1 2 static const char help[] = "Tries to solve u`` + u^{2} = f for an easy case and an impossible case.\n\n"; 3 4 /* 5 This example was contributed by Peter Graf to show how SNES fails when given a nonlinear problem with no solution. 6 7 Run with -n 14 to see fail to converge and -n 15 to see convergence 8 9 The option -second_order uses a different discretization of the Neumann boundary condition and always converges 10 11 */ 12 13 #include <petscsnes.h> 14 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; 20 21 /* 22 User-defined routines 23 */ 24 PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *); 25 PetscErrorCode FormFunction(SNES, Vec, Vec, void *); 26 27 int main(int argc, char **argv) 28 { 29 SNES snes; /* SNES context */ 30 Vec x, r, F; /* vectors */ 31 Mat J; /* Jacobian */ 32 PetscInt it, n = 11, i; 33 PetscReal h, xp = 0.0; 34 PetscScalar v; 35 const PetscScalar a = X0DOT; 36 const PetscScalar b = X1; 37 const PetscScalar k = KPOW; 38 PetscScalar v2; 39 PetscScalar *xx; 40 41 PetscFunctionBeginUser; 42 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 43 PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL)); 44 PetscCall(PetscOptionsGetBool(NULL, NULL, "-second_order", &second_order, NULL)); 45 h = 1.0 / (n - 1); 46 47 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 48 Create nonlinear solver context 49 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 50 51 PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes)); 52 53 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 54 Create vector data structures; set function evaluation routine 55 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 56 57 PetscCall(VecCreate(PETSC_COMM_SELF, &x)); 58 PetscCall(VecSetSizes(x, PETSC_DECIDE, n)); 59 PetscCall(VecSetFromOptions(x)); 60 PetscCall(VecDuplicate(x, &r)); 61 PetscCall(VecDuplicate(x, &F)); 62 63 PetscCall(SNESSetFunction(snes, r, FormFunction, (void *)F)); 64 65 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 66 Create matrix data structures; set Jacobian evaluation routine 67 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 68 69 PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, n, n, 3, NULL, &J)); 70 71 /* 72 Note that in this case we create separate matrices for the Jacobian 73 and preconditioner matrix. Both of these are computed in the 74 routine FormJacobian() 75 */ 76 /* PetscCall(SNESSetJacobian(snes,NULL,JPrec,FormJacobian,0)); */ 77 PetscCall(SNESSetJacobian(snes, J, J, FormJacobian, 0)); 78 /* PetscCall(SNESSetJacobian(snes,J,JPrec,FormJacobian,0)); */ 79 80 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 81 Customize nonlinear solver; set runtime options 82 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 83 84 PetscCall(SNESSetFromOptions(snes)); 85 86 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 87 Initialize application: 88 Store right-hand-side of PDE and exact solution 89 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 90 91 /* set right hand side and initial guess to be exact solution of continuim problem */ 92 #define SQR(x) ((x) * (x)) 93 xp = 0.0; 94 for (i = 0; i < n; i++) { 95 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.); 96 PetscCall(VecSetValues(F, 1, &i, &v, INSERT_VALUES)); 97 v2 = a * xp + (b - a) * PetscPowScalar(xp, k); 98 PetscCall(VecSetValues(x, 1, &i, &v2, INSERT_VALUES)); 99 xp += h; 100 } 101 102 /* perturb initial guess */ 103 PetscCall(VecGetArray(x, &xx)); 104 for (i = 0; i < n; i++) { 105 v2 = xx[i] * sperturb; 106 PetscCall(VecSetValues(x, 1, &i, &v2, INSERT_VALUES)); 107 } 108 PetscCall(VecRestoreArray(x, &xx)); 109 110 PetscCall(SNESSolve(snes, NULL, x)); 111 PetscCall(SNESGetIterationNumber(snes, &it)); 112 PetscCall(PetscPrintf(PETSC_COMM_SELF, "SNES iterations = %" PetscInt_FMT "\n\n", it)); 113 114 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 115 Free work space. All PETSc objects should be destroyed when they 116 are no longer needed. 117 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 118 119 PetscCall(VecDestroy(&x)); 120 PetscCall(VecDestroy(&r)); 121 PetscCall(VecDestroy(&F)); 122 PetscCall(MatDestroy(&J)); 123 PetscCall(SNESDestroy(&snes)); 124 PetscCall(PetscFinalize()); 125 return 0; 126 } 127 128 PetscErrorCode FormFunction(SNES snes, Vec x, Vec f, void *dummy) 129 { 130 const PetscScalar *xx; 131 PetscScalar *ff, *FF, d, d2; 132 PetscInt i, n; 133 134 PetscCall(VecGetArrayRead(x, &xx)); 135 PetscCall(VecGetArray(f, &ff)); 136 PetscCall(VecGetArray((Vec)dummy, &FF)); 137 PetscCall(VecGetSize(x, &n)); 138 d = (PetscReal)(n - 1); 139 d2 = d * d; 140 141 if (second_order) ff[0] = d * (0.5 * d * (-xx[2] + 4. * xx[1] - 3. * xx[0]) - X0DOT); 142 else ff[0] = d * (d * (xx[1] - xx[0]) - X0DOT); 143 144 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]; 145 146 ff[n - 1] = d * d * (xx[n - 1] - X1); 147 PetscCall(VecRestoreArrayRead(x, &xx)); 148 PetscCall(VecRestoreArray(f, &ff)); 149 PetscCall(VecRestoreArray((Vec)dummy, &FF)); 150 return 0; 151 } 152 153 PetscErrorCode FormJacobian(SNES snes, Vec x, Mat jac, Mat prejac, void *dummy) 154 { 155 const PetscScalar *xx; 156 PetscScalar A[3], d, d2; 157 PetscInt i, n, j[3]; 158 159 PetscCall(VecGetSize(x, &n)); 160 PetscCall(VecGetArrayRead(x, &xx)); 161 d = (PetscReal)(n - 1); 162 d2 = d * d; 163 164 i = 0; 165 if (second_order) { 166 j[0] = 0; 167 j[1] = 1; 168 j[2] = 2; 169 A[0] = -3. * d * d * 0.5; 170 A[1] = 4. * d * d * 0.5; 171 A[2] = -1. * d * d * 0.5; 172 PetscCall(MatSetValues(prejac, 1, &i, 3, j, A, INSERT_VALUES)); 173 } else { 174 j[0] = 0; 175 j[1] = 1; 176 A[0] = -d * d; 177 A[1] = d * d; 178 PetscCall(MatSetValues(prejac, 1, &i, 2, j, A, INSERT_VALUES)); 179 } 180 for (i = 1; i < n - 1; i++) { 181 j[0] = i - 1; 182 j[1] = i; 183 j[2] = i + 1; 184 A[0] = d2; 185 A[1] = -2. * d2 + 2. * xx[i]; 186 A[2] = d2; 187 PetscCall(MatSetValues(prejac, 1, &i, 3, j, A, INSERT_VALUES)); 188 } 189 190 i = n - 1; 191 A[0] = d * d; 192 PetscCall(MatSetValues(prejac, 1, &i, 1, &i, &A[0], INSERT_VALUES)); 193 194 PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY)); 195 PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY)); 196 PetscCall(MatAssemblyBegin(prejac, MAT_FINAL_ASSEMBLY)); 197 PetscCall(MatAssemblyEnd(prejac, MAT_FINAL_ASSEMBLY)); 198 199 PetscCall(VecRestoreArrayRead(x, &xx)); 200 return 0; 201 } 202 203 /*TEST 204 205 test: 206 args: -n 14 -snes_monitor_short -snes_converged_reason 207 requires: !single 208 209 test: 210 suffix: 2 211 args: -n 15 -snes_monitor_short -snes_converged_reason 212 requires: !single 213 214 test: 215 suffix: 3 216 args: -n 14 -second_order -snes_monitor_short -snes_converged_reason 217 requires: !single 218 219 TEST*/ 220