Actual source code: ex1.c
1: /*$Id: ex1.c,v 1.31 2001/08/07 21:31:30 bsmith Exp $*/
3: static char help[] ="Solves the time dependent Bratu problem using pseudo-timestepping.";
5: /*
6: Concepts: TS^pseudo-timestepping
7: Concepts: pseudo-timestepping
8: Concepts: nonlinear problems
9: Processors: 1
11: */
13: /* ------------------------------------------------------------------------
15: This code demonstrates how one may solve a nonlinear problem
16: with pseudo-timestepping. In this simple example, the pseudo-timestep
17: is the same for all grid points, i.e., this is equivalent to using
18: the backward Euler method with a variable timestep.
20: Note: This example does not require pseudo-timestepping since it
21: is an easy nonlinear problem, but it is included to demonstrate how
22: the pseudo-timestepping may be done.
24: See snes/examples/tutorials/ex4.c[ex4f.F] and
25: snes/examples/tutorials/ex5.c[ex5f.F] where the problem is described
26: and solved using Newton's method alone.
28: ----------------------------------------------------------------------------- */
29: /*
30: Include "petscts.h" to use the PETSc timestepping routines. Note that
31: this file automatically includes "petsc.h" and other lower-level
32: PETSc include files.
33: */
34: #include petscts.h
36: /*
37: Create an application context to contain data needed by the
38: application-provided call-back routines, FormJacobian() and
39: FormFunction().
40: */
41: typedef struct {
42: PetscReal param; /* test problem parameter */
43: int mx; /* Discretization in x-direction */
44: int my; /* Discretization in y-direction */
45: } AppCtx;
47: /*
48: User-defined routines
49: */
50: extern int FormJacobian(TS,PetscReal,Vec,Mat*,Mat*,MatStructure*,void*),
51: FormFunction(TS,PetscReal,Vec,Vec,void*),
52: FormInitialGuess(Vec,AppCtx*);
54: int main(int argc,char **argv)
55: {
56: TS ts; /* timestepping context */
57: Vec x,r; /* solution, residual vectors */
58: Mat J; /* Jacobian matrix */
59: AppCtx user; /* user-defined work context */
60: int its; /* iterations for convergence */
61: int ierr,N;
62: PetscReal param_max = 6.81,param_min = 0.,dt;
63: PetscReal ftime;
65: PetscInitialize(&argc,&argv,PETSC_NULL,help);
66: user.mx = 4;
67: user.my = 4;
68: user.param = 6.0;
69:
70: /*
71: Allow user to set the grid dimensions and nonlinearity parameter at run-time
72: */
73: PetscOptionsGetInt(PETSC_NULL,"-mx",&user.mx,PETSC_NULL);
74: PetscOptionsGetInt(PETSC_NULL,"-my",&user.my,PETSC_NULL);
75: PetscOptionsGetReal(PETSC_NULL,"-param",&user.param,PETSC_NULL);
76: if (user.param >= param_max || user.param <= param_min) {
77: SETERRQ(1,"Parameter is out of range");
78: }
79: dt = .5/PetscMax(user.mx,user.my);
80: PetscOptionsGetReal(PETSC_NULL,"-dt",&dt,PETSC_NULL);
81: N = user.mx*user.my;
82:
83: /*
84: Create vectors to hold the solution and function value
85: */
86: VecCreateSeq(PETSC_COMM_SELF,N,&x);
87: VecDuplicate(x,&r);
89: /*
90: Create matrix to hold Jacobian. Preallocate 5 nonzeros per row
91: in the sparse matrix. Note that this is not the optimal strategy; see
92: the Performance chapter of the users manual for information on
93: preallocating memory in sparse matrices.
94: */
95: MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,5,0,&J);
97: /*
98: Create timestepper context
99: */
100: TSCreate(PETSC_COMM_WORLD,&ts);
101: TSSetProblemType(ts,TS_NONLINEAR);
103: /*
104: Tell the timestepper context where to compute solutions
105: */
106: TSSetSolution(ts,x);
108: /*
109: Provide the call-back for the nonlinear function we are
110: evaluating. Thus whenever the timestepping routines need the
111: function they will call this routine. Note the final argument
112: is the application context used by the call-back functions.
113: */
114: TSSetRHSFunction(ts,FormFunction,&user);
116: /*
117: Set the Jacobian matrix and the function used to compute
118: Jacobians.
119: */
120: TSSetRHSJacobian(ts,J,J,FormJacobian,&user);
122: /*
123: For the initial guess for the problem
124: */
125: FormInitialGuess(x,&user);
127: /*
128: This indicates that we are using pseudo timestepping to
129: find a steady state solution to the nonlinear problem.
130: */
131: TSSetType(ts,TS_PSEUDO);
133: /*
134: Set the initial time to start at (this is arbitrary for
135: steady state problems; and the initial timestep given above
136: */
137: TSSetInitialTimeStep(ts,0.0,dt);
139: /*
140: Set a large number of timesteps and final duration time
141: to insure convergence to steady state.
142: */
143: TSSetDuration(ts,1000,1.e12);
145: /*
146: Use the default strategy for increasing the timestep
147: */
148: TSPseudoSetTimeStep(ts,TSPseudoDefaultTimeStep,0);
150: /*
151: Set any additional options from the options database. This
152: includes all options for the nonlinear and linear solvers used
153: internally the the timestepping routines.
154: */
155: TSSetFromOptions(ts);
157: TSSetUp(ts);
159: /*
160: Perform the solve. This is where the timestepping takes place.
161: */
162: TSStep(ts,&its,&ftime);
163:
164: printf("Number of pseudo timesteps = %d final time %4.2en",its,ftime);
166: /*
167: Free the data structures constructed above
168: */
169: VecDestroy(x);
170: VecDestroy(r);
171: MatDestroy(J);
172: TSDestroy(ts);
173: PetscFinalize();
175: return 0;
176: }
177: /* ------------------------------------------------------------------ */
178: /* Bratu (Solid Fuel Ignition) Test Problem */
179: /* ------------------------------------------------------------------ */
181: /* -------------------- Form initial approximation ----------------- */
183: int FormInitialGuess(Vec X,AppCtx *user)
184: {
185: int i,j,row,mx,my,ierr;
186: PetscReal one = 1.0,lambda;
187: PetscReal temp1,temp,hx,hy;
188: PetscScalar *x;
190: mx = user->mx;
191: my = user->my;
192: lambda = user->param;
194: hx = one / (PetscReal)(mx-1);
195: hy = one / (PetscReal)(my-1);
197: VecGetArray(X,&x);
198: temp1 = lambda/(lambda + one);
199: for (j=0; j<my; j++) {
200: temp = (PetscReal)(PetscMin(j,my-j-1))*hy;
201: for (i=0; i<mx; i++) {
202: row = i + j*mx;
203: if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
204: x[row] = 0.0;
205: continue;
206: }
207: x[row] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,mx-i-1))*hx,temp));
208: }
209: }
210: VecRestoreArray(X,&x);
211: return 0;
212: }
213: /* -------------------- Evaluate Function F(x) --------------------- */
215: int FormFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
216: {
217: AppCtx *user = (AppCtx*)ptr;
218: int ierr,i,j,row,mx,my;
219: PetscReal two = 2.0,one = 1.0,lambda;
220: PetscReal hx,hy,hxdhy,hydhx;
221: PetscScalar ut,ub,ul,ur,u,uxx,uyy,sc,*x,*f;
223: mx = user->mx;
224: my = user->my;
225: lambda = user->param;
227: hx = one / (PetscReal)(mx-1);
228: hy = one / (PetscReal)(my-1);
229: sc = hx*hy;
230: hxdhy = hx/hy;
231: hydhx = hy/hx;
233: VecGetArray(X,&x);
234: VecGetArray(F,&f);
235: for (j=0; j<my; j++) {
236: for (i=0; i<mx; i++) {
237: row = i + j*mx;
238: if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
239: f[row] = x[row];
240: continue;
241: }
242: u = x[row];
243: ub = x[row - mx];
244: ul = x[row - 1];
245: ut = x[row + mx];
246: ur = x[row + 1];
247: uxx = (-ur + two*u - ul)*hydhx;
248: uyy = (-ut + two*u - ub)*hxdhy;
249: f[row] = -uxx + -uyy + sc*lambda*PetscExpScalar(u);
250: }
251: }
252: VecRestoreArray(X,&x);
253: VecRestoreArray(F,&f);
254: return 0;
255: }
256: /* -------------------- Evaluate Jacobian F'(x) -------------------- */
258: int FormJacobian(TS ts,PetscReal t,Vec X,Mat *J,Mat *B,MatStructure *flag,void *ptr)
259: {
260: AppCtx *user = (AppCtx*)ptr;
261: Mat jac = *B;
262: int i,j,row,mx,my,col[5],ierr;
263: PetscScalar two = 2.0,one = 1.0,lambda,v[5],sc,*x;
264: PetscReal hx,hy,hxdhy,hydhx;
267: mx = user->mx;
268: my = user->my;
269: lambda = user->param;
271: hx = 1.0 / (PetscReal)(mx-1);
272: hy = 1.0 / (PetscReal)(my-1);
273: sc = hx*hy;
274: hxdhy = hx/hy;
275: hydhx = hy/hx;
277: VecGetArray(X,&x);
278: for (j=0; j<my; j++) {
279: for (i=0; i<mx; i++) {
280: row = i + j*mx;
281: if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
282: MatSetValues(jac,1,&row,1,&row,&one,INSERT_VALUES);
283: continue;
284: }
285: v[0] = hxdhy; col[0] = row - mx;
286: v[1] = hydhx; col[1] = row - 1;
287: v[2] = -two*(hydhx + hxdhy) + sc*lambda*PetscExpScalar(x[row]); col[2] = row;
288: v[3] = hydhx; col[3] = row + 1;
289: v[4] = hxdhy; col[4] = row + mx;
290: MatSetValues(jac,1,&row,5,col,v,INSERT_VALUES);
291: }
292: }
293: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
294: VecRestoreArray(X,&x);
295: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
296: *flag = SAME_NONZERO_PATTERN;
297: return 0;
298: }