1 2 static char help[] = "Newton method to solve u'' + u^{2} = f, sequentially.\n\ 3 This example employs a user-defined monitoring routine.\n\n"; 4 5 /* 6 Include "petscdraw.h" so that we can use PETSc drawing routines. 7 Include "petscsnes.h" so that we can use SNES solvers. Note that this 8 file automatically includes: 9 petscsys.h - base PETSc routines petscvec.h - vectors 10 petscmat.h - matrices 11 petscis.h - index sets petscksp.h - Krylov subspace methods 12 petscviewer.h - viewers petscpc.h - preconditioners 13 petscksp.h - linear solvers 14 */ 15 16 #include <petscsnes.h> 17 18 /* 19 User-defined routines 20 */ 21 extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *); 22 extern PetscErrorCode FormFunction(SNES, Vec, Vec, void *); 23 extern PetscErrorCode FormInitialGuess(Vec); 24 extern PetscErrorCode Monitor(SNES, PetscInt, PetscReal, void *); 25 26 /* 27 User-defined context for monitoring 28 */ 29 typedef struct { 30 PetscViewer viewer; 31 } MonitorCtx; 32 33 int main(int argc, char **argv) 34 { 35 SNES snes; /* SNES context */ 36 Vec x, r, F, U; /* vectors */ 37 Mat J; /* Jacobian matrix */ 38 MonitorCtx monP; /* monitoring context */ 39 PetscInt its, n = 5, i, maxit, maxf; 40 PetscMPIInt size; 41 PetscScalar h, xp, v, none = -1.0; 42 PetscReal abstol, rtol, stol, norm; 43 44 PetscFunctionBeginUser; 45 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 46 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 47 PetscCheck(size == 1, PETSC_COMM_SELF, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!"); 48 PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL)); 49 h = 1.0 / (n - 1); 50 51 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 52 Create nonlinear solver context 53 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 54 55 PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes)); 56 57 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 58 Create vector data structures; set function evaluation routine 59 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 60 /* 61 Note that we form 1 vector from scratch and then duplicate as needed. 62 */ 63 PetscCall(VecCreate(PETSC_COMM_WORLD, &x)); 64 PetscCall(VecSetSizes(x, PETSC_DECIDE, n)); 65 PetscCall(VecSetFromOptions(x)); 66 PetscCall(VecDuplicate(x, &r)); 67 PetscCall(VecDuplicate(x, &F)); 68 PetscCall(VecDuplicate(x, &U)); 69 70 /* 71 Set function evaluation routine and vector 72 */ 73 PetscCall(SNESSetFunction(snes, r, FormFunction, (void *)F)); 74 75 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 76 Create matrix data structure; set Jacobian evaluation routine 77 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 78 79 PetscCall(MatCreate(PETSC_COMM_WORLD, &J)); 80 PetscCall(MatSetSizes(J, PETSC_DECIDE, PETSC_DECIDE, n, n)); 81 PetscCall(MatSetFromOptions(J)); 82 PetscCall(MatSeqAIJSetPreallocation(J, 3, NULL)); 83 84 /* 85 Set Jacobian matrix data structure and default Jacobian evaluation 86 routine. User can override with: 87 -snes_fd : default finite differencing approximation of Jacobian 88 -snes_mf : matrix-free Newton-Krylov method with no preconditioning 89 (unless user explicitly sets preconditioner) 90 -snes_mf_operator : form preconditioning matrix as set by the user, 91 but use matrix-free approx for Jacobian-vector 92 products within Newton-Krylov method 93 */ 94 95 PetscCall(SNESSetJacobian(snes, J, J, FormJacobian, NULL)); 96 97 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 98 Customize nonlinear solver; set runtime options 99 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 100 101 /* 102 Set an optional user-defined monitoring routine 103 */ 104 PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD, 0, 0, 0, 0, 400, 400, &monP.viewer)); 105 PetscCall(SNESMonitorSet(snes, Monitor, &monP, 0)); 106 107 /* 108 Set names for some vectors to facilitate monitoring (optional) 109 */ 110 PetscCall(PetscObjectSetName((PetscObject)x, "Approximate Solution")); 111 PetscCall(PetscObjectSetName((PetscObject)U, "Exact Solution")); 112 113 /* 114 Set SNES/KSP/KSP/PC runtime options, e.g., 115 -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc> 116 */ 117 PetscCall(SNESSetFromOptions(snes)); 118 119 /* 120 Print parameters used for convergence testing (optional) ... just 121 to demonstrate this routine; this information is also printed with 122 the option -snes_view 123 */ 124 PetscCall(SNESGetTolerances(snes, &abstol, &rtol, &stol, &maxit, &maxf)); 125 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)); 126 127 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 128 Initialize application: 129 Store right-hand-side of PDE and exact solution 130 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 131 132 xp = 0.0; 133 for (i = 0; i < n; i++) { 134 v = 6.0 * xp + PetscPowScalar(xp + 1.e-12, 6.0); /* +1.e-12 is to prevent 0^6 */ 135 PetscCall(VecSetValues(F, 1, &i, &v, INSERT_VALUES)); 136 v = xp * xp * xp; 137 PetscCall(VecSetValues(U, 1, &i, &v, INSERT_VALUES)); 138 xp += h; 139 } 140 141 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 142 Evaluate initial guess; then solve nonlinear system 143 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 144 /* 145 Note: The user should initialize the vector, x, with the initial guess 146 for the nonlinear solver prior to calling SNESSolve(). In particular, 147 to employ an initial guess of zero, the user should explicitly set 148 this vector to zero by calling VecSet(). 149 */ 150 PetscCall(FormInitialGuess(x)); 151 PetscCall(SNESSolve(snes, NULL, x)); 152 PetscCall(SNESGetIterationNumber(snes, &its)); 153 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "number of SNES iterations = %" PetscInt_FMT "\n\n", its)); 154 155 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 156 Check solution and clean up 157 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 158 159 /* 160 Check the error 161 */ 162 PetscCall(VecAXPY(x, none, U)); 163 PetscCall(VecNorm(x, NORM_2, &norm)); 164 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its)); 165 166 /* 167 Free work space. All PETSc objects should be destroyed when they 168 are no longer needed. 169 */ 170 PetscCall(VecDestroy(&x)); 171 PetscCall(VecDestroy(&r)); 172 PetscCall(VecDestroy(&U)); 173 PetscCall(VecDestroy(&F)); 174 PetscCall(MatDestroy(&J)); 175 PetscCall(SNESDestroy(&snes)); 176 PetscCall(PetscViewerDestroy(&monP.viewer)); 177 PetscCall(PetscFinalize()); 178 return 0; 179 } 180 /* ------------------------------------------------------------------- */ 181 /* 182 FormInitialGuess - Computes initial guess. 183 184 Input/Output Parameter: 185 . x - the solution vector 186 */ 187 PetscErrorCode FormInitialGuess(Vec x) 188 { 189 PetscScalar pfive = .50; 190 PetscFunctionBeginUser; 191 PetscCall(VecSet(x, pfive)); 192 PetscFunctionReturn(PETSC_SUCCESS); 193 } 194 /* ------------------------------------------------------------------- */ 195 /* 196 FormFunction - Evaluates nonlinear function, F(x). 197 198 Input Parameters: 199 . snes - the SNES context 200 . x - input vector 201 . ctx - optional user-defined context, as set by SNESSetFunction() 202 203 Output Parameter: 204 . f - function vector 205 206 Note: 207 The user-defined context can contain any application-specific data 208 needed for the function evaluation (such as various parameters, work 209 vectors, and grid information). In this program the context is just 210 a vector containing the right-hand-side of the discretized PDE. 211 */ 212 213 PetscErrorCode FormFunction(SNES snes, Vec x, Vec f, void *ctx) 214 { 215 Vec g = (Vec)ctx; 216 const PetscScalar *xx, *gg; 217 PetscScalar *ff, d; 218 PetscInt i, n; 219 220 PetscFunctionBeginUser; 221 /* 222 Get pointers to vector data. 223 - For default PETSc vectors, VecGetArray() returns a pointer to 224 the data array. Otherwise, the routine is implementation dependent. 225 - You MUST call VecRestoreArray() when you no longer need access to 226 the array. 227 */ 228 PetscCall(VecGetArrayRead(x, &xx)); 229 PetscCall(VecGetArray(f, &ff)); 230 PetscCall(VecGetArrayRead(g, &gg)); 231 232 /* 233 Compute function 234 */ 235 PetscCall(VecGetSize(x, &n)); 236 d = (PetscReal)(n - 1); 237 d = d * d; 238 ff[0] = xx[0]; 239 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]; 240 ff[n - 1] = xx[n - 1] - 1.0; 241 242 /* 243 Restore vectors 244 */ 245 PetscCall(VecRestoreArrayRead(x, &xx)); 246 PetscCall(VecRestoreArray(f, &ff)); 247 PetscCall(VecRestoreArrayRead(g, &gg)); 248 PetscFunctionReturn(PETSC_SUCCESS); 249 } 250 /* ------------------------------------------------------------------- */ 251 /* 252 FormJacobian - Evaluates Jacobian matrix. 253 254 Input Parameters: 255 . snes - the SNES context 256 . x - input vector 257 . dummy - optional user-defined context (not used here) 258 259 Output Parameters: 260 . jac - Jacobian matrix 261 . B - optionally different preconditioning matrix 262 263 */ 264 265 PetscErrorCode FormJacobian(SNES snes, Vec x, Mat jac, Mat B, void *dummy) 266 { 267 const PetscScalar *xx; 268 PetscScalar A[3], d; 269 PetscInt i, n, j[3]; 270 271 PetscFunctionBeginUser; 272 /* 273 Get pointer to vector data 274 */ 275 PetscCall(VecGetArrayRead(x, &xx)); 276 277 /* 278 Compute Jacobian entries and insert into matrix. 279 - Note that in this case we set all elements for a particular 280 row at once. 281 */ 282 PetscCall(VecGetSize(x, &n)); 283 d = (PetscReal)(n - 1); 284 d = d * d; 285 286 /* 287 Interior grid points 288 */ 289 for (i = 1; i < n - 1; i++) { 290 j[0] = i - 1; 291 j[1] = i; 292 j[2] = i + 1; 293 A[0] = A[2] = d; 294 A[1] = -2.0 * d + 2.0 * xx[i]; 295 PetscCall(MatSetValues(B, 1, &i, 3, j, A, INSERT_VALUES)); 296 } 297 298 /* 299 Boundary points 300 */ 301 i = 0; 302 A[0] = 1.0; 303 304 PetscCall(MatSetValues(B, 1, &i, 1, &i, A, INSERT_VALUES)); 305 306 i = n - 1; 307 A[0] = 1.0; 308 309 PetscCall(MatSetValues(B, 1, &i, 1, &i, A, INSERT_VALUES)); 310 311 /* 312 Restore vector 313 */ 314 PetscCall(VecRestoreArrayRead(x, &xx)); 315 316 /* 317 Assemble matrix 318 */ 319 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 320 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 321 if (jac != B) { 322 PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY)); 323 PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY)); 324 } 325 PetscFunctionReturn(PETSC_SUCCESS); 326 } 327 /* ------------------------------------------------------------------- */ 328 /* 329 Monitor - User-defined monitoring routine that views the 330 current iterate with an x-window plot. 331 332 Input Parameters: 333 snes - the SNES context 334 its - iteration number 335 norm - 2-norm function value (may be estimated) 336 ctx - optional user-defined context for private data for the 337 monitor routine, as set by SNESMonitorSet() 338 339 Note: 340 See the manpage for PetscViewerDrawOpen() for useful runtime options, 341 such as -nox to deactivate all x-window output. 342 */ 343 PetscErrorCode Monitor(SNES snes, PetscInt its, PetscReal fnorm, void *ctx) 344 { 345 MonitorCtx *monP = (MonitorCtx *)ctx; 346 Vec x; 347 SNESConvergedReason reason; 348 349 PetscFunctionBeginUser; 350 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "iter = %" PetscInt_FMT ", SNES Function norm %g\n", its, (double)fnorm)); 351 PetscCall(SNESGetConvergedReason(snes, &reason)); 352 PetscCall(SNESGetSolution(snes, &x)); 353 PetscCall(VecView(x, monP->viewer)); 354 PetscCall(PetscPrintf(PETSC_COMM_WORLD, " converged = %s\n", SNESConvergedReasons[reason])); 355 PetscFunctionReturn(PETSC_SUCCESS); 356 } 357 358 /*TEST 359 360 test: 361 args: -nox -snes_monitor_cancel -snes_monitor_short -snes_view -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always 362 363 test: 364 suffix: 2 365 args: -nox -snes_monitor_cancel -snes_monitor_short -snes_type newtontr -snes_view 366 requires: !single 367 368 test: 369 suffix: 3 370 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 371 372 test: 373 suffix: 4 374 args: -nox -snes_monitor_cancel -snes_monitor_short -snes_type newtontrdc -snes_view 375 requires: !single 376 377 test: 378 suffix: 5 379 filter: grep -v atol | sed -e "s/CONVERGED_ITS/DIVERGED_MAX_IT/g" | sed -e "s/CONVERGED_FNORM_RELATIVE/DIVERGED_MAX_IT/g" 380 args: -nox -snes_type {{newtonls newtontr ncg ngmres qn anderson nrichardson ms ksponly ksptransposeonly vinewtonrsls vinewtonssls fas ms}} -snes_max_it 1 381 requires: !single 382 383 TEST*/ 384