Actual source code: ex59.c
petsc-3.9.4 2018-09-11
2: static const char help[] = "Tries to solve u`` + u^{2} = f for an easy case and an impossible case.\n\n";
4: /*
5: This example was contributed by Peter Graf to show how SNES fails when given a nonlinear problem with no solution.
7: Run with -n 14 to see fail to converge and -n 15 to see convergence
9: The option -second_order uses a different discretization of the Neumann boundary condition and always converges
11: */
13: #include <petscsnes.h>
15: PetscBool second_order = PETSC_FALSE;
16: #define X0DOT -2.0
17: #define X1 5.0
18: #define KPOW 2.0
19: const PetscScalar sperturb = 1.1;
21: /*
22: User-defined routines
23: */
24: PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);
25: PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
27: int main(int argc,char **argv)
28: {
29: SNES snes; /* SNES context */
30: Vec x,r,F; /* vectors */
31: Mat J; /* Jacobian */
32: PetscErrorCode ierr;
33: PetscInt it,n = 11,i;
34: PetscReal h,xp = 0.0;
35: PetscScalar v;
36: const PetscScalar a = X0DOT;
37: const PetscScalar b = X1;
38: const PetscScalar k = KPOW;
39: PetscScalar v2;
40: PetscScalar *xx;
43: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
44: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
45: PetscOptionsGetBool(NULL,NULL,"-second_order",&second_order,NULL);
46: h = 1.0/(n-1);
48: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
49: Create nonlinear solver context
50: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
52: SNESCreate(PETSC_COMM_WORLD,&snes);
54: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: Create vector data structures; set function evaluation routine
56: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
58: VecCreate(PETSC_COMM_SELF,&x);
59: VecSetSizes(x,PETSC_DECIDE,n);
60: VecSetFromOptions(x);
61: VecDuplicate(x,&r);
62: VecDuplicate(x,&F);
64: SNESSetFunction(snes,r,FormFunction,(void*)F);
66: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
67: Create matrix data structures; set Jacobian evaluation routine
68: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
70: MatCreateSeqAIJ(PETSC_COMM_SELF,n,n,3,NULL,&J);
72: /*
73: Note that in this case we create separate matrices for the Jacobian
74: and preconditioner matrix. Both of these are computed in the
75: routine FormJacobian()
76: */
77: /* SNESSetJacobian(snes,NULL,JPrec,FormJacobian,0); */
78: SNESSetJacobian(snes,J,J,FormJacobian,0);
79: /* SNESSetJacobian(snes,J,JPrec,FormJacobian,0); */
81: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82: Customize nonlinear solver; set runtime options
83: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
85: SNESSetFromOptions(snes);
87: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
88: Initialize application:
89: Store right-hand-side of PDE and exact solution
90: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
92: /* set right hand side and initial guess to be exact solution of continuim problem */
93: #define SQR(x) ((x)*(x))
94: xp = 0.0;
95: for (i=0; i<n; i++)
96: {
97: v = k*(k-1.)*(b-a)*PetscPowScalar(xp,k-2.) + SQR(a*xp) + SQR(b-a)*PetscPowScalar(xp,2.*k) + 2.*a*(b-a)*PetscPowScalar(xp,k+1.);
98: VecSetValues(F,1,&i,&v,INSERT_VALUES);
99: v2 = a*xp + (b-a)*PetscPowScalar(xp,k);
100: VecSetValues(x,1,&i,&v2,INSERT_VALUES);
101: xp += h;
102: }
104: /* perturb initial guess */
105: VecGetArray(x,&xx);
106: for (i=0; i<n; i++) {
107: v2 = xx[i]*sperturb;
108: VecSetValues(x,1,&i,&v2,INSERT_VALUES);
109: }
110: VecRestoreArray(x,&xx);
113: SNESSolve(snes,NULL,x);
114: SNESGetIterationNumber(snes,&it);
115: PetscPrintf(PETSC_COMM_SELF,"SNES iterations = %D\n\n",it);
117: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
118: Free work space. All PETSc objects should be destroyed when they
119: are no longer needed.
120: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
122: VecDestroy(&x); VecDestroy(&r);
123: VecDestroy(&F); MatDestroy(&J);
124: SNESDestroy(&snes);
125: PetscFinalize();
126: return ierr;
127: }
129: PetscErrorCode FormFunction(SNES snes,Vec x,Vec f,void *dummy)
130: {
131: const PetscScalar *xx;
132: PetscScalar *ff,*FF,d,d2;
133: PetscErrorCode ierr;
134: PetscInt i,n;
136: VecGetArrayRead(x,&xx);
137: VecGetArray(f,&ff);
138: VecGetArray((Vec)dummy,&FF);
139: VecGetSize(x,&n);
140: d = (PetscReal)(n - 1); d2 = d*d;
142: if (second_order) ff[0] = d*(0.5*d*(-xx[2] + 4.*xx[1] - 3.*xx[0]) - X0DOT);
143: else ff[0] = d*(d*(xx[1] - xx[0]) - X0DOT);
145: for (i=1; i<n-1; i++) ff[i] = d2*(xx[i-1] - 2.*xx[i] + xx[i+1]) + xx[i]*xx[i] - FF[i];
147: ff[n-1] = d*d*(xx[n-1] - X1);
148: VecRestoreArrayRead(x,&xx);
149: VecRestoreArray(f,&ff);
150: VecRestoreArray((Vec)dummy,&FF);
151: return 0;
152: }
154: PetscErrorCode FormJacobian(SNES snes,Vec x,Mat jac,Mat prejac,void *dummy)
155: {
156: const PetscScalar *xx;
157: PetscScalar A[3],d,d2;
158: PetscInt i,n,j[3];
159: PetscErrorCode ierr;
161: VecGetSize(x,&n);
162: VecGetArrayRead(x,&xx);
163: d = (PetscReal)(n - 1); d2 = d*d;
165: i = 0;
166: if (second_order) {
167: j[0] = 0; j[1] = 1; j[2] = 2;
168: A[0] = -3.*d*d*0.5; A[1] = 4.*d*d*0.5; A[2] = -1.*d*d*0.5;
169: MatSetValues(prejac,1,&i,3,j,A,INSERT_VALUES);
170: } else {
171: j[0] = 0; j[1] = 1;
172: A[0] = -d*d; A[1] = d*d;
173: MatSetValues(prejac,1,&i,2,j,A,INSERT_VALUES);
174: }
175: for (i=1; i<n-1; i++) {
176: j[0] = i - 1; j[1] = i; j[2] = i + 1;
177: A[0] = d2; A[1] = -2.*d2 + 2.*xx[i]; A[2] = d2;
178: MatSetValues(prejac,1,&i,3,j,A,INSERT_VALUES);
179: }
181: i = n-1;
182: A[0] = d*d;
183: MatSetValues(prejac,1,&i,1,&i,&A[0],INSERT_VALUES);
185: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
186: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
187: MatAssemblyBegin(prejac,MAT_FINAL_ASSEMBLY);
188: MatAssemblyEnd(prejac,MAT_FINAL_ASSEMBLY);
190: VecRestoreArrayRead(x,&xx);
191: return 0;
192: }
195: /*TEST
197: test:
198: args: -n 14 -snes_monitor_short -snes_converged_reason
199: requires: !single
201: test:
202: suffix: 2
203: args: -n 15 -snes_monitor_short -snes_converged_reason
204: requires: !single
206: test:
207: suffix: 3
208: args: -n 14 -second_order -snes_monitor_short -snes_converged_reason
209: requires: !single
211: TEST*/