1 static char help[] = "Newton method to solve u'' + u^{2} = f, sequentially.\n\ 2 This example employs a user-defined monitoring routine.\n\n"; 3 4 /* 5 Include "petscdraw.h" so that we can use PETSc drawing routines. 6 Include "petscsnes.h" so that we can use SNES solvers. Note that this 7 file automatically includes: 8 petscsys.h - base PETSc routines petscvec.h - vectors 9 petscmat.h - matrices 10 petscis.h - index sets petscksp.h - Krylov subspace methods 11 petscviewer.h - viewers petscpc.h - preconditioners 12 petscksp.h - linear solvers 13 */ 14 15 #include <petscsnes.h> 16 17 /* 18 User-defined routines 19 */ 20 extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *); 21 extern PetscErrorCode FormFunction(SNES, Vec, Vec, void *); 22 extern PetscErrorCode FormInitialGuess(Vec); 23 extern PetscErrorCode Monitor(SNES, PetscInt, PetscReal, void *); 24 25 /* 26 User-defined context for monitoring 27 */ 28 typedef struct { 29 PetscViewer viewer; 30 } MonitorCtx; 31 32 int main(int argc, char **argv) 33 { 34 SNES snes; /* SNES context */ 35 Vec x, r, F, U; /* vectors */ 36 Mat J; /* Jacobian matrix */ 37 MonitorCtx monP; /* monitoring context */ 38 PetscInt its, n = 5, i, maxit, maxf; 39 PetscMPIInt size; 40 PetscScalar h, xp, v, none = -1.0; 41 PetscReal abstol, rtol, stol, norm; 42 43 PetscFunctionBeginUser; 44 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 45 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 46 PetscCheck(size == 1, PETSC_COMM_SELF, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!"); 47 PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL)); 48 h = 1.0 / (n - 1); 49 50 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 51 Create nonlinear solver context 52 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 53 54 PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes)); 55 56 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 57 Create vector data structures; set function evaluation routine 58 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 59 /* 60 Note that we form 1 vector from scratch and then duplicate as needed. 61 */ 62 PetscCall(VecCreate(PETSC_COMM_WORLD, &x)); 63 PetscCall(VecSetSizes(x, PETSC_DECIDE, n)); 64 PetscCall(VecSetFromOptions(x)); 65 PetscCall(VecDuplicate(x, &r)); 66 PetscCall(VecDuplicate(x, &F)); 67 PetscCall(VecDuplicate(x, &U)); 68 69 /* 70 Set function evaluation routine and vector 71 */ 72 PetscCall(SNESSetFunction(snes, r, FormFunction, (void *)F)); 73 74 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 75 Create matrix data structure; set Jacobian evaluation routine 76 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 77 78 PetscCall(MatCreate(PETSC_COMM_WORLD, &J)); 79 PetscCall(MatSetSizes(J, PETSC_DECIDE, PETSC_DECIDE, n, n)); 80 PetscCall(MatSetFromOptions(J)); 81 PetscCall(MatSeqAIJSetPreallocation(J, 3, NULL)); 82 83 /* 84 Set Jacobian matrix data structure and default Jacobian evaluation 85 routine. User can override with: 86 -snes_fd : default finite differencing approximation of Jacobian 87 -snes_mf : matrix-free Newton-Krylov method with no preconditioning 88 (unless user explicitly sets preconditioner) 89 -snes_mf_operator : form matrix used to construct the preconditioner as set by the user, 90 but use matrix-free approx for Jacobian-vector 91 products within Newton-Krylov method 92 */ 93 94 PetscCall(SNESSetJacobian(snes, J, J, FormJacobian, NULL)); 95 96 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 97 Customize nonlinear solver; set runtime options 98 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 99 100 /* 101 Set an optional user-defined monitoring routine 102 */ 103 PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD, 0, 0, 0, 0, 400, 400, &monP.viewer)); 104 PetscCall(SNESMonitorSet(snes, Monitor, &monP, 0)); 105 106 /* 107 Set names for some vectors to facilitate monitoring (optional) 108 */ 109 PetscCall(PetscObjectSetName((PetscObject)x, "Approximate Solution")); 110 PetscCall(PetscObjectSetName((PetscObject)U, "Exact Solution")); 111 112 /* 113 Set SNES/KSP/KSP/PC runtime options, e.g., 114 -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc> 115 */ 116 PetscCall(SNESSetFromOptions(snes)); 117 118 /* 119 Print parameters used for convergence testing (optional) ... just 120 to demonstrate this routine; this information is also printed with 121 the option -snes_view 122 */ 123 PetscCall(SNESGetTolerances(snes, &abstol, &rtol, &stol, &maxit, &maxf)); 124 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "atol=%g, rtol=%g, stol=%g, maxit=%" PetscInt_FMT ", maxf=%" PetscInt_FMT "\n", (double)abstol, (double)rtol, (double)stol, maxit, maxf)); 125 126 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 127 Initialize application: 128 Store right-hand side of PDE and exact solution 129 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 130 131 xp = 0.0; 132 for (i = 0; i < n; i++) { 133 v = 6.0 * xp + PetscPowScalar(xp + 1.e-12, 6.0); /* +1.e-12 is to prevent 0^6 */ 134 PetscCall(VecSetValues(F, 1, &i, &v, INSERT_VALUES)); 135 v = xp * xp * xp; 136 PetscCall(VecSetValues(U, 1, &i, &v, INSERT_VALUES)); 137 xp += h; 138 } 139 140 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 141 Evaluate initial guess; then solve nonlinear system 142 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 143 /* 144 Note: The user should initialize the vector, x, with the initial guess 145 for the nonlinear solver prior to calling SNESSolve(). In particular, 146 to employ an initial guess of zero, the user should explicitly set 147 this vector to zero by calling VecSet(). 148 */ 149 PetscCall(FormInitialGuess(x)); 150 PetscCall(SNESSolve(snes, NULL, x)); 151 PetscCall(SNESGetIterationNumber(snes, &its)); 152 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "number of SNES iterations = %" PetscInt_FMT "\n\n", its)); 153 154 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 155 Check solution and clean up 156 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 157 158 /* 159 Check the error 160 */ 161 PetscCall(VecAXPY(x, none, U)); 162 PetscCall(VecNorm(x, NORM_2, &norm)); 163 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its)); 164 165 /* 166 Free work space. All PETSc objects should be destroyed when they 167 are no longer needed. 168 */ 169 PetscCall(VecDestroy(&x)); 170 PetscCall(VecDestroy(&r)); 171 PetscCall(VecDestroy(&U)); 172 PetscCall(VecDestroy(&F)); 173 PetscCall(MatDestroy(&J)); 174 PetscCall(SNESDestroy(&snes)); 175 PetscCall(PetscViewerDestroy(&monP.viewer)); 176 PetscCall(PetscFinalize()); 177 return 0; 178 } 179 /* ------------------------------------------------------------------- */ 180 /* 181 FormInitialGuess - Computes initial guess. 182 183 Input/Output Parameter: 184 . x - the solution vector 185 */ 186 PetscErrorCode FormInitialGuess(Vec x) 187 { 188 PetscFunctionBeginUser; 189 PetscCall(VecSet(x, 0.5)); 190 PetscFunctionReturn(PETSC_SUCCESS); 191 } 192 /* ------------------------------------------------------------------- */ 193 /* 194 FormFunction - Evaluates nonlinear function, F(x). 195 196 Input Parameters: 197 . snes - the SNES context 198 . x - input vector 199 . ctx - optional user-defined context, as set by SNESSetFunction() 200 201 Output Parameter: 202 . f - function vector 203 204 Note: 205 The user-defined context can contain any application-specific data 206 needed for the function evaluation (such as various parameters, work 207 vectors, and grid information). In this program the context is just 208 a vector containing the right-hand side of the discretized PDE. 209 */ 210 211 PetscErrorCode FormFunction(SNES snes, Vec x, Vec f, void *ctx) 212 { 213 Vec g = (Vec)ctx; 214 const PetscScalar *xx, *gg; 215 PetscScalar *ff, d; 216 PetscInt i, n; 217 218 PetscFunctionBeginUser; 219 /* 220 Get pointers to vector data. 221 - For default PETSc vectors, VecGetArray() returns a pointer to 222 the data array. Otherwise, the routine is implementation dependent. 223 - You MUST call VecRestoreArray() when you no longer need access to 224 the array. 225 */ 226 PetscCall(VecGetArrayRead(x, &xx)); 227 PetscCall(VecGetArray(f, &ff)); 228 PetscCall(VecGetArrayRead(g, &gg)); 229 230 /* 231 Compute function 232 */ 233 PetscCall(VecGetSize(x, &n)); 234 d = (PetscReal)(n - 1); 235 d = d * d; 236 ff[0] = xx[0]; 237 for (i = 1; i < n - 1; i++) ff[i] = d * (xx[i - 1] - 2.0 * xx[i] + xx[i + 1]) + xx[i] * xx[i] - gg[i]; 238 ff[n - 1] = xx[n - 1] - 1.0; 239 240 /* 241 Restore vectors 242 */ 243 PetscCall(VecRestoreArrayRead(x, &xx)); 244 PetscCall(VecRestoreArray(f, &ff)); 245 PetscCall(VecRestoreArrayRead(g, &gg)); 246 PetscFunctionReturn(PETSC_SUCCESS); 247 } 248 /* ------------------------------------------------------------------- */ 249 /* 250 FormJacobian - Evaluates Jacobian matrix. 251 252 Input Parameters: 253 . snes - the SNES context 254 . x - input vector 255 . dummy - optional user-defined context (not used here) 256 257 Output Parameters: 258 . jac - Jacobian matrix 259 . B - optionally different matrix used to construct the preconditioner 260 261 */ 262 263 PetscErrorCode FormJacobian(SNES snes, Vec x, Mat jac, Mat B, void *dummy) 264 { 265 const PetscScalar *xx; 266 PetscScalar A[3], d; 267 PetscInt i, n, j[3]; 268 269 PetscFunctionBeginUser; 270 /* 271 Get pointer to vector data 272 */ 273 PetscCall(VecGetArrayRead(x, &xx)); 274 275 /* 276 Compute Jacobian entries and insert into matrix. 277 - Note that in this case we set all elements for a particular 278 row at once. 279 */ 280 PetscCall(VecGetSize(x, &n)); 281 d = (PetscReal)(n - 1); 282 d = d * d; 283 284 /* 285 Interior grid points 286 */ 287 for (i = 1; i < n - 1; i++) { 288 j[0] = i - 1; 289 j[1] = i; 290 j[2] = i + 1; 291 A[0] = A[2] = d; 292 A[1] = -2.0 * d + 2.0 * xx[i]; 293 PetscCall(MatSetValues(B, 1, &i, 3, j, A, INSERT_VALUES)); 294 } 295 296 /* 297 Boundary points 298 */ 299 i = 0; 300 A[0] = 1.0; 301 302 PetscCall(MatSetValues(B, 1, &i, 1, &i, A, INSERT_VALUES)); 303 304 i = n - 1; 305 A[0] = 1.0; 306 307 PetscCall(MatSetValues(B, 1, &i, 1, &i, A, INSERT_VALUES)); 308 309 /* 310 Restore vector 311 */ 312 PetscCall(VecRestoreArrayRead(x, &xx)); 313 314 /* 315 Assemble matrix 316 */ 317 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 318 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 319 if (jac != B) { 320 PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY)); 321 PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY)); 322 } 323 PetscFunctionReturn(PETSC_SUCCESS); 324 } 325 /* ------------------------------------------------------------------- */ 326 /* 327 Monitor - User-defined monitoring routine that views the 328 current iterate with an x-window plot. 329 330 Input Parameters: 331 snes - the SNES context 332 its - iteration number 333 norm - 2-norm function value (may be estimated) 334 ctx - optional user-defined context for private data for the 335 monitor routine, as set by SNESMonitorSet() 336 337 Note: 338 See the manpage for PetscViewerDrawOpen() for useful runtime options, 339 such as -nox to deactivate all x-window output. 340 */ 341 PetscErrorCode Monitor(SNES snes, PetscInt its, PetscReal fnorm, void *ctx) 342 { 343 MonitorCtx *monP = (MonitorCtx *)ctx; 344 Vec x; 345 SNESConvergedReason reason; 346 347 PetscFunctionBeginUser; 348 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "iter = %" PetscInt_FMT ", SNES Function norm %g\n", its, (double)fnorm)); 349 PetscCall(SNESGetConvergedReason(snes, &reason)); 350 PetscCall(SNESGetSolution(snes, &x)); 351 PetscCall(VecView(x, monP->viewer)); 352 PetscCall(PetscPrintf(PETSC_COMM_WORLD, " converged = %s\n", SNESConvergedReasons[reason])); 353 PetscFunctionReturn(PETSC_SUCCESS); 354 } 355 356 /*TEST 357 358 test: 359 args: -nox -snes_monitor_cancel -snes_monitor_short -snes_view -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always 360 361 test: 362 suffix: 2 363 args: -nox -snes_monitor_cancel -snes_monitor_short -snes_type newtontr -snes_view 364 requires: !single 365 366 test: 367 suffix: 3 368 args: -nox -malloc no -options_left no -snes_monitor_cancel -snes_monitor_short -snes_view -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always 369 370 test: 371 suffix: 4 372 args: -nox -snes_monitor_cancel -snes_monitor_short -snes_type newtontrdc -snes_view 373 requires: !single 374 375 test: 376 suffix: 5 377 filter: grep -v atol | sed -e "s/CONVERGED_ITS/DIVERGED_MAX_IT/g" | sed -e "s/CONVERGED_FNORM_RELATIVE/DIVERGED_MAX_IT/g" 378 args: -nox -snes_type {{newtonls newtontr ncg ngmres qn anderson nrichardson ms ksponly ksptransposeonly vinewtonrsls vinewtonssls fas ms}} -snes_max_it 1 379 requires: !single 380 381 TEST*/ 382