Actual source code: ex17.c
petsc-3.7.5 2017-01-01
1: static const char help[] = "Time-dependent PDE in 1d. Simplified from ex15.c for illustrating how to solve DAEs. \n";
2: /*
3: u_t = uxx
4: 0 < x < 1;
5: At t=0: u(x) = exp(c*r*r*r), if r=PetscSqrtReal((x-.5)*(x-.5)) < .125
6: u(x) = 0.0 if r >= .125
9: Boundary conditions:
10: Dirichlet BC:
11: At x=0, x=1, u = 0.0
13: Neumann BC:
14: At x=0, x=1: du(x,t)/dx = 0
16: mpiexec -n 2 ./ex17 -da_grid_x 40 -ts_max_steps 2 -snes_monitor -ksp_monitor
17: ./ex17 -da_grid_x 40 -monitor_solution
18: ./ex17 -da_grid_x 100 -ts_type theta -ts_theta_theta 0.5 # Midpoint is not L-stable
19: ./ex17 -jac_type fd_coloring -da_grid_x 500 -boundary 1
20: ./ex17 -da_grid_x 100 -ts_type gl -ts_adapt_type none -ts_max_steps 2
21: */
23: #include <petscdm.h>
24: #include <petscdmda.h>
25: #include <petscts.h>
27: typedef enum {JACOBIAN_ANALYTIC,JACOBIAN_FD_COLORING,JACOBIAN_FD_FULL} JacobianType;
28: static const char *const JacobianTypes[] = {"analytic","fd_coloring","fd_full","JacobianType","fd_",0};
30: /*
31: User-defined data structures and routines
32: */
33: typedef struct {
34: PetscReal c;
35: PetscInt boundary; /* Type of boundary condition */
36: PetscBool viewJacobian;
37: } AppCtx;
39: static PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*);
40: static PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);
41: static PetscErrorCode FormInitialSolution(TS,Vec,void*);
45: int main(int argc,char **argv)
46: {
47: TS ts; /* nonlinear solver */
48: Vec u; /* solution, residual vectors */
49: Mat J; /* Jacobian matrix */
50: PetscInt maxsteps = 1000; /* iterations for convergence */
51: PetscInt nsteps;
52: PetscReal vmin,vmax,norm;
54: DM da;
55: PetscReal ftime,dt;
56: AppCtx user; /* user-defined work context */
57: JacobianType jacType;
59: PetscInitialize(&argc,&argv,(char*)0,help);
61: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
62: Create distributed array (DMDA) to manage parallel grid and vectors
63: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
64: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,-11,1,1,NULL,&da);
66: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
67: Extract global vectors from DMDA;
68: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
69: DMCreateGlobalVector(da,&u);
71: /* Initialize user application context */
72: user.c = -30.0;
73: user.boundary = 0; /* 0: Dirichlet BC; 1: Neumann BC */
74: user.viewJacobian = PETSC_FALSE;
76: PetscOptionsGetInt(NULL,NULL,"-boundary",&user.boundary,NULL);
77: PetscOptionsHasName(NULL,NULL,"-viewJacobian",&user.viewJacobian);
79: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
80: Create timestepping solver context
81: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
82: TSCreate(PETSC_COMM_WORLD,&ts);
83: TSSetProblemType(ts,TS_NONLINEAR);
84: TSSetType(ts,TSTHETA);
85: TSThetaSetTheta(ts,1.0); /* Make the Theta method behave like backward Euler */
86: TSSetIFunction(ts,NULL,FormIFunction,&user);
88: DMSetMatType(da,MATAIJ);
89: DMCreateMatrix(da,&J);
90: jacType = JACOBIAN_ANALYTIC; /* use user-provide Jacobian */
92: TSSetDM(ts,da); /* Use TSGetDM() to access. Setting here allows easy use of geometric multigrid. */
94: ftime = 1.0;
95: TSSetDuration(ts,maxsteps,ftime);
96: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
98: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
99: Set initial conditions
100: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101: FormInitialSolution(ts,u,&user);
102: TSSetSolution(ts,u);
103: dt = .01;
104: TSSetInitialTimeStep(ts,0.0,dt);
107: /* Use slow fd Jacobian or fast fd Jacobian with colorings.
108: Note: this requirs snes which is not created until TSSetUp()/TSSetFromOptions() is called */
109: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Options for Jacobian evaluation",NULL);
110: PetscOptionsEnum("-jac_type","Type of Jacobian","",JacobianTypes,(PetscEnum)jacType,(PetscEnum*)&jacType,0);
111: PetscOptionsEnd();
112: if (jacType == JACOBIAN_ANALYTIC) {
113: TSSetIJacobian(ts,J,J,FormIJacobian,&user);
114: } else if (jacType == JACOBIAN_FD_COLORING) {
115: SNES snes;
116: TSGetSNES(ts,&snes);
117: SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,0);
118: } else if (jacType == JACOBIAN_FD_FULL) {
119: SNES snes;
120: TSGetSNES(ts,&snes);
121: SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,&user);
122: }
124: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: Set runtime options
126: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127: TSSetFromOptions(ts);
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: Integrate ODE system
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
132: TSSolve(ts,u);
134: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135: Compute diagnostics of the solution
136: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137: VecNorm(u,NORM_1,&norm);
138: VecMax(u,NULL,&vmax);
139: VecMin(u,NULL,&vmin);
140: TSGetTimeStepNumber(ts,&nsteps);
141: TSGetTime(ts,&ftime);
142: PetscPrintf(PETSC_COMM_WORLD,"timestep %D: time %g, solution norm %g, max %g, min %g\n",nsteps,(double)ftime,(double)norm,(double)vmax,(double)vmin);
144: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145: Free work space.
146: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147: MatDestroy(&J);
148: VecDestroy(&u);
149: TSDestroy(&ts);
150: DMDestroy(&da);
151: PetscFinalize();
152: return(0);
153: }
154: /* ------------------------------------------------------------------- */
157: static PetscErrorCode FormIFunction(TS ts,PetscReal ftime,Vec U,Vec Udot,Vec F,void *ptr)
158: {
159: AppCtx *user=(AppCtx*)ptr;
160: DM da;
162: PetscInt i,Mx,xs,xm;
163: PetscReal hx,sx;
164: PetscScalar *u,*udot,*f;
165: Vec localU;
168: TSGetDM(ts,&da);
169: DMGetLocalVector(da,&localU);
170: DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
171: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
173: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
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,&u);
186: DMDAVecGetArrayRead(da,Udot,&udot);
187: DMDAVecGetArray(da,F,&f);
189: /* Get local grid boundaries */
190: DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
192: /* Compute function over the locally owned part of the grid */
193: for (i=xs; i<xs+xm; i++) {
194: if (user->boundary == 0) { /* Dirichlet BC */
195: if (i == 0 || i == Mx-1) f[i] = u[i]; /* F = U */
196: else f[i] = udot[i] + (2.*u[i] - u[i-1] - u[i+1])*sx;
197: } else { /* Neumann BC */
198: if (i == 0) f[i] = u[0] - u[1];
199: else if (i == Mx-1) f[i] = u[i] - u[i-1];
200: else f[i] = udot[i] + (2.*u[i] - u[i-1] - u[i+1])*sx;
201: }
202: }
204: /* Restore vectors */
205: DMDAVecRestoreArrayRead(da,localU,&u);
206: DMDAVecRestoreArrayRead(da,Udot,&udot);
207: DMDAVecRestoreArray(da,F,&f);
208: DMRestoreLocalVector(da,&localU);
209: return(0);
210: }
212: /* --------------------------------------------------------------------- */
213: /*
214: IJacobian - Compute IJacobian = dF/dU + a dF/dUdot
215: */
218: PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx)
219: {
221: PetscInt i,rstart,rend,Mx;
222: PetscReal hx,sx;
223: AppCtx *user = (AppCtx*)ctx;
224: DM da;
225: MatStencil col[3],row;
226: PetscInt nc;
227: PetscScalar vals[3];
230: TSGetDM(ts,&da);
231: MatGetOwnershipRange(Jpre,&rstart,&rend);
232: DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
233: PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
234: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
235: for (i=rstart; i<rend; i++) {
236: nc = 0;
237: row.i = i;
238: if (user->boundary == 0 && (i == 0 || i == Mx-1)) {
239: col[nc].i = i; vals[nc++] = 1.0;
240: } else if (user->boundary > 0 && i == 0) { /* Left Neumann */
241: col[nc].i = i; vals[nc++] = 1.0;
242: col[nc].i = i+1; vals[nc++] = -1.0;
243: } else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */
244: col[nc].i = i-1; vals[nc++] = -1.0;
245: col[nc].i = i; vals[nc++] = 1.0;
246: } else { /* Interior */
247: col[nc].i = i-1; vals[nc++] = -1.0*sx;
248: col[nc].i = i; vals[nc++] = 2.0*sx + a;
249: col[nc].i = i+1; vals[nc++] = -1.0*sx;
250: }
251: MatSetValuesStencil(Jpre,1,&row,nc,col,vals,INSERT_VALUES);
252: }
254: MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
255: MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
256: if (J != Jpre) {
257: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
258: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
259: }
260: if (user->viewJacobian) {
261: PetscPrintf(PETSC_COMM_WORLD,"Jpre:\n");
262: MatView(Jpre,PETSC_VIEWER_STDOUT_WORLD);
263: }
264: return(0);
265: }
267: /* ------------------------------------------------------------------- */
270: PetscErrorCode FormInitialSolution(TS ts,Vec U,void *ptr)
271: {
272: AppCtx *user=(AppCtx*)ptr;
273: PetscReal c =user->c;
274: DM da;
276: PetscInt i,xs,xm,Mx;
277: PetscScalar *u;
278: PetscReal hx,x,r;
281: TSGetDM(ts,&da);
282: DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
284: hx = 1.0/(PetscReal)(Mx-1);
286: /* Get pointers to vector data */
287: DMDAVecGetArray(da,U,&u);
289: /* Get local grid boundaries */
290: DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
292: /* Compute function over the locally owned part of the grid */
293: for (i=xs; i<xs+xm; i++) {
294: x = i*hx;
295: r = PetscSqrtReal((x-.5)*(x-.5));
296: if (r < .125) u[i] = PetscExpReal(c*r*r*r);
297: else u[i] = 0.0;
298: }
300: /* Restore vectors */
301: DMDAVecRestoreArray(da,U,&u);
302: return(0);
303: }