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 { 96 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.); 97 PetscCall(VecSetValues(F,1,&i,&v,INSERT_VALUES)); 98 v2 = a*xp + (b-a)*PetscPowScalar(xp,k); 99 PetscCall(VecSetValues(x,1,&i,&v2,INSERT_VALUES)); 100 xp += h; 101 } 102 103 /* perturb initial guess */ 104 PetscCall(VecGetArray(x,&xx)); 105 for (i=0; i<n; i++) { 106 v2 = xx[i]*sperturb; 107 PetscCall(VecSetValues(x,1,&i,&v2,INSERT_VALUES)); 108 } 109 PetscCall(VecRestoreArray(x,&xx)); 110 111 PetscCall(SNESSolve(snes,NULL,x)); 112 PetscCall(SNESGetIterationNumber(snes,&it)); 113 PetscCall(PetscPrintf(PETSC_COMM_SELF,"SNES iterations = %" PetscInt_FMT "\n\n",it)); 114 115 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 116 Free work space. All PETSc objects should be destroyed when they 117 are no longer needed. 118 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 119 120 PetscCall(VecDestroy(&x)); PetscCall(VecDestroy(&r)); 121 PetscCall(VecDestroy(&F)); PetscCall(MatDestroy(&J)); 122 PetscCall(SNESDestroy(&snes)); 123 PetscCall(PetscFinalize()); 124 return 0; 125 } 126 127 PetscErrorCode FormFunction(SNES snes,Vec x,Vec f,void *dummy) 128 { 129 const PetscScalar *xx; 130 PetscScalar *ff,*FF,d,d2; 131 PetscInt i,n; 132 133 PetscCall(VecGetArrayRead(x,&xx)); 134 PetscCall(VecGetArray(f,&ff)); 135 PetscCall(VecGetArray((Vec)dummy,&FF)); 136 PetscCall(VecGetSize(x,&n)); 137 d = (PetscReal)(n - 1); d2 = d*d; 138 139 if (second_order) ff[0] = d*(0.5*d*(-xx[2] + 4.*xx[1] - 3.*xx[0]) - X0DOT); 140 else ff[0] = d*(d*(xx[1] - xx[0]) - X0DOT); 141 142 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]; 143 144 ff[n-1] = d*d*(xx[n-1] - X1); 145 PetscCall(VecRestoreArrayRead(x,&xx)); 146 PetscCall(VecRestoreArray(f,&ff)); 147 PetscCall(VecRestoreArray((Vec)dummy,&FF)); 148 return 0; 149 } 150 151 PetscErrorCode FormJacobian(SNES snes,Vec x,Mat jac,Mat prejac,void *dummy) 152 { 153 const PetscScalar *xx; 154 PetscScalar A[3],d,d2; 155 PetscInt i,n,j[3]; 156 157 PetscCall(VecGetSize(x,&n)); 158 PetscCall(VecGetArrayRead(x,&xx)); 159 d = (PetscReal)(n - 1); d2 = d*d; 160 161 i = 0; 162 if (second_order) { 163 j[0] = 0; j[1] = 1; j[2] = 2; 164 A[0] = -3.*d*d*0.5; A[1] = 4.*d*d*0.5; A[2] = -1.*d*d*0.5; 165 PetscCall(MatSetValues(prejac,1,&i,3,j,A,INSERT_VALUES)); 166 } else { 167 j[0] = 0; j[1] = 1; 168 A[0] = -d*d; A[1] = d*d; 169 PetscCall(MatSetValues(prejac,1,&i,2,j,A,INSERT_VALUES)); 170 } 171 for (i=1; i<n-1; i++) { 172 j[0] = i - 1; j[1] = i; j[2] = i + 1; 173 A[0] = d2; A[1] = -2.*d2 + 2.*xx[i]; A[2] = d2; 174 PetscCall(MatSetValues(prejac,1,&i,3,j,A,INSERT_VALUES)); 175 } 176 177 i = n-1; 178 A[0] = d*d; 179 PetscCall(MatSetValues(prejac,1,&i,1,&i,&A[0],INSERT_VALUES)); 180 181 PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY)); 182 PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY)); 183 PetscCall(MatAssemblyBegin(prejac,MAT_FINAL_ASSEMBLY)); 184 PetscCall(MatAssemblyEnd(prejac,MAT_FINAL_ASSEMBLY)); 185 186 PetscCall(VecRestoreArrayRead(x,&xx)); 187 return 0; 188 } 189 190 /*TEST 191 192 test: 193 args: -n 14 -snes_monitor_short -snes_converged_reason 194 requires: !single 195 196 test: 197 suffix: 2 198 args: -n 15 -snes_monitor_short -snes_converged_reason 199 requires: !single 200 201 test: 202 suffix: 3 203 args: -n 14 -second_order -snes_monitor_short -snes_converged_reason 204 requires: !single 205 206 TEST*/ 207