1 static char help[] = "Newton method to solve u'' + u^{2} = f, sequentially.\n\ 2 This example tests PCVPBJacobiSetBlocks().\n\n"; 3 4 /* 5 Include "petscsnes.h" so that we can use SNES solvers. Note that this 6 file automatically includes: 7 petscsys.h - base PETSc routines petscvec.h - vectors 8 petscmat.h - matrices 9 petscis.h - index sets petscksp.h - Krylov subspace methods 10 petscviewer.h - viewers petscpc.h - preconditioners 11 petscksp.h - linear solvers 12 */ 13 14 #include <petscsnes.h> 15 16 /* 17 User-defined routines 18 */ 19 extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *); 20 extern PetscErrorCode FormFunction(SNES, Vec, Vec, void *); 21 extern PetscErrorCode FormInitialGuess(Vec); 22 23 int main(int argc, char **argv) 24 { 25 SNES snes; /* SNES context */ 26 Vec x, r, F, U; /* vectors */ 27 Mat J; /* Jacobian matrix */ 28 PetscInt its, n = 5, nb, maxit, maxf, *lens; 29 PetscMPIInt size; 30 PetscScalar h, xp, v, none = -1.0; 31 PetscReal abstol, rtol, stol, norm; 32 KSP ksp; 33 PC pc; 34 35 PetscFunctionBeginUser; 36 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 37 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 38 PetscCheck(size == 1, PETSC_COMM_SELF, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only"); 39 PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL)); 40 PetscCheck(n % 5 == 0, PETSC_COMM_SELF, PETSC_ERR_SUP, "n must be a multiple of 5"); 41 h = 1.0 / (n - 1); 42 43 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 44 Create vector data structures 45 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 46 /* 47 Note that we form 1 vector from scratch and then duplicate as needed. 48 */ 49 PetscCall(VecCreate(PETSC_COMM_WORLD, &x)); 50 PetscCall(VecSetSizes(x, PETSC_DECIDE, n)); 51 PetscCall(VecSetFromOptions(x)); 52 PetscCall(VecDuplicate(x, &r)); 53 PetscCall(VecDuplicate(x, &F)); 54 PetscCall(VecDuplicate(x, &U)); 55 56 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 57 Create matrix data structure 58 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 59 60 PetscCall(MatCreate(PETSC_COMM_WORLD, &J)); 61 PetscCall(MatSetSizes(J, PETSC_DECIDE, PETSC_DECIDE, n, n)); 62 PetscCall(MatSetFromOptions(J)); 63 PetscCall(MatSeqAIJSetPreallocation(J, 3, NULL)); 64 PetscCall(MatSetBlockSize(J, 5)); 65 66 nb = 3 * n / 5; 67 PetscCall(PetscMalloc1(nb, &lens)); 68 for (PetscInt i = 0; i < nb / 3; i++) { 69 lens[3 * i + 0] = 1; 70 lens[3 * i + 1] = 2; 71 lens[3 * i + 2] = 2; 72 } 73 PetscCall(MatSetVariableBlockSizes(J, nb, lens)); 74 PetscCall(PetscFree(lens)); 75 76 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 77 Create nonlinear solver context 78 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 79 80 PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes)); 81 PetscCall(SNESGetKSP(snes, &ksp)); 82 PetscCall(KSPGetPC(ksp, &pc)); 83 PetscCall(PCSetType(pc, PCVPBJACOBI)); 84 85 /* 86 Set function evaluation routine and vector 87 */ 88 PetscCall(SNESSetFunction(snes, r, FormFunction, (void *)F)); 89 90 /* 91 Set Jacobian matrix data structure and default Jacobian evaluation 92 routine. User can override with: 93 -snes_fd : default finite differencing approximation of Jacobian 94 -snes_mf : matrix-free Newton-Krylov method with no preconditioning 95 (unless user explicitly sets preconditioner) 96 -snes_mf_operator : form matrix used to construct the preconditioner as set by the user, 97 but use matrix-free approx for Jacobian-vector 98 products within Newton-Krylov method 99 */ 100 101 PetscCall(SNESSetJacobian(snes, J, J, FormJacobian, NULL)); 102 103 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 104 Customize nonlinear solver; set runtime options 105 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 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 (PetscInt 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(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 PetscScalar pfive = .50; 189 190 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 matrix used to construct the preconditioner 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] = d; 294 A[1] = -2.0 * d + 2.0 * xx[i]; 295 A[2] = d; 296 PetscCall(MatSetValues(B, 1, &i, 3, j, A, INSERT_VALUES)); 297 } 298 299 /* 300 Boundary points 301 */ 302 i = 0; 303 A[0] = 1.0; 304 305 PetscCall(MatSetValues(B, 1, &i, 1, &i, A, INSERT_VALUES)); 306 307 i = n - 1; 308 A[0] = 1.0; 309 310 PetscCall(MatSetValues(B, 1, &i, 1, &i, A, INSERT_VALUES)); 311 312 /* 313 Restore vector 314 */ 315 PetscCall(VecRestoreArrayRead(x, &xx)); 316 317 /* 318 Assemble matrix 319 */ 320 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 321 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 322 if (jac != B) { 323 PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY)); 324 PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY)); 325 } 326 PetscFunctionReturn(PETSC_SUCCESS); 327 } 328 329 /*TEST 330 331 testset: 332 args: -snes_monitor_short -snes_view -ksp_monitor 333 output_file: output/ex5_1.out 334 filter: grep -v "type: seqaij" 335 336 test: 337 suffix: 1 338 339 test: 340 suffix: cuda 341 requires: cuda 342 args: -mat_type aijcusparse -vec_type cuda 343 344 test: 345 suffix: kok 346 requires: kokkos_kernels 347 args: -mat_type aijkokkos -vec_type kokkos 348 349 # this is just a test for SNESKSPTRANSPOSEONLY and KSPSolveTranspose() to behave properly 350 # the solution is wrong on purpose 351 test: 352 requires: !single !complex 353 suffix: transpose_only 354 args: -snes_monitor_short -snes_view -ksp_monitor -snes_type ksptransposeonly -pc_type ilu -snes_test_jacobian -snes_test_jacobian_view -ksp_view_rhs -ksp_view_solution -ksp_view_mat_explicit -ksp_view_preconditioned_operator_explicit 355 356 test: 357 requires: mumps 358 suffix: mumps 359 args: -pc_type lu -pc_factor_mat_solver_type mumps -mat_mumps_icntl_15 1 -snes_monitor_short -ksp_monitor 360 361 test: 362 suffix: fieldsplit_1 363 args: -snes_monitor_short -snes_view -ksp_monitor -pc_type fieldsplit -pc_fieldsplit_0_fields 0,1 -pc_fieldsplit_1_fields 2,3,4 364 365 test: 366 suffix: fieldsplit_2 367 args: -snes_monitor_short -snes_view -ksp_monitor -pc_type fieldsplit -pc_fieldsplit_0_fields 1,0 -pc_fieldsplit_1_fields 2,3,4 368 369 TEST*/ 370