Actual source code: ex43.c
petsc-3.4.5 2014-06-29
2: static char help[] = "Newton's method to solve a many-variable system that comes from the 2 variable Rosenbrock function + trivial.\n\n";
4: /*
6: ./ex43 -snes_monitor_range -snes_max_it 1000 -snes_rtol 1.e-14 -n 10 -snes_converged_reason -sub_snes_monito -sub_snes_mf -sub_snes_converged_reason -sub_snes_rtol 1.e-10 -sub_snes_max_it 1000 -sub_snes_monitor
8: Accelerates Newton's method by solving a small problem defined by those elements with large residual plus one level of overlap
10: This is a toy code for playing around
12: Counts residual entries as small if they are less then .2 times the maximum
13: Decides to solve a reduced problem if the number of large entries is less than 20 percent of all entries (and this has been true for criteria_reduce iterations)
14: */
15: #include "ex43-44.h"
18: extern PetscErrorCode FormJacobian1(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
19: extern PetscErrorCode FormFunction1(SNES,Vec,Vec,void*);
21: typedef struct {
22: PetscInt n,p;
23: } Ctx;
27: int main(int argc,char **argv)
28: {
29: SNES snes; /* nonlinear solver context */
30: Vec x,r; /* solution, residual vectors */
31: Mat J; /* Jacobian matrix */
32: PetscErrorCode ierr;
33: PetscScalar *xx;
34: PetscInt i,max_snes_solves = 20,snes_steps_per_solve = 2,criteria_reduce = 1;
35: Ctx ctx;
36: SNESConvergedReason reason;
38: PetscInitialize(&argc,&argv,(char*)0,help);
39: ctx.n = 0;
40: PetscOptionsGetInt(NULL,"-n",&ctx.n,NULL);
41: ctx.p = 0;
42: PetscOptionsGetInt(NULL,"-p",&ctx.p,NULL);
43: PetscOptionsGetInt(NULL,"-max_snes_solves",&max_snes_solves,NULL);
44: PetscOptionsGetInt(NULL,"-snes_steps_per_solve",&snes_steps_per_solve,NULL);
45: PetscOptionsGetInt(NULL,"-criteria_reduce",&criteria_reduce,NULL);
47: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
48: Create nonlinear solver context
49: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
50: SNESCreate(PETSC_COMM_WORLD,&snes);
52: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
53: Create matrix and vector data structures; set corresponding routines
54: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
55: /*
56: Create vectors for solution and nonlinear function
57: */
58: VecCreate(PETSC_COMM_WORLD,&x);
59: VecSetSizes(x,PETSC_DECIDE,2+ctx.n+ctx.p);
60: VecSetFromOptions(x);
61: VecDuplicate(x,&r);
63: /*
64: Create Jacobian matrix data structure
65: */
66: MatCreate(PETSC_COMM_WORLD,&J);
67: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,2+ctx.p+ctx.n,2+ctx.p+ctx.n);
68: MatSetFromOptions(J);
69: MatSetUp(J);
71: /*
72: Set function evaluation routine and vector.
73: */
74: SNESSetFunction(snes,r,FormFunction1,(void*)&ctx);
76: /*
77: Set Jacobian matrix data structure and Jacobian evaluation routine
78: */
79: SNESSetJacobian(snes,J,J,FormJacobian1,(void*)&ctx);
81: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82: Customize nonlinear solver; set runtime options
83: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
84: SNESSetFromOptions(snes);
86: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87: Evaluate initial guess; then solve nonlinear system
88: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
89: VecSet(x,0.0);
90: VecGetArray(x,&xx);
91: xx[0] = -1.2;
92: for (i=1; i<ctx.p+2; i++) xx[i] = 1.0;
93: VecRestoreArray(x,&xx);
95: /*
96: Note: The user should initialize the vector, x, with the initial guess
97: for the nonlinear solver prior to calling SNESSolve(). In particular,
98: to employ an initial guess of zero, the user should explicitly set
99: this vector to zero by calling VecSet().
100: */
102: SNESMonitorSet(snes,MonitorRange,0,0);
103: SNESSetTolerances(snes,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,snes_steps_per_solve,PETSC_DEFAULT);
104: for (i=0; i<max_snes_solves; i++) {
105: SNESSolve(snes,NULL,x);
106: SNESGetConvergedReason(snes,&reason);
107: if (reason && reason != SNES_DIVERGED_MAX_IT) break;
108: if (CountGood > criteria_reduce) {
109: SolveSubproblem(snes);
110: CountGood = 0;
111: }
112: }
114: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
115: Free work space. All PETSc objects should be destroyed when they
116: are no longer needed.
117: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119: VecDestroy(&x); VecDestroy(&r);
120: MatDestroy(&J); SNESDestroy(&snes);
121: PetscFinalize();
122: return 0;
123: }
124: /* ------------------------------------------------------------------- */
127: /*
128: FormFunction1 - Evaluates nonlinear function, F(x).
130: Input Parameters:
131: . snes - the SNES context
132: . x - input vector
133: . ctx - optional user-defined context
135: Output Parameter:
136: . f - function vector
137: */
138: PetscErrorCode FormFunction1(SNES snes,Vec x,Vec f,void *ictx)
139: {
141: PetscScalar *xx,*ff;
142: PetscInt i;
143: Ctx *ctx = (Ctx*)ictx;
145: /*
146: Get pointers to vector data.
147: - For default PETSc vectors, VecGetArray() returns a pointer to
148: the data array. Otherwise, the routine is implementation dependent.
149: - You MUST call VecRestoreArray() when you no longer need access to
150: the array.
151: */
152: VecGetArray(x,&xx);
153: VecGetArray(f,&ff);
155: /* Compute function */
156: ff[0] = -2.0 + 2.0*xx[0] + 400.0*xx[0]*xx[0]*xx[0] - 400.0*xx[0]*xx[1];
157: for (i=1; i<1+ctx->p; i++) {
158: ff[i] = -2.0 + 2.0*xx[i] + 400.0*xx[i]*xx[i]*xx[i] - 400.0*xx[i]*xx[i+1] + 200.0*(xx[i] - xx[i-1]*xx[i-1]);
159: }
160: ff[ctx->p+1] = -200.0*xx[ctx->p]*xx[ctx->p] + 200.0*xx[ctx->p+1];
161: for (i=ctx->p+2; i<2+ctx->p+ctx->n; i++) {
162: ff[i] = xx[i] - xx[0] + .7*xx[1] - .2*xx[i-1]*xx[i-1];
163: }
165: /* Restore vectors */
166: VecRestoreArray(x,&xx);
167: VecRestoreArray(f,&ff);
168: return 0;
169: }
170: /* ------------------------------------------------------------------- */
173: /*
174: FormJacobian1 - Evaluates Jacobian matrix.
176: Input Parameters:
177: . snes - the SNES context
178: . x - input vector
179: . dummy - optional user-defined context (not used here)
181: Output Parameters:
182: . jac - Jacobian matrix
183: . B - optionally different preconditioning matrix
184: . flag - flag indicating matrix structure
185: */
186: PetscErrorCode FormJacobian1(SNES snes,Vec x,Mat *jac,Mat *B,MatStructure *flag,void *ictx)
187: {
188: PetscScalar *xx;
190: PetscInt i;
191: Ctx *ctx = (Ctx*)ictx;
193: MatZeroEntries(*B);
194: /*
195: Get pointer to vector data
196: */
197: VecGetArray(x,&xx);
199: /*
200: Compute Jacobian entries and insert into matrix.
201: - Since this is such a small problem, we set all entries for
202: the matrix at once.
203: */
204: MatSetValue(*B,0,0, 2.0 + 1200.0*xx[0]*xx[0] - 400.0*xx[1],ADD_VALUES);
205: MatSetValue(*B,0,1,-400.0*xx[0],ADD_VALUES);
207: for (i=1; i<ctx->p+1; i++) {
208: MatSetValue(*B,i,i-1, -400.0*xx[i-1],ADD_VALUES);
209: MatSetValue(*B,i,i, 2.0 + 1200.0*xx[i]*xx[i] - 400.0*xx[i+1] + 200.0,ADD_VALUES);
210: MatSetValue(*B,i,i+1,-400.0*xx[i],ADD_VALUES);
211: }
213: MatSetValue(*B,ctx->p+1,ctx->p, -400.0*xx[ctx->p],ADD_VALUES);
214: MatSetValue(*B,ctx->p+1,ctx->p+1,200,ADD_VALUES);
216: *flag = SAME_NONZERO_PATTERN;
218: for (i=ctx->p+2; i<2+ctx->p+ctx->n; i++) {
219: MatSetValue(*B,i,i,1.0,ADD_VALUES);
220: MatSetValue(*B,i,0,-1.0,ADD_VALUES);
221: MatSetValue(*B,i,1,.7,ADD_VALUES);
222: MatSetValue(*B,i,i-1,-.4*xx[i-1],ADD_VALUES);
223: }
224: /*
225: Restore vector
226: */
227: VecRestoreArray(x,&xx);
229: /*
230: Assemble matrix
231: */
232: MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
233: MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);
234: if (*jac != *B) {
235: MatAssemblyBegin(*jac,MAT_FINAL_ASSEMBLY);
236: MatAssemblyEnd(*jac,MAT_FINAL_ASSEMBLY);
237: }
238: return 0;
239: }