or 9 */
36: PetscReal c;
37: PetscInt boundary; /* Type of boundary condition */
38: PetscBool viewJacobian;
39: } AppCtx;
41: extern PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*);
42: extern PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);
43: extern PetscErrorCode FormInitialSolution(Vec,void*);
45: int main(int argc,char **argv)
46: {
47: TS ts; /* nonlinear solver */
48: Vec u,r; /* solution, residual vectors */
49: Mat J,Jmf = NULL; /* Jacobian matrices */
51: DM da;
52: PetscReal dt;
53: AppCtx user; /* user-defined work context */
54: SNES snes;
55: PetscInt Jtype; /* Jacobian type
56: 0: user provide Jacobian;
57: 1: slow finite difference;
58: 2: fd with coloring; */
60: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
61: /* Initialize user application context */
62: user.da = NULL;
63: user.nstencilpts = 5;
64: user.c = -30.0;
65: user.boundary = 0; /* 0: Drichlet BC; 1: Neumann BC */
66: user.viewJacobian = PETSC_FALSE;
68: PetscOptionsGetInt(NULL,NULL,"-nstencilpts",&user.nstencilpts,NULL);
69: PetscOptionsGetInt(NULL,NULL,"-boundary",&user.boundary,NULL);
70: PetscOptionsHasName(NULL,NULL,"-viewJacobian",&user.viewJacobian);
72: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
73: Create distributed array (DMDA) to manage parallel grid and vectors
74: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
75: if (user.nstencilpts == 5) {
76: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
77: } else if (user.nstencilpts == 9) {
78: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
79: } else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"nstencilpts %d is not supported",user.nstencilpts);
80: DMSetFromOptions(da);
81: DMSetUp(da);
82: user.da = da;
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: Extract global vectors from DMDA;
86: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
87: DMCreateGlobalVector(da,&u);
88: VecDuplicate(u,&r);
90: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
91: Create timestepping solver context
92: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
93: TSCreate(PETSC_COMM_WORLD,&ts);
94: TSSetProblemType(ts,TS_NONLINEAR);
95: TSSetType(ts,TSBEULER);
96: TSSetDM(ts,da);
97: TSSetIFunction(ts,r,FormIFunction,&user);
98: TSSetMaxTime(ts,1.0);
99: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
101: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102: Set initial conditions
103: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
104: FormInitialSolution(u,&user);
105: TSSetSolution(ts,u);
106: dt = .01;
107: TSSetTimeStep(ts,dt);
109: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110: Set Jacobian evaluation routine
111: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
112: DMSetMatType(da,MATAIJ);
113: DMCreateMatrix(da,&J);
114: Jtype = 0;
115: PetscOptionsGetInt(NULL,NULL, "-Jtype",&Jtype,NULL);
116: if (Jtype == 0) { /* use user provided Jacobian evaluation routine */
117: if (user.nstencilpts != 5) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"user Jacobian routine FormIJacobian() does not support nstencilpts=%D",user.nstencilpts);
118: TSSetIJacobian(ts,J,J,FormIJacobian,&user);
119: } else { /* use finite difference Jacobian J as preconditioner and '-snes_mf_operator' for Mat*vec */
120: TSGetSNES(ts,&snes);
121: MatCreateSNESMF(snes,&Jmf);
122: if (Jtype == 1) { /* slow finite difference J; */
123: SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefault,NULL);
124: } else if (Jtype == 2) { /* Use coloring to compute finite difference J efficiently */
125: SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefaultColor,0);
126: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Jtype is not supported");
127: }
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: Sets various TS parameters from user options
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
132: TSSetFromOptions(ts);
134: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135: Solve nonlinear system
136: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137: TSSolve(ts,u);
139: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140: Free work space.
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
142: MatDestroy(&J);
143: MatDestroy(&Jmf);
144: VecDestroy(&u);
145: VecDestroy(&r);
146: TSDestroy(&ts);
147: DMDestroy(&da);
149: PetscFinalize();
150: return ierr;
151: }
153: /* --------------------------------------------------------------------- */
154: /*
155: FormIFunction = Udot - RHSFunction
156: */
157: PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
158: {
160: AppCtx *user=(AppCtx*)ctx;
161: DM da = (DM)user->da;
162: PetscInt i,j,Mx,My,xs,ys,xm,ym;
163: PetscReal hx,hy,sx,sy;
164: PetscScalar u,uxx,uyy,**uarray,**f,**udot;
165: Vec localU;
168: DMGetLocalVector(da,&localU);
169: 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);
171: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
172: hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
173: if (user->nstencilpts == 9 && hx != hy) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"hx must equal hy when nstencilpts = 9 for this example");
175: /*
176: Scatter ghost points to local vector,using the 2-step process
177: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
178: By placing code between these two statements, computations can be
179: done while messages are in transition.
180: */
181: DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
182: DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);
184: /* Get pointers to vector data */
185: DMDAVecGetArrayRead(da,localU,&uarray);
186: DMDAVecGetArray(da,F,&f);
187: DMDAVecGetArray(da,Udot,&udot);
189: /* Get local grid boundaries */
190: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
192: /* Compute function over the locally owned part of the grid */
193: for (j=ys; j<ys+ym; j++) {
194: for (i=xs; i<xs+xm; i++) {
195: /* Boundary conditions */
196: if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
197: if (user->boundary == 0) { /* Drichlet BC */
198: f[j][i] = uarray[j][i]; /* F = U */
199: } else { /* Neumann BC */
200: if (i == 0 && j == 0) { /* SW corner */
201: f[j][i] = uarray[j][i] - uarray[j+1][i+1];
202: } else if (i == Mx-1 && j == 0) { /* SE corner */
203: f[j][i] = uarray[j][i] - uarray[j+1][i-1];
204: } else if (i == 0 && j == My-1) { /* NW corner */
205: f[j][i] = uarray[j][i] - uarray[j-1][i+1];
206: } else if (i == Mx-1 && j == My-1) { /* NE corner */
207: f[j][i] = uarray[j][i] - uarray[j-1][i-1];
208: } else if (i == 0) { /* Left */
209: f[j][i] = uarray[j][i] - uarray[j][i+1];
210: } else if (i == Mx-1) { /* Right */
211: f[j][i] = uarray[j][i] - uarray[j][i-1];
212: } else if (j == 0) { /* Bottom */
213: f[j][i] = uarray[j][i] - uarray[j+1][i];
214: } else if (j == My-1) { /* Top */
215: f[j][i] = uarray[j][i] - uarray[j-1][i];
216: }
217: }
218: } else { /* Interior */
219: u = uarray[j][i];
220: /* 5-point stencil */
221: uxx = (-2.0*u + uarray[j][i-1] + uarray[j][i+1]);
222: uyy = (-2.0*u + uarray[j-1][i] + uarray[j+1][i]);
223: if (user->nstencilpts == 9) {
224: /* 9-point stencil: assume hx=hy */
225: 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;
226: 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;
227: }
228: f[j][i] = udot[j][i] - (uxx*sx + uyy*sy);
229: }
230: }
231: }
233: /* Restore vectors */
234: DMDAVecRestoreArrayRead(da,localU,&uarray);
235: DMDAVecRestoreArray(da,F,&f);
236: DMDAVecRestoreArray(da,Udot,&udot);
237: DMRestoreLocalVector(da,&localU);
238: PetscLogFlops(11.0*ym*xm);
239: return(0);
240: }
242: /* --------------------------------------------------------------------- */
243: /*
244: FormIJacobian() - Compute IJacobian = dF/dU + a dF/dUdot
245: This routine is not used with option '-use_coloring'
246: */
247: PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx)
248: {
250: PetscInt i,j,Mx,My,xs,ys,xm,ym,nc;
251: AppCtx *user = (AppCtx*)ctx;
252: DM da = (DM)user->da;
253: MatStencil col[5],row;
254: PetscScalar vals[5],hx,hy,sx,sy;
257: 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);
258: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
260: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
261: hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
263: for (j=ys; j<ys+ym; j++) {
264: for (i=xs; i<xs+xm; i++) {
265: nc = 0;
266: row.j = j; row.i = i;
267: if (user->boundary == 0 && (i == 0 || i == Mx-1 || j == 0 || j == My-1)) {
268: col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
270: } else if (user->boundary > 0 && i == 0) { /* Left Neumann */
271: col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
272: col[nc].j = j; col[nc].i = i+1; vals[nc++] = -1.0;
273: } else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */
274: col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
275: col[nc].j = j; col[nc].i = i-1; vals[nc++] = -1.0;
276: } else if (user->boundary > 0 && j == 0) { /* Bottom Neumann */
277: col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
278: col[nc].j = j+1; col[nc].i = i; vals[nc++] = -1.0;
279: } else if (user->boundary > 0 && j == My-1) { /* Top Neumann */
280: col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
281: col[nc].j = j-1; col[nc].i = i; vals[nc++] = -1.0;
282: } else { /* Interior */
283: col[nc].j = j-1; col[nc].i = i; vals[nc++] = -sy;
284: col[nc].j = j; col[nc].i = i-1; vals[nc++] = -sx;
285: col[nc].j = j; col[nc].i = i; vals[nc++] = 2.0*(sx + sy) + a;
286: col[nc].j = j; col[nc].i = i+1; vals[nc++] = -sx;
287: col[nc].j = j+1; col[nc].i = i; vals[nc++] = -sy;
288: }
289: MatSetValuesStencil(Jpre,1,&row,nc,col,vals,INSERT_VALUES);
290: }
291: }
292: MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
293: MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
294: if (J != Jpre) {
295: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
296: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
297: }
299: if (user->viewJacobian) {
300: PetscPrintf(PetscObjectComm((PetscObject)Jpre),"Jpre:\n");
301: MatView(Jpre,PETSC_VIEWER_STDOUT_WORLD);
302: }
303: return(0);
304: }
306: /* ------------------------------------------------------------------- */
307: PetscErrorCode FormInitialSolution(Vec U,void *ptr)
308: {
309: AppCtx *user=(AppCtx*)ptr;
310: DM da =user->da;
311: PetscReal c =user->c;
313: PetscInt i,j,xs,ys,xm,ym,Mx,My;
314: PetscScalar **u;
315: PetscReal hx,hy,x,y,r;
318: 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);
320: hx = 1.0/(PetscReal)(Mx-1);
321: hy = 1.0/(PetscReal)(My-1);
323: /* Get pointers to vector data */
324: DMDAVecGetArray(da,U,&u);
326: /* Get local grid boundaries */
327: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
329: /* Compute function over the locally owned part of the grid */
330: for (j=ys; j<ys+ym; j++) {
331: y = j*hy;
332: for (i=xs; i<xs+xm; i++) {
333: x = i*hx;
334: r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
335: if (r < .125) u[j][i] = PetscExpReal(c*r*r*r);
336: else u[j][i] = 0.0;
337: }
338: }
340: /* Restore vectors */
341: DMDAVecRestoreArray(da,U,&u);
342: return(0);
343: }
345: /*TEST
347: test:
348: args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -ts_monitor
350: test:
351: suffix: 2
352: args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -Jtype 2 -ts_monitor
354: test:
355: suffix: 3
356: requires: !single
357: args: -da_grid_x 20 -da_grid_y 20 -boundary 1 -ts_max_steps 10 -ts_monitor
359: test:
360: suffix: 4
361: requires: !single
362: nsize: 2
363: args: -da_grid_x 20 -da_grid_y 20 -boundary 1 -ts_max_steps 10 -ts_monitor
365: test:
366: suffix: 5
367: nsize: 1
368: args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -Jtype 1 -ts_monitor
371: TEST*/