1 static const char help[] = "-Laplacian u = b as a nonlinear problem.\n\n"; 2 3 /* 4 5 The linear and nonlinear versions of these should give almost identical results on this problem 6 7 Richardson 8 Nonlinear: 9 -snes_rtol 1.e-12 -snes_monitor -snes_type nrichardson -snes_linesearch_monitor 10 11 Linear: 12 -snes_rtol 1.e-12 -snes_monitor -ksp_rtol 1.e-12 -ksp_monitor -ksp_type richardson -pc_type none -ksp_richardson_self_scale -info 13 14 GMRES 15 Nonlinear: 16 -snes_rtol 1.e-12 -snes_monitor -snes_type ngmres 17 18 Linear: 19 -snes_rtol 1.e-12 -snes_monitor -ksp_type gmres -ksp_monitor -ksp_rtol 1.e-12 -pc_type none 20 21 CG 22 Nonlinear: 23 -snes_rtol 1.e-12 -snes_monitor -snes_type ncg -snes_linesearch_monitor 24 25 Linear: 26 -snes_rtol 1.e-12 -snes_monitor -ksp_type cg -ksp_monitor -ksp_rtol 1.e-12 -pc_type none 27 28 Multigrid 29 Linear: 30 1 level: 31 -snes_rtol 1.e-12 -snes_monitor -pc_type mg -mg_levels_ksp_type richardson -mg_levels_pc_type none -mg_levels_ksp_monitor 32 -mg_levels_ksp_richardson_self_scale -ksp_type richardson -ksp_monitor -ksp_rtol 1.e-12 -ksp_monitor_true_residual 33 34 n levels: 35 -da_refine n 36 37 Nonlinear: 38 1 level: 39 -snes_rtol 1.e-12 -snes_monitor -snes_type fas -fas_levels_snes_monitor 40 41 n levels: 42 -da_refine n -fas_coarse_snes_type newtonls -fas_coarse_pc_type lu -fas_coarse_ksp_type preonly 43 44 */ 45 46 /* 47 Include "petscdmda.h" so that we can use distributed arrays (DMDAs). 48 Include "petscsnes.h" so that we can use SNES solvers. Note that this 49 */ 50 #include <petscdm.h> 51 #include <petscdmda.h> 52 #include <petscsnes.h> 53 54 /* 55 User-defined routines 56 */ 57 extern PetscErrorCode FormMatrix(DM, Mat); 58 extern PetscErrorCode MyComputeFunction(SNES, Vec, Vec, void *); 59 extern PetscErrorCode MyComputeJacobian(SNES, Vec, Mat, Mat, void *); 60 extern PetscErrorCode NonlinearGS(SNES, Vec); 61 62 int main(int argc, char **argv) 63 { 64 SNES snes; /* nonlinear solver */ 65 SNES psnes; /* nonlinear Gauss-Seidel approximate solver */ 66 Vec x, b; /* solution vector */ 67 PetscInt its; /* iterations for convergence */ 68 DM da; 69 PetscBool use_ngs_as_npc = PETSC_FALSE; /* use the nonlinear Gauss-Seidel approximate solver */ 70 71 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 72 Initialize program 73 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 74 75 PetscFunctionBeginUser; 76 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 77 78 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 79 Create nonlinear solver context 80 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 81 PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes)); 82 83 PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_ngs_as_npc", &use_ngs_as_npc, 0)); 84 85 if (use_ngs_as_npc) { 86 PetscCall(SNESGetNPC(snes, &psnes)); 87 PetscCall(SNESSetType(psnes, SNESSHELL)); 88 PetscCall(SNESShellSetSolve(psnes, NonlinearGS)); 89 } 90 91 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 92 Create distributed array (DMDA) to manage parallel grid and vectors 93 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 94 PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, 4, 4, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, NULL, &da)); 95 PetscCall(DMSetFromOptions(da)); 96 PetscCall(DMSetUp(da)); 97 PetscCall(DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0)); 98 PetscCall(SNESSetDM(snes, da)); 99 if (use_ngs_as_npc) PetscCall(SNESShellSetContext(psnes, da)); 100 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 101 Extract global vectors from DMDA; then duplicate for remaining 102 vectors that are the same types 103 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 104 PetscCall(DMCreateGlobalVector(da, &x)); 105 PetscCall(DMCreateGlobalVector(da, &b)); 106 PetscCall(VecSet(b, 1.0)); 107 108 PetscCall(SNESSetFunction(snes, NULL, MyComputeFunction, NULL)); 109 PetscCall(SNESSetJacobian(snes, NULL, NULL, MyComputeJacobian, NULL)); 110 111 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 112 Customize nonlinear solver; set runtime options 113 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 114 PetscCall(SNESSetFromOptions(snes)); 115 116 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 117 Solve nonlinear system 118 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 119 PetscCall(SNESSolve(snes, b, x)); 120 PetscCall(SNESGetIterationNumber(snes, &its)); 121 122 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 123 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 124 125 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 126 Free work space. All PETSc objects should be destroyed when they 127 are no longer needed. 128 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 129 PetscCall(VecDestroy(&x)); 130 PetscCall(VecDestroy(&b)); 131 PetscCall(SNESDestroy(&snes)); 132 PetscCall(DMDestroy(&da)); 133 PetscCall(PetscFinalize()); 134 return 0; 135 } 136 137 /* ------------------------------------------------------------------- */ 138 PetscErrorCode MyComputeFunction(SNES snes, Vec x, Vec F, void *ctx) 139 { 140 Mat J; 141 DM dm; 142 143 PetscFunctionBeginUser; 144 PetscCall(SNESGetDM(snes, &dm)); 145 PetscCall(DMGetApplicationContext(dm, &J)); 146 if (!J) { 147 PetscCall(DMSetMatType(dm, MATAIJ)); 148 PetscCall(DMCreateMatrix(dm, &J)); 149 PetscCall(MatSetDM(J, NULL)); 150 PetscCall(FormMatrix(dm, J)); 151 PetscCall(DMSetApplicationContext(dm, J)); 152 PetscCall(DMSetApplicationContextDestroy(dm, (PetscErrorCode(*)(void **))MatDestroy)); 153 } 154 PetscCall(MatMult(J, x, F)); 155 PetscFunctionReturn(0); 156 } 157 158 PetscErrorCode MyComputeJacobian(SNES snes, Vec x, Mat J, Mat Jp, void *ctx) 159 { 160 DM dm; 161 162 PetscFunctionBeginUser; 163 PetscCall(SNESGetDM(snes, &dm)); 164 PetscCall(FormMatrix(dm, Jp)); 165 PetscFunctionReturn(0); 166 } 167 168 PetscErrorCode FormMatrix(DM da, Mat jac) 169 { 170 PetscInt i, j, nrows = 0; 171 MatStencil col[5], row, *rows; 172 PetscScalar v[5], hx, hy, hxdhy, hydhx; 173 DMDALocalInfo info; 174 175 PetscFunctionBeginUser; 176 PetscCall(DMDAGetLocalInfo(da, &info)); 177 hx = 1.0 / (PetscReal)(info.mx - 1); 178 hy = 1.0 / (PetscReal)(info.my - 1); 179 hxdhy = hx / hy; 180 hydhx = hy / hx; 181 182 PetscCall(PetscMalloc1(info.ym * info.xm, &rows)); 183 /* 184 Compute entries for the locally owned part of the Jacobian. 185 - Currently, all PETSc parallel matrix formats are partitioned by 186 contiguous chunks of rows across the processors. 187 - Each processor needs to insert only elements that it owns 188 locally (but any non-local elements will be sent to the 189 appropriate processor during matrix assembly). 190 - Here, we set all entries for a particular row at once. 191 - We can set matrix entries either using either 192 MatSetValuesLocal() or MatSetValues(), as discussed above. 193 */ 194 for (j = info.ys; j < info.ys + info.ym; j++) { 195 for (i = info.xs; i < info.xs + info.xm; i++) { 196 row.j = j; 197 row.i = i; 198 /* boundary points */ 199 if (i == 0 || j == 0 || i == info.mx - 1 || j == info.my - 1) { 200 v[0] = 2.0 * (hydhx + hxdhy); 201 PetscCall(MatSetValuesStencil(jac, 1, &row, 1, &row, v, INSERT_VALUES)); 202 rows[nrows].i = i; 203 rows[nrows++].j = j; 204 } else { 205 /* interior grid points */ 206 v[0] = -hxdhy; 207 col[0].j = j - 1; 208 col[0].i = i; 209 v[1] = -hydhx; 210 col[1].j = j; 211 col[1].i = i - 1; 212 v[2] = 2.0 * (hydhx + hxdhy); 213 col[2].j = row.j; 214 col[2].i = row.i; 215 v[3] = -hydhx; 216 col[3].j = j; 217 col[3].i = i + 1; 218 v[4] = -hxdhy; 219 col[4].j = j + 1; 220 col[4].i = i; 221 PetscCall(MatSetValuesStencil(jac, 1, &row, 5, col, v, INSERT_VALUES)); 222 } 223 } 224 } 225 226 /* 227 Assemble matrix, using the 2-step process: 228 MatAssemblyBegin(), MatAssemblyEnd(). 229 */ 230 PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY)); 231 PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY)); 232 PetscCall(MatZeroRowsColumnsStencil(jac, nrows, rows, 2.0 * (hydhx + hxdhy), NULL, NULL)); 233 PetscCall(PetscFree(rows)); 234 /* 235 Tell the matrix we will never add a new nonzero location to the 236 matrix. If we do, it will generate an error. 237 */ 238 PetscCall(MatSetOption(jac, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE)); 239 PetscFunctionReturn(0); 240 } 241 242 /* ------------------------------------------------------------------- */ 243 /* 244 Applies some sweeps on nonlinear Gauss-Seidel on each process 245 246 */ 247 PetscErrorCode NonlinearGS(SNES snes, Vec X) 248 { 249 PetscInt i, j, Mx, My, xs, ys, xm, ym, its, l; 250 PetscReal hx, hy, hxdhy, hydhx; 251 PetscScalar **x, F, J, u, uxx, uyy; 252 DM da; 253 Vec localX; 254 255 PetscFunctionBeginUser; 256 PetscCall(SNESGetTolerances(snes, NULL, NULL, NULL, &its, NULL)); 257 PetscCall(SNESShellGetContext(snes, &da)); 258 259 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &Mx, &My, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE)); 260 261 hx = 1.0 / (PetscReal)(Mx - 1); 262 hy = 1.0 / (PetscReal)(My - 1); 263 hxdhy = hx / hy; 264 hydhx = hy / hx; 265 266 PetscCall(DMGetLocalVector(da, &localX)); 267 268 for (l = 0; l < its; l++) { 269 PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX)); 270 PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX)); 271 /* 272 Get a pointer to vector data. 273 - For default PETSc vectors, VecGetArray() returns a pointer to 274 the data array. Otherwise, the routine is implementation dependent. 275 - You MUST call VecRestoreArray() when you no longer need access to 276 the array. 277 */ 278 PetscCall(DMDAVecGetArray(da, localX, &x)); 279 280 /* 281 Get local grid boundaries (for 2-dimensional DMDA): 282 xs, ys - starting grid indices (no ghost points) 283 xm, ym - widths of local grid (no ghost points) 284 285 */ 286 PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL)); 287 288 for (j = ys; j < ys + ym; j++) { 289 for (i = xs; i < xs + xm; i++) { 290 if (i == 0 || j == 0 || i == Mx - 1 || j == My - 1) { 291 /* boundary conditions are all zero Dirichlet */ 292 x[j][i] = 0.0; 293 } else { 294 u = x[j][i]; 295 uxx = (2.0 * u - x[j][i - 1] - x[j][i + 1]) * hydhx; 296 uyy = (2.0 * u - x[j - 1][i] - x[j + 1][i]) * hxdhy; 297 F = uxx + uyy; 298 J = 2.0 * (hydhx + hxdhy); 299 u = u - F / J; 300 301 x[j][i] = u; 302 } 303 } 304 } 305 306 /* 307 Restore vector 308 */ 309 PetscCall(DMDAVecRestoreArray(da, localX, &x)); 310 PetscCall(DMLocalToGlobalBegin(da, localX, INSERT_VALUES, X)); 311 PetscCall(DMLocalToGlobalEnd(da, localX, INSERT_VALUES, X)); 312 } 313 PetscCall(DMRestoreLocalVector(da, &localX)); 314 PetscFunctionReturn(0); 315 } 316 317 /*TEST 318 319 test: 320 args: -snes_monitor_short -snes_type nrichardson 321 requires: !single 322 323 test: 324 suffix: 2 325 args: -snes_monitor_short -ksp_monitor_short -ksp_type richardson -pc_type none -ksp_richardson_self_scale 326 requires: !single 327 328 test: 329 suffix: 3 330 args: -snes_monitor_short -snes_type ngmres 331 332 test: 333 suffix: 4 334 args: -snes_monitor_short -ksp_type gmres -ksp_monitor_short -pc_type none 335 336 test: 337 suffix: 5 338 args: -snes_monitor_short -snes_type ncg 339 340 test: 341 suffix: 6 342 args: -snes_monitor_short -ksp_type cg -ksp_monitor_short -pc_type none 343 344 test: 345 suffix: 7 346 args: -da_refine 2 -snes_monitor_short -pc_type mg -mg_levels_ksp_type richardson -mg_levels_pc_type none -mg_levels_ksp_monitor_short -mg_levels_ksp_richardson_self_scale -ksp_type richardson -ksp_monitor_short 347 requires: !single 348 349 test: 350 suffix: 8 351 args: -da_refine 2 -snes_monitor_short -snes_type fas -fas_levels_snes_monitor_short -fas_coarse_snes_type newtonls -fas_coarse_pc_type lu -fas_coarse_ksp_type preonly -snes_type fas -snes_rtol 1.e-5 352 353 test: 354 suffix: 9 355 args: -snes_monitor_short -ksp_type gmres -ksp_monitor_short -pc_type none -snes_type newtontrdc 356 357 test: 358 suffix: 10 359 args: -snes_monitor_short -ksp_type gmres -ksp_monitor_short -pc_type none -snes_type newtontrdc -snes_trdc_use_cauchy false 360 361 TEST*/ 362