1Timestep: 0000 time = 0 L_2 Error: 1.0821e-16 20 TS dt 0.1 time 0. 3 0 SNES Function norm 0.38487 4 0 KSP unpreconditioned resid norm 3.848701079585e-01 true resid norm 3.848701079585e-01 ||r(i)||/||b|| 1.000000000000e+00 5 1 KSP unpreconditioned resid norm 6.306958768405e-02 true resid norm 6.306958768405e-02 ||r(i)||/||b|| 1.638723984531e-01 6 2 KSP unpreconditioned resid norm 5.760676204313e-03 true resid norm 5.760676204313e-03 ||r(i)||/||b|| 1.496784521633e-02 7 3 KSP unpreconditioned resid norm 4.612023997603e-04 true resid norm 4.612023997603e-04 ||r(i)||/||b|| 1.198332606829e-03 8 4 KSP unpreconditioned resid norm 7.800377626583e-05 true resid norm 7.800377626586e-05 ||r(i)||/||b|| 2.026755901611e-04 9 5 KSP unpreconditioned resid norm 5.796001277060e-06 true resid norm 5.796001277043e-06 ||r(i)||/||b|| 1.505962961839e-05 10 6 KSP unpreconditioned resid norm 6.294785394574e-07 true resid norm 6.294785394633e-07 ||r(i)||/||b|| 1.635561002132e-06 11 7 KSP unpreconditioned resid norm 4.711800149142e-09 true resid norm 4.711800136142e-09 ||r(i)||/||b|| 1.224257233469e-08 12 8 KSP unpreconditioned resid norm 1.845375931471e-11 true resid norm 1.845373359363e-11 ||r(i)||/||b|| 4.794795234038e-11 13 1 SNES Function norm 1.845e-11 14 Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1 15SNES Object: 1 MPI process 16 type: newtonls 17 maximum iterations=50, maximum function evaluations=10000 18 tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 19 total number of linear solver iterations=8 20 total number of function evaluations=2 21 norm schedule ALWAYS 22 SNESLineSearch Object: 1 MPI process 23 type: bt 24 interpolation: cubic 25 alpha=1.000000e-04 26 maxlambda=1.000000e+00, minlambda=1.000000e-12 27 tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08 28 maximum iterations=40 29 KSP Object: 1 MPI process 30 type: fgmres 31 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 32 happy breakdown tolerance=1e-30 33 maximum iterations=10000, initial guess is zero 34 tolerances: relative=1e-09, absolute=1e-50, divergence=10000. 35 right preconditioning 36 using UNPRECONDITIONED norm type for convergence test 37 PC Object: 1 MPI process 38 type: mg 39 type is MULTIPLICATIVE, levels=2 cycles=v 40 Cycles per PCApply=1 41 Not using Galerkin computed coarse grid matrices 42 Coarse grid solver -- level 0 ------------------------------- 43 KSP Object: (mg_coarse_) 1 MPI process 44 type: preonly 45 maximum iterations=10000, initial guess is zero 46 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 47 left preconditioning 48 not checking for convergence 49 PC Object: (mg_coarse_) 1 MPI process 50 type: lu 51 out-of-place factorization 52 tolerance for zero pivot 2.22045e-14 53 using diagonal shift on blocks to prevent zero pivot [INBLOCKS] 54 matrix ordering: nd 55 factor fill ratio given 1., needed 1. 56 Factored matrix: 57 Mat Object: (mg_coarse_) 1 MPI process 58 type: seqaij 59 rows=1, cols=1 60 package used to perform factorization: petsc 61 total: nonzeros=1, allocated nonzeros=1 62 not using I-node routines 63 linear system matrix, which is also used to construct the preconditioner: 64 Mat Object: 1 MPI process 65 type: seqaij 66 rows=1, cols=1 67 total: nonzeros=1, allocated nonzeros=1 68 total number of mallocs used during MatSetValues calls=0 69 not using I-node routines 70 Down solver (pre-smoother) on level 1 ------------------------------- 71 KSP Object: (mg_levels_1_) 1 MPI process 72 type: chebyshev 73 Chebyshev polynomial of first kind 74 eigenvalue targets used: min 0.151841, max 1.67025 75 eigenvalues estimated via gmres: min 0.994613, max 1.51841 76 eigenvalues estimated using gmres with transform: [0. 0.1; 0. 1.1] 77 KSP Object: (mg_levels_1_esteig_) 1 MPI process 78 type: gmres 79 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 80 happy breakdown tolerance=1e-30 81 maximum iterations=10, initial guess is zero 82 tolerances: relative=1e-12, absolute=1e-50, divergence=10000. 83 left preconditioning 84 using PRECONDITIONED norm type for convergence test 85 estimating eigenvalues using a noisy random number generated right-hand side 86 maximum iterations=2, nonzero initial guess 87 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 88 left preconditioning 89 not checking for convergence 90 PC Object: (mg_levels_1_) 1 MPI process 91 type: sor 92 type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. 93 linear system matrix, which is also used to construct the preconditioner: 94 Mat Object: 1 MPI process 95 type: seqaij 96 rows=9, cols=9 97 total: nonzeros=41, allocated nonzeros=41 98 total number of mallocs used during MatSetValues calls=0 99 not using I-node routines 100 Up solver (post-smoother) same as down solver (pre-smoother) 101 linear system matrix, which is also used to construct the preconditioner: 102 Mat Object: 1 MPI process 103 type: seqaij 104 rows=9, cols=9 105 total: nonzeros=41, allocated nonzeros=41 106 total number of mallocs used during MatSetValues calls=0 107 not using I-node routines 108Timestep: 0001 time = 0.1 L_2 Error: 0.042609 1091 TS dt 0.1 time 0.1 110 0 SNES Function norm 0.383649 111 0 KSP unpreconditioned resid norm 3.836491353067e-01 true resid norm 3.836491353067e-01 ||r(i)||/||b|| 1.000000000000e+00 112 1 KSP unpreconditioned resid norm 6.087119748495e-02 true resid norm 6.087119748495e-02 ||r(i)||/||b|| 1.586637160965e-01 113 2 KSP unpreconditioned resid norm 5.740698672644e-03 true resid norm 5.740698672644e-03 ||r(i)||/||b|| 1.496340834459e-02 114 3 KSP unpreconditioned resid norm 4.605229592736e-04 true resid norm 4.605229592736e-04 ||r(i)||/||b|| 1.200375334889e-03 115 4 KSP unpreconditioned resid norm 7.848908845461e-05 true resid norm 7.848908845462e-05 ||r(i)||/||b|| 2.045855997874e-04 116 5 KSP unpreconditioned resid norm 5.648624058193e-06 true resid norm 5.648624058220e-06 ||r(i)||/||b|| 1.472341141523e-05 117 6 KSP unpreconditioned resid norm 6.188836190140e-07 true resid norm 6.188836190145e-07 ||r(i)||/||b|| 1.613150042733e-06 118 7 KSP unpreconditioned resid norm 4.800059529470e-09 true resid norm 4.800059540549e-09 ||r(i)||/||b|| 1.251158701742e-08 119 8 KSP unpreconditioned resid norm 1.774392929439e-11 true resid norm 1.774395612425e-11 ||r(i)||/||b|| 4.625047860478e-11 120 1 SNES Function norm 1.774e-11 121 Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1 122SNES Object: 1 MPI process 123 type: newtonls 124 maximum iterations=50, maximum function evaluations=10000 125 tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 126 total number of linear solver iterations=8 127 total number of function evaluations=2 128 norm schedule ALWAYS 129 SNESLineSearch Object: 1 MPI process 130 type: bt 131 interpolation: cubic 132 alpha=1.000000e-04 133 maxlambda=1.000000e+00, minlambda=1.000000e-12 134 tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08 135 maximum iterations=40 136 KSP Object: 1 MPI process 137 type: fgmres 138 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 139 happy breakdown tolerance=1e-30 140 maximum iterations=10000, initial guess is zero 141 tolerances: relative=1e-09, absolute=1e-50, divergence=10000. 142 right preconditioning 143 using UNPRECONDITIONED norm type for convergence test 144 PC Object: 1 MPI process 145 type: mg 146 type is MULTIPLICATIVE, levels=2 cycles=v 147 Cycles per PCApply=1 148 Not using Galerkin computed coarse grid matrices 149 Coarse grid solver -- level 0 ------------------------------- 150 KSP Object: (mg_coarse_) 1 MPI process 151 type: preonly 152 maximum iterations=10000, initial guess is zero 153 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 154 left preconditioning 155 not checking for convergence 156 PC Object: (mg_coarse_) 1 MPI process 157 type: lu 158 out-of-place factorization 159 tolerance for zero pivot 2.22045e-14 160 using diagonal shift on blocks to prevent zero pivot [INBLOCKS] 161 matrix ordering: nd 162 factor fill ratio given 1., needed 1. 163 Factored matrix: 164 Mat Object: (mg_coarse_) 1 MPI process 165 type: seqaij 166 rows=1, cols=1 167 package used to perform factorization: petsc 168 total: nonzeros=1, allocated nonzeros=1 169 not using I-node routines 170 linear system matrix, which is also used to construct the preconditioner: 171 Mat Object: 1 MPI process 172 type: seqaij 173 rows=1, cols=1 174 total: nonzeros=1, allocated nonzeros=1 175 total number of mallocs used during MatSetValues calls=0 176 not using I-node routines 177 Down solver (pre-smoother) on level 1 ------------------------------- 178 KSP Object: (mg_levels_1_) 1 MPI process 179 type: chebyshev 180 Chebyshev polynomial of first kind 181 eigenvalue targets used: min 0.151841, max 1.67025 182 eigenvalues estimated via gmres: min 0.994613, max 1.51841 183 eigenvalues estimated using gmres with transform: [0. 0.1; 0. 1.1] 184 KSP Object: (mg_levels_1_esteig_) 1 MPI process 185 type: gmres 186 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 187 happy breakdown tolerance=1e-30 188 maximum iterations=10, initial guess is zero 189 tolerances: relative=1e-12, absolute=1e-50, divergence=10000. 190 left preconditioning 191 using PRECONDITIONED norm type for convergence test 192 estimating eigenvalues using a noisy random number generated right-hand side 193 maximum iterations=2, nonzero initial guess 194 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 195 left preconditioning 196 not checking for convergence 197 PC Object: (mg_levels_1_) 1 MPI process 198 type: sor 199 type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. 200 linear system matrix, which is also used to construct the preconditioner: 201 Mat Object: 1 MPI process 202 type: seqaij 203 rows=9, cols=9 204 total: nonzeros=41, allocated nonzeros=41 205 total number of mallocs used during MatSetValues calls=0 206 not using I-node routines 207 Up solver (post-smoother) same as down solver (pre-smoother) 208 linear system matrix, which is also used to construct the preconditioner: 209 Mat Object: 1 MPI process 210 type: seqaij 211 rows=9, cols=9 212 total: nonzeros=41, allocated nonzeros=41 213 total number of mallocs used during MatSetValues calls=0 214 not using I-node routines 215Timestep: 0002 time = 0.2 L_2 Error: 0.084372 2162 TS dt 0.1 time 0.2 217 0 SNES Function norm 0.380922 218 0 KSP unpreconditioned resid norm 3.809222270566e-01 true resid norm 3.809222270566e-01 ||r(i)||/||b|| 1.000000000000e+00 219 1 KSP unpreconditioned resid norm 5.968841254678e-02 true resid norm 5.968841254678e-02 ||r(i)||/||b|| 1.566944859270e-01 220 2 KSP unpreconditioned resid norm 5.800384745162e-03 true resid norm 5.800384745162e-03 ||r(i)||/||b|| 1.522721525069e-02 221 3 KSP unpreconditioned resid norm 4.622462756028e-04 true resid norm 4.622462756028e-04 ||r(i)||/||b|| 1.213492526216e-03 222 4 KSP unpreconditioned resid norm 7.972477625283e-05 true resid norm 7.972477625284e-05 ||r(i)||/||b|| 2.092941041243e-04 223 5 KSP unpreconditioned resid norm 5.651496202770e-06 true resid norm 5.651496202787e-06 ||r(i)||/||b|| 1.483635188856e-05 224 6 KSP unpreconditioned resid norm 6.078212012816e-07 true resid norm 6.078212013076e-07 ||r(i)||/||b|| 1.595656956026e-06 225 7 KSP unpreconditioned resid norm 4.860650279105e-09 true resid norm 4.860650279805e-09 ||r(i)||/||b|| 1.276021700641e-08 226 8 KSP unpreconditioned resid norm 1.731140125257e-11 true resid norm 1.731140182079e-11 ||r(i)||/||b|| 4.544602701334e-11 227 1 SNES Function norm 1.731e-11 228 Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1 229SNES Object: 1 MPI process 230 type: newtonls 231 maximum iterations=50, maximum function evaluations=10000 232 tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 233 total number of linear solver iterations=8 234 total number of function evaluations=2 235 norm schedule ALWAYS 236 SNESLineSearch Object: 1 MPI process 237 type: bt 238 interpolation: cubic 239 alpha=1.000000e-04 240 maxlambda=1.000000e+00, minlambda=1.000000e-12 241 tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08 242 maximum iterations=40 243 KSP Object: 1 MPI process 244 type: fgmres 245 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 246 happy breakdown tolerance=1e-30 247 maximum iterations=10000, initial guess is zero 248 tolerances: relative=1e-09, absolute=1e-50, divergence=10000. 249 right preconditioning 250 using UNPRECONDITIONED norm type for convergence test 251 PC Object: 1 MPI process 252 type: mg 253 type is MULTIPLICATIVE, levels=2 cycles=v 254 Cycles per PCApply=1 255 Not using Galerkin computed coarse grid matrices 256 Coarse grid solver -- level 0 ------------------------------- 257 KSP Object: (mg_coarse_) 1 MPI process 258 type: preonly 259 maximum iterations=10000, initial guess is zero 260 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 261 left preconditioning 262 not checking for convergence 263 PC Object: (mg_coarse_) 1 MPI process 264 type: lu 265 out-of-place factorization 266 tolerance for zero pivot 2.22045e-14 267 using diagonal shift on blocks to prevent zero pivot [INBLOCKS] 268 matrix ordering: nd 269 factor fill ratio given 1., needed 1. 270 Factored matrix: 271 Mat Object: (mg_coarse_) 1 MPI process 272 type: seqaij 273 rows=1, cols=1 274 package used to perform factorization: petsc 275 total: nonzeros=1, allocated nonzeros=1 276 not using I-node routines 277 linear system matrix, which is also used to construct the preconditioner: 278 Mat Object: 1 MPI process 279 type: seqaij 280 rows=1, cols=1 281 total: nonzeros=1, allocated nonzeros=1 282 total number of mallocs used during MatSetValues calls=0 283 not using I-node routines 284 Down solver (pre-smoother) on level 1 ------------------------------- 285 KSP Object: (mg_levels_1_) 1 MPI process 286 type: chebyshev 287 Chebyshev polynomial of first kind 288 eigenvalue targets used: min 0.151841, max 1.67025 289 eigenvalues estimated via gmres: min 0.994613, max 1.51841 290 eigenvalues estimated using gmres with transform: [0. 0.1; 0. 1.1] 291 KSP Object: (mg_levels_1_esteig_) 1 MPI process 292 type: gmres 293 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 294 happy breakdown tolerance=1e-30 295 maximum iterations=10, initial guess is zero 296 tolerances: relative=1e-12, absolute=1e-50, divergence=10000. 297 left preconditioning 298 using PRECONDITIONED norm type for convergence test 299 estimating eigenvalues using a noisy random number generated right-hand side 300 maximum iterations=2, nonzero initial guess 301 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 302 left preconditioning 303 not checking for convergence 304 PC Object: (mg_levels_1_) 1 MPI process 305 type: sor 306 type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. 307 linear system matrix, which is also used to construct the preconditioner: 308 Mat Object: 1 MPI process 309 type: seqaij 310 rows=9, cols=9 311 total: nonzeros=41, allocated nonzeros=41 312 total number of mallocs used during MatSetValues calls=0 313 not using I-node routines 314 Up solver (post-smoother) same as down solver (pre-smoother) 315 linear system matrix, which is also used to construct the preconditioner: 316 Mat Object: 1 MPI process 317 type: seqaij 318 rows=9, cols=9 319 total: nonzeros=41, allocated nonzeros=41 320 total number of mallocs used during MatSetValues calls=0 321 not using I-node routines 322Timestep: 0003 time = 0.3 L_2 Error: 0.12562 3233 TS dt 0.1 time 0.3 324 0 SNES Function norm 0.377457 325 0 KSP unpreconditioned resid norm 3.774573494154e-01 true resid norm 3.774573494154e-01 ||r(i)||/||b|| 1.000000000000e+00 326 1 KSP unpreconditioned resid norm 5.954853714304e-02 true resid norm 5.954853714304e-02 ||r(i)||/||b|| 1.577622935022e-01 327 2 KSP unpreconditioned resid norm 5.848939409168e-03 true resid norm 5.848939409168e-03 ||r(i)||/||b|| 1.549562995190e-02 328 3 KSP unpreconditioned resid norm 4.630907205003e-04 true resid norm 4.630907205002e-04 ||r(i)||/||b|| 1.226868999153e-03 329 4 KSP unpreconditioned resid norm 8.053803471345e-05 true resid norm 8.053803471342e-05 ||r(i)||/||b|| 2.133698942096e-04 330 5 KSP unpreconditioned resid norm 5.701869061872e-06 true resid norm 5.701869061870e-06 ||r(i)||/||b|| 1.510599560639e-05 331 6 KSP unpreconditioned resid norm 6.025388075754e-07 true resid norm 6.025388075944e-07 ||r(i)||/||b|| 1.596309645388e-06 332 7 KSP unpreconditioned resid norm 4.883261060044e-09 true resid norm 4.883261063505e-09 ||r(i)||/||b|| 1.293725256924e-08 333 8 KSP unpreconditioned resid norm 1.729375636379e-11 true resid norm 1.729375104729e-11 ||r(i)||/||b|| 4.581643747055e-11 334 1 SNES Function norm 1.729e-11 335 Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1 336SNES Object: 1 MPI process 337 type: newtonls 338 maximum iterations=50, maximum function evaluations=10000 339 tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 340 total number of linear solver iterations=8 341 total number of function evaluations=2 342 norm schedule ALWAYS 343 SNESLineSearch Object: 1 MPI process 344 type: bt 345 interpolation: cubic 346 alpha=1.000000e-04 347 maxlambda=1.000000e+00, minlambda=1.000000e-12 348 tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08 349 maximum iterations=40 350 KSP Object: 1 MPI process 351 type: fgmres 352 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 353 happy breakdown tolerance=1e-30 354 maximum iterations=10000, initial guess is zero 355 tolerances: relative=1e-09, absolute=1e-50, divergence=10000. 356 right preconditioning 357 using UNPRECONDITIONED norm type for convergence test 358 PC Object: 1 MPI process 359 type: mg 360 type is MULTIPLICATIVE, levels=2 cycles=v 361 Cycles per PCApply=1 362 Not using Galerkin computed coarse grid matrices 363 Coarse grid solver -- level 0 ------------------------------- 364 KSP Object: (mg_coarse_) 1 MPI process 365 type: preonly 366 maximum iterations=10000, initial guess is zero 367 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 368 left preconditioning 369 not checking for convergence 370 PC Object: (mg_coarse_) 1 MPI process 371 type: lu 372 out-of-place factorization 373 tolerance for zero pivot 2.22045e-14 374 using diagonal shift on blocks to prevent zero pivot [INBLOCKS] 375 matrix ordering: nd 376 factor fill ratio given 1., needed 1. 377 Factored matrix: 378 Mat Object: (mg_coarse_) 1 MPI process 379 type: seqaij 380 rows=1, cols=1 381 package used to perform factorization: petsc 382 total: nonzeros=1, allocated nonzeros=1 383 not using I-node routines 384 linear system matrix, which is also used to construct the preconditioner: 385 Mat Object: 1 MPI process 386 type: seqaij 387 rows=1, cols=1 388 total: nonzeros=1, allocated nonzeros=1 389 total number of mallocs used during MatSetValues calls=0 390 not using I-node routines 391 Down solver (pre-smoother) on level 1 ------------------------------- 392 KSP Object: (mg_levels_1_) 1 MPI process 393 type: chebyshev 394 Chebyshev polynomial of first kind 395 eigenvalue targets used: min 0.151841, max 1.67025 396 eigenvalues estimated via gmres: min 0.994613, max 1.51841 397 eigenvalues estimated using gmres with transform: [0. 0.1; 0. 1.1] 398 KSP Object: (mg_levels_1_esteig_) 1 MPI process 399 type: gmres 400 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 401 happy breakdown tolerance=1e-30 402 maximum iterations=10, initial guess is zero 403 tolerances: relative=1e-12, absolute=1e-50, divergence=10000. 404 left preconditioning 405 using PRECONDITIONED norm type for convergence test 406 estimating eigenvalues using a noisy random number generated right-hand side 407 maximum iterations=2, nonzero initial guess 408 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 409 left preconditioning 410 not checking for convergence 411 PC Object: (mg_levels_1_) 1 MPI process 412 type: sor 413 type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. 414 linear system matrix, which is also used to construct the preconditioner: 415 Mat Object: 1 MPI process 416 type: seqaij 417 rows=9, cols=9 418 total: nonzeros=41, allocated nonzeros=41 419 total number of mallocs used during MatSetValues calls=0 420 not using I-node routines 421 Up solver (post-smoother) same as down solver (pre-smoother) 422 linear system matrix, which is also used to construct the preconditioner: 423 Mat Object: 1 MPI process 424 type: seqaij 425 rows=9, cols=9 426 total: nonzeros=41, allocated nonzeros=41 427 total number of mallocs used during MatSetValues calls=0 428 not using I-node routines 429Timestep: 0004 time = 0.4 L_2 Error: 0.16664 4304 TS dt 0.1 time 0.4 431 0 SNES Function norm 0.37449 432 0 KSP unpreconditioned resid norm 3.744902213650e-01 true resid norm 3.744902213650e-01 ||r(i)||/||b|| 1.000000000000e+00 433 1 KSP unpreconditioned resid norm 5.982974938131e-02 true resid norm 5.982974938131e-02 ||r(i)||/||b|| 1.597631819684e-01 434 2 KSP unpreconditioned resid norm 5.840834302842e-03 true resid norm 5.840834302842e-03 ||r(i)||/||b|| 1.559676052836e-02 435 3 KSP unpreconditioned resid norm 4.612964201615e-04 true resid norm 4.612964201614e-04 ||r(i)||/||b|| 1.231798305654e-03 436 4 KSP unpreconditioned resid norm 8.073771822390e-05 true resid norm 8.073771822391e-05 ||r(i)||/||b|| 2.155936620444e-04 437 5 KSP unpreconditioned resid norm 5.730193368363e-06 true resid norm 5.730193368351e-06 ||r(i)||/||b|| 1.530131640678e-05 438 6 KSP unpreconditioned resid norm 6.010616249637e-07 true resid norm 6.010616249715e-07 ||r(i)||/||b|| 1.605012869978e-06 439 7 KSP unpreconditioned resid norm 4.858498871957e-09 true resid norm 4.858498872870e-09 ||r(i)||/||b|| 1.297363347743e-08 440 8 KSP unpreconditioned resid norm 1.751406135113e-11 true resid norm 1.751403567040e-11 ||r(i)||/||b|| 4.676767154710e-11 441 1 SNES Function norm 1.751e-11 442 Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1 443SNES Object: 1 MPI process 444 type: newtonls 445 maximum iterations=50, maximum function evaluations=10000 446 tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 447 total number of linear solver iterations=8 448 total number of function evaluations=2 449 norm schedule ALWAYS 450 SNESLineSearch Object: 1 MPI process 451 type: bt 452 interpolation: cubic 453 alpha=1.000000e-04 454 maxlambda=1.000000e+00, minlambda=1.000000e-12 455 tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08 456 maximum iterations=40 457 KSP Object: 1 MPI process 458 type: fgmres 459 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 460 happy breakdown tolerance=1e-30 461 maximum iterations=10000, initial guess is zero 462 tolerances: relative=1e-09, absolute=1e-50, divergence=10000. 463 right preconditioning 464 using UNPRECONDITIONED norm type for convergence test 465 PC Object: 1 MPI process 466 type: mg 467 type is MULTIPLICATIVE, levels=2 cycles=v 468 Cycles per PCApply=1 469 Not using Galerkin computed coarse grid matrices 470 Coarse grid solver -- level 0 ------------------------------- 471 KSP Object: (mg_coarse_) 1 MPI process 472 type: preonly 473 maximum iterations=10000, initial guess is zero 474 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 475 left preconditioning 476 not checking for convergence 477 PC Object: (mg_coarse_) 1 MPI process 478 type: lu 479 out-of-place factorization 480 tolerance for zero pivot 2.22045e-14 481 using diagonal shift on blocks to prevent zero pivot [INBLOCKS] 482 matrix ordering: nd 483 factor fill ratio given 1., needed 1. 484 Factored matrix: 485 Mat Object: (mg_coarse_) 1 MPI process 486 type: seqaij 487 rows=1, cols=1 488 package used to perform factorization: petsc 489 total: nonzeros=1, allocated nonzeros=1 490 not using I-node routines 491 linear system matrix, which is also used to construct the preconditioner: 492 Mat Object: 1 MPI process 493 type: seqaij 494 rows=1, cols=1 495 total: nonzeros=1, allocated nonzeros=1 496 total number of mallocs used during MatSetValues calls=0 497 not using I-node routines 498 Down solver (pre-smoother) on level 1 ------------------------------- 499 KSP Object: (mg_levels_1_) 1 MPI process 500 type: chebyshev 501 Chebyshev polynomial of first kind 502 eigenvalue targets used: min 0.151841, max 1.67025 503 eigenvalues estimated via gmres: min 0.994613, max 1.51841 504 eigenvalues estimated using gmres with transform: [0. 0.1; 0. 1.1] 505 KSP Object: (mg_levels_1_esteig_) 1 MPI process 506 type: gmres 507 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 508 happy breakdown tolerance=1e-30 509 maximum iterations=10, initial guess is zero 510 tolerances: relative=1e-12, absolute=1e-50, divergence=10000. 511 left preconditioning 512 using PRECONDITIONED norm type for convergence test 513 estimating eigenvalues using a noisy random number generated right-hand side 514 maximum iterations=2, nonzero initial guess 515 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 516 left preconditioning 517 not checking for convergence 518 PC Object: (mg_levels_1_) 1 MPI process 519 type: sor 520 type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. 521 linear system matrix, which is also used to construct the preconditioner: 522 Mat Object: 1 MPI process 523 type: seqaij 524 rows=9, cols=9 525 total: nonzeros=41, allocated nonzeros=41 526 total number of mallocs used during MatSetValues calls=0 527 not using I-node routines 528 Up solver (post-smoother) same as down solver (pre-smoother) 529 linear system matrix, which is also used to construct the preconditioner: 530 Mat Object: 1 MPI process 531 type: seqaij 532 rows=9, cols=9 533 total: nonzeros=41, allocated nonzeros=41 534 total number of mallocs used during MatSetValues calls=0 535 not using I-node routines 536Timestep: 0005 time = 0.5 L_2 Error: 0.2076 5375 TS dt 0.1 time 0.5 538 0 SNES Function norm 0.372928 539 0 KSP unpreconditioned resid norm 3.729281667988e-01 true resid norm 3.729281667988e-01 ||r(i)||/||b|| 1.000000000000e+00 540 1 KSP unpreconditioned resid norm 6.002541949214e-02 true resid norm 6.002541949214e-02 ||r(i)||/||b|| 1.609570551010e-01 541 2 KSP unpreconditioned resid norm 5.775316419172e-03 true resid norm 5.775316419172e-03 ||r(i)||/||b|| 1.548640444284e-02 542 3 KSP unpreconditioned resid norm 4.576993940278e-04 true resid norm 4.576993940278e-04 ||r(i)||/||b|| 1.227312482070e-03 543 4 KSP unpreconditioned resid norm 8.039211062475e-05 true resid norm 8.039211062473e-05 ||r(i)||/||b|| 2.155699616760e-04 544 5 KSP unpreconditioned resid norm 5.708171590220e-06 true resid norm 5.708171590238e-06 ||r(i)||/||b|| 1.530635682265e-05 545 6 KSP unpreconditioned resid norm 5.991553964591e-07 true resid norm 5.991553964691e-07 ||r(i)||/||b|| 1.606624143229e-06 546 7 KSP unpreconditioned resid norm 4.791537579858e-09 true resid norm 4.791537591102e-09 ||r(i)||/||b|| 1.284841966278e-08 547 8 KSP unpreconditioned resid norm 1.772048749492e-11 true resid norm 1.772051502236e-11 ||r(i)||/||b|| 4.751723414853e-11 548 1 SNES Function norm 1.772e-11 549 Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1 550SNES Object: 1 MPI process 551 type: newtonls 552 maximum iterations=50, maximum function evaluations=10000 553 tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 554 total number of linear solver iterations=8 555 total number of function evaluations=2 556 norm schedule ALWAYS 557 SNESLineSearch Object: 1 MPI process 558 type: bt 559 interpolation: cubic 560 alpha=1.000000e-04 561 maxlambda=1.000000e+00, minlambda=1.000000e-12 562 tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08 563 maximum iterations=40 564 KSP Object: 1 MPI process 565 type: fgmres 566 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 567 happy breakdown tolerance=1e-30 568 maximum iterations=10000, initial guess is zero 569 tolerances: relative=1e-09, absolute=1e-50, divergence=10000. 570 right preconditioning 571 using UNPRECONDITIONED norm type for convergence test 572 PC Object: 1 MPI process 573 type: mg 574 type is MULTIPLICATIVE, levels=2 cycles=v 575 Cycles per PCApply=1 576 Not using Galerkin computed coarse grid matrices 577 Coarse grid solver -- level 0 ------------------------------- 578 KSP Object: (mg_coarse_) 1 MPI process 579 type: preonly 580 maximum iterations=10000, initial guess is zero 581 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 582 left preconditioning 583 not checking for convergence 584 PC Object: (mg_coarse_) 1 MPI process 585 type: lu 586 out-of-place factorization 587 tolerance for zero pivot 2.22045e-14 588 using diagonal shift on blocks to prevent zero pivot [INBLOCKS] 589 matrix ordering: nd 590 factor fill ratio given 1., needed 1. 591 Factored matrix: 592 Mat Object: (mg_coarse_) 1 MPI process 593 type: seqaij 594 rows=1, cols=1 595 package used to perform factorization: petsc 596 total: nonzeros=1, allocated nonzeros=1 597 not using I-node routines 598 linear system matrix, which is also used to construct the preconditioner: 599 Mat Object: 1 MPI process 600 type: seqaij 601 rows=1, cols=1 602 total: nonzeros=1, allocated nonzeros=1 603 total number of mallocs used during MatSetValues calls=0 604 not using I-node routines 605 Down solver (pre-smoother) on level 1 ------------------------------- 606 KSP Object: (mg_levels_1_) 1 MPI process 607 type: chebyshev 608 Chebyshev polynomial of first kind 609 eigenvalue targets used: min 0.151841, max 1.67025 610 eigenvalues estimated via gmres: min 0.994613, max 1.51841 611 eigenvalues estimated using gmres with transform: [0. 0.1; 0. 1.1] 612 KSP Object: (mg_levels_1_esteig_) 1 MPI process 613 type: gmres 614 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 615 happy breakdown tolerance=1e-30 616 maximum iterations=10, initial guess is zero 617 tolerances: relative=1e-12, absolute=1e-50, divergence=10000. 618 left preconditioning 619 using PRECONDITIONED norm type for convergence test 620 estimating eigenvalues using a noisy random number generated right-hand side 621 maximum iterations=2, nonzero initial guess 622 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 623 left preconditioning 624 not checking for convergence 625 PC Object: (mg_levels_1_) 1 MPI process 626 type: sor 627 type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. 628 linear system matrix, which is also used to construct the preconditioner: 629 Mat Object: 1 MPI process 630 type: seqaij 631 rows=9, cols=9 632 total: nonzeros=41, allocated nonzeros=41 633 total number of mallocs used during MatSetValues calls=0 634 not using I-node routines 635 Up solver (post-smoother) same as down solver (pre-smoother) 636 linear system matrix, which is also used to construct the preconditioner: 637 Mat Object: 1 MPI process 638 type: seqaij 639 rows=9, cols=9 640 total: nonzeros=41, allocated nonzeros=41 641 total number of mallocs used during MatSetValues calls=0 642 not using I-node routines 643Timestep: 0006 time = 0.6 L_2 Error: 0.24859 6446 TS dt 0.1 time 0.6 645 0 SNES Function norm 0.372986 646 0 KSP unpreconditioned resid norm 3.729860798745e-01 true resid norm 3.729860798745e-01 ||r(i)||/||b|| 1.000000000000e+00 647 1 KSP unpreconditioned resid norm 5.998286066860e-02 true resid norm 5.998286066860e-02 ||r(i)||/||b|| 1.608179605222e-01 648 2 KSP unpreconditioned resid norm 5.687596001641e-03 true resid norm 5.687596001641e-03 ||r(i)||/||b|| 1.524881572941e-02 649 3 KSP unpreconditioned resid norm 4.534382695579e-04 true resid norm 4.534382695579e-04 ||r(i)||/||b|| 1.215697566275e-03 650 4 KSP unpreconditioned resid norm 7.976964452116e-05 true resid norm 7.976964452115e-05 ||r(i)||/||b|| 2.138676181910e-04 651 5 KSP unpreconditioned resid norm 5.651631937849e-06 true resid norm 5.651631937845e-06 ||r(i)||/||b|| 1.515239372940e-05 652 6 KSP unpreconditioned resid norm 5.948808411325e-07 true resid norm 5.948808411183e-07 ||r(i)||/||b|| 1.594914323126e-06 653 7 KSP unpreconditioned resid norm 4.702487381111e-09 true resid norm 4.702487348039e-09 ||r(i)||/||b|| 1.260767519695e-08 654 8 KSP unpreconditioned resid norm 1.779657220875e-11 true resid norm 1.779659688198e-11 ||r(i)||/||b|| 4.771383663424e-11 655 1 SNES Function norm 1.780e-11 656 Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1 657SNES Object: 1 MPI process 658 type: newtonls 659 maximum iterations=50, maximum function evaluations=10000 660 tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 661 total number of linear solver iterations=8 662 total number of function evaluations=2 663 norm schedule ALWAYS 664 SNESLineSearch Object: 1 MPI process 665 type: bt 666 interpolation: cubic 667 alpha=1.000000e-04 668 maxlambda=1.000000e+00, minlambda=1.000000e-12 669 tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08 670 maximum iterations=40 671 KSP Object: 1 MPI process 672 type: fgmres 673 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 674 happy breakdown tolerance=1e-30 675 maximum iterations=10000, initial guess is zero 676 tolerances: relative=1e-09, absolute=1e-50, divergence=10000. 677 right preconditioning 678 using UNPRECONDITIONED norm type for convergence test 679 PC Object: 1 MPI process 680 type: mg 681 type is MULTIPLICATIVE, levels=2 cycles=v 682 Cycles per PCApply=1 683 Not using Galerkin computed coarse grid matrices 684 Coarse grid solver -- level 0 ------------------------------- 685 KSP Object: (mg_coarse_) 1 MPI process 686 type: preonly 687 maximum iterations=10000, initial guess is zero 688 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 689 left preconditioning 690 not checking for convergence 691 PC Object: (mg_coarse_) 1 MPI process 692 type: lu 693 out-of-place factorization 694 tolerance for zero pivot 2.22045e-14 695 using diagonal shift on blocks to prevent zero pivot [INBLOCKS] 696 matrix ordering: nd 697 factor fill ratio given 1., needed 1. 698 Factored matrix: 699 Mat Object: (mg_coarse_) 1 MPI process 700 type: seqaij 701 rows=1, cols=1 702 package used to perform factorization: petsc 703 total: nonzeros=1, allocated nonzeros=1 704 not using I-node routines 705 linear system matrix, which is also used to construct the preconditioner: 706 Mat Object: 1 MPI process 707 type: seqaij 708 rows=1, cols=1 709 total: nonzeros=1, allocated nonzeros=1 710 total number of mallocs used during MatSetValues calls=0 711 not using I-node routines 712 Down solver (pre-smoother) on level 1 ------------------------------- 713 KSP Object: (mg_levels_1_) 1 MPI process 714 type: chebyshev 715 Chebyshev polynomial of first kind 716 eigenvalue targets used: min 0.151841, max 1.67025 717 eigenvalues estimated via gmres: min 0.994613, max 1.51841 718 eigenvalues estimated using gmres with transform: [0. 0.1; 0. 1.1] 719 KSP Object: (mg_levels_1_esteig_) 1 MPI process 720 type: gmres 721 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 722 happy breakdown tolerance=1e-30 723 maximum iterations=10, initial guess is zero 724 tolerances: relative=1e-12, absolute=1e-50, divergence=10000. 725 left preconditioning 726 using PRECONDITIONED norm type for convergence test 727 estimating eigenvalues using a noisy random number generated right-hand side 728 maximum iterations=2, nonzero initial guess 729 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 730 left preconditioning 731 not checking for convergence 732 PC Object: (mg_levels_1_) 1 MPI process 733 type: sor 734 type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. 735 linear system matrix, which is also used to construct the preconditioner: 736 Mat Object: 1 MPI process 737 type: seqaij 738 rows=9, cols=9 739 total: nonzeros=41, allocated nonzeros=41 740 total number of mallocs used during MatSetValues calls=0 741 not using I-node routines 742 Up solver (post-smoother) same as down solver (pre-smoother) 743 linear system matrix, which is also used to construct the preconditioner: 744 Mat Object: 1 MPI process 745 type: seqaij 746 rows=9, cols=9 747 total: nonzeros=41, allocated nonzeros=41 748 total number of mallocs used during MatSetValues calls=0 749 not using I-node routines 750Timestep: 0007 time = 0.7 L_2 Error: 0.28962 7517 TS dt 0.1 time 0.7 752 0 SNES Function norm 0.374276 753 0 KSP unpreconditioned resid norm 3.742759385298e-01 true resid norm 3.742759385298e-01 ||r(i)||/||b|| 1.000000000000e+00 754 1 KSP unpreconditioned resid norm 5.979030900298e-02 true resid norm 5.979030900298e-02 ||r(i)||/||b|| 1.597492727901e-01 755 2 KSP unpreconditioned resid norm 5.617806615202e-03 true resid norm 5.617806615202e-03 ||r(i)||/||b|| 1.500979901959e-02 756 3 KSP unpreconditioned resid norm 4.495138691066e-04 true resid norm 4.495138691066e-04 ||r(i)||/||b|| 1.201022622166e-03 757 4 KSP unpreconditioned resid norm 7.920536127941e-05 true resid norm 7.920536127941e-05 ||r(i)||/||b|| 2.116229047225e-04 758 5 KSP unpreconditioned resid norm 5.595911671793e-06 true resid norm 5.595911671801e-06 ||r(i)||/||b|| 1.495129955129e-05 759 6 KSP unpreconditioned resid norm 5.892156061787e-07 true resid norm 5.892156061538e-07 ||r(i)||/||b|| 1.574281286872e-06 760 7 KSP unpreconditioned resid norm 4.617371734791e-09 true resid norm 4.617371702498e-09 ||r(i)||/||b|| 1.233681149965e-08 761 8 KSP unpreconditioned resid norm 1.776419283029e-11 true resid norm 1.776421370272e-11 ||r(i)||/||b|| 4.746287931973e-11 762 1 SNES Function norm 1.776e-11 763 Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1 764SNES Object: 1 MPI process 765 type: newtonls 766 maximum iterations=50, maximum function evaluations=10000 767 tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 768 total number of linear solver iterations=8 769 total number of function evaluations=2 770 norm schedule ALWAYS 771 SNESLineSearch Object: 1 MPI process 772 type: bt 773 interpolation: cubic 774 alpha=1.000000e-04 775 maxlambda=1.000000e+00, minlambda=1.000000e-12 776 tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08 777 maximum iterations=40 778 KSP Object: 1 MPI process 779 type: fgmres 780 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 781 happy breakdown tolerance=1e-30 782 maximum iterations=10000, initial guess is zero 783 tolerances: relative=1e-09, absolute=1e-50, divergence=10000. 784 right preconditioning 785 using UNPRECONDITIONED norm type for convergence test 786 PC Object: 1 MPI process 787 type: mg 788 type is MULTIPLICATIVE, levels=2 cycles=v 789 Cycles per PCApply=1 790 Not using Galerkin computed coarse grid matrices 791 Coarse grid solver -- level 0 ------------------------------- 792 KSP Object: (mg_coarse_) 1 MPI process 793 type: preonly 794 maximum iterations=10000, initial guess is zero 795 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 796 left preconditioning 797 not checking for convergence 798 PC Object: (mg_coarse_) 1 MPI process 799 type: lu 800 out-of-place factorization 801 tolerance for zero pivot 2.22045e-14 802 using diagonal shift on blocks to prevent zero pivot [INBLOCKS] 803 matrix ordering: nd 804 factor fill ratio given 1., needed 1. 805 Factored matrix: 806 Mat Object: (mg_coarse_) 1 MPI process 807 type: seqaij 808 rows=1, cols=1 809 package used to perform factorization: petsc 810 total: nonzeros=1, allocated nonzeros=1 811 not using I-node routines 812 linear system matrix, which is also used to construct the preconditioner: 813 Mat Object: 1 MPI process 814 type: seqaij 815 rows=1, cols=1 816 total: nonzeros=1, allocated nonzeros=1 817 total number of mallocs used during MatSetValues calls=0 818 not using I-node routines 819 Down solver (pre-smoother) on level 1 ------------------------------- 820 KSP Object: (mg_levels_1_) 1 MPI process 821 type: chebyshev 822 Chebyshev polynomial of first kind 823 eigenvalue targets used: min 0.151841, max 1.67025 824 eigenvalues estimated via gmres: min 0.994613, max 1.51841 825 eigenvalues estimated using gmres with transform: [0. 0.1; 0. 1.1] 826 KSP Object: (mg_levels_1_esteig_) 1 MPI process 827 type: gmres 828 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 829 happy breakdown tolerance=1e-30 830 maximum iterations=10, initial guess is zero 831 tolerances: relative=1e-12, absolute=1e-50, divergence=10000. 832 left preconditioning 833 using PRECONDITIONED norm type for convergence test 834 estimating eigenvalues using a noisy random number generated right-hand side 835 maximum iterations=2, nonzero initial guess 836 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 837 left preconditioning 838 not checking for convergence 839 PC Object: (mg_levels_1_) 1 MPI process 840 type: sor 841 type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. 842 linear system matrix, which is also used to construct the preconditioner: 843 Mat Object: 1 MPI process 844 type: seqaij 845 rows=9, cols=9 846 total: nonzeros=41, allocated nonzeros=41 847 total number of mallocs used during MatSetValues calls=0 848 not using I-node routines 849 Up solver (post-smoother) same as down solver (pre-smoother) 850 linear system matrix, which is also used to construct the preconditioner: 851 Mat Object: 1 MPI process 852 type: seqaij 853 rows=9, cols=9 854 total: nonzeros=41, allocated nonzeros=41 855 total number of mallocs used during MatSetValues calls=0 856 not using I-node routines 857Timestep: 0008 time = 0.8 L_2 Error: 0.33068 8588 TS dt 0.1 time 0.8 859 0 SNES Function norm 0.376133 860 0 KSP unpreconditioned resid norm 3.761327824878e-01 true resid norm 3.761327824878e-01 ||r(i)||/||b|| 1.000000000000e+00 861 1 KSP unpreconditioned resid norm 5.960286328784e-02 true resid norm 5.960286328784e-02 ||r(i)||/||b|| 1.584622932721e-01 862 2 KSP unpreconditioned resid norm 5.587587079708e-03 true resid norm 5.587587079708e-03 ||r(i)||/||b|| 1.485535784132e-02 863 3 KSP unpreconditioned resid norm 4.467633715519e-04 true resid norm 4.467633715519e-04 ||r(i)||/||b|| 1.187780997437e-03 864 4 KSP unpreconditioned resid norm 7.887710489546e-05 true resid norm 7.887710489544e-05 ||r(i)||/||b|| 2.097054778734e-04 865 5 KSP unpreconditioned resid norm 5.566404901123e-06 true resid norm 5.566404901117e-06 ||r(i)||/||b|| 1.479904214756e-05 866 6 KSP unpreconditioned resid norm 5.843952130956e-07 true resid norm 5.843952130851e-07 ||r(i)||/||b|| 1.553693908890e-06 867 7 KSP unpreconditioned resid norm 4.557400918821e-09 true resid norm 4.557400934472e-09 ||r(i)||/||b|| 1.211646829699e-08 868 8 KSP unpreconditioned resid norm 1.769382827441e-11 true resid norm 1.769385166385e-11 ||r(i)||/||b|| 4.704150365949e-11 869 1 SNES Function norm 1.769e-11 870 Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1 871SNES Object: 1 MPI process 872 type: newtonls 873 maximum iterations=50, maximum function evaluations=10000 874 tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 875 total number of linear solver iterations=8 876 total number of function evaluations=2 877 norm schedule ALWAYS 878 SNESLineSearch Object: 1 MPI process 879 type: bt 880 interpolation: cubic 881 alpha=1.000000e-04 882 maxlambda=1.000000e+00, minlambda=1.000000e-12 883 tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08 884 maximum iterations=40 885 KSP Object: 1 MPI process 886 type: fgmres 887 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 888 happy breakdown tolerance=1e-30 889 maximum iterations=10000, initial guess is zero 890 tolerances: relative=1e-09, absolute=1e-50, divergence=10000. 891 right preconditioning 892 using UNPRECONDITIONED norm type for convergence test 893 PC Object: 1 MPI process 894 type: mg 895 type is MULTIPLICATIVE, levels=2 cycles=v 896 Cycles per PCApply=1 897 Not using Galerkin computed coarse grid matrices 898 Coarse grid solver -- level 0 ------------------------------- 899 KSP Object: (mg_coarse_) 1 MPI process 900 type: preonly 901 maximum iterations=10000, initial guess is zero 902 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 903 left preconditioning 904 not checking for convergence 905 PC Object: (mg_coarse_) 1 MPI process 906 type: lu 907 out-of-place factorization 908 tolerance for zero pivot 2.22045e-14 909 using diagonal shift on blocks to prevent zero pivot [INBLOCKS] 910 matrix ordering: nd 911 factor fill ratio given 1., needed 1. 912 Factored matrix: 913 Mat Object: (mg_coarse_) 1 MPI process 914 type: seqaij 915 rows=1, cols=1 916 package used to perform factorization: petsc 917 total: nonzeros=1, allocated nonzeros=1 918 not using I-node routines 919 linear system matrix, which is also used to construct the preconditioner: 920 Mat Object: 1 MPI process 921 type: seqaij 922 rows=1, cols=1 923 total: nonzeros=1, allocated nonzeros=1 924 total number of mallocs used during MatSetValues calls=0 925 not using I-node routines 926 Down solver (pre-smoother) on level 1 ------------------------------- 927 KSP Object: (mg_levels_1_) 1 MPI process 928 type: chebyshev 929 Chebyshev polynomial of first kind 930 eigenvalue targets used: min 0.151841, max 1.67025 931 eigenvalues estimated via gmres: min 0.994613, max 1.51841 932 eigenvalues estimated using gmres with transform: [0. 0.1; 0. 1.1] 933 KSP Object: (mg_levels_1_esteig_) 1 MPI process 934 type: gmres 935 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 936 happy breakdown tolerance=1e-30 937 maximum iterations=10, initial guess is zero 938 tolerances: relative=1e-12, absolute=1e-50, divergence=10000. 939 left preconditioning 940 using PRECONDITIONED norm type for convergence test 941 estimating eigenvalues using a noisy random number generated right-hand side 942 maximum iterations=2, nonzero initial guess 943 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 944 left preconditioning 945 not checking for convergence 946 PC Object: (mg_levels_1_) 1 MPI process 947 type: sor 948 type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. 949 linear system matrix, which is also used to construct the preconditioner: 950 Mat Object: 1 MPI process 951 type: seqaij 952 rows=9, cols=9 953 total: nonzeros=41, allocated nonzeros=41 954 total number of mallocs used during MatSetValues calls=0 955 not using I-node routines 956 Up solver (post-smoother) same as down solver (pre-smoother) 957 linear system matrix, which is also used to construct the preconditioner: 958 Mat Object: 1 MPI process 959 type: seqaij 960 rows=9, cols=9 961 total: nonzeros=41, allocated nonzeros=41 962 total number of mallocs used during MatSetValues calls=0 963 not using I-node routines 964Timestep: 0009 time = 0.9 L_2 Error: 0.37179 9659 TS dt 0.1 time 0.9 966 0 SNES Function norm 0.377927 967 0 KSP unpreconditioned resid norm 3.779274613460e-01 true resid norm 3.779274613460e-01 ||r(i)||/||b|| 1.000000000000e+00 968 1 KSP unpreconditioned resid norm 5.952775794612e-02 true resid norm 5.952775794612e-02 ||r(i)||/||b|| 1.575110676904e-01 969 2 KSP unpreconditioned resid norm 5.596783441033e-03 true resid norm 5.596783441033e-03 ||r(i)||/||b|| 1.480914729271e-02 970 3 KSP unpreconditioned resid norm 4.456392946867e-04 true resid norm 4.456392946866e-04 ||r(i)||/||b|| 1.179166216447e-03 971 4 KSP unpreconditioned resid norm 7.879630242934e-05 true resid norm 7.879630242930e-05 ||r(i)||/||b|| 2.084958371341e-04 972 5 KSP unpreconditioned resid norm 5.569022502593e-06 true resid norm 5.569022502581e-06 ||r(i)||/||b|| 1.473569156035e-05 973 6 KSP unpreconditioned resid norm 5.821644196935e-07 true resid norm 5.821644196750e-07 ||r(i)||/||b|| 1.540413119496e-06 974 7 KSP unpreconditioned resid norm 4.532618828776e-09 true resid norm 4.532618817180e-09 ||r(i)||/||b|| 1.199335661144e-08 975 8 KSP unpreconditioned resid norm 1.763889785026e-11 true resid norm 1.763888741317e-11 ||r(i)||/||b|| 4.667267985859e-11 976 1 SNES Function norm 1.764e-11 977 Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1 978SNES Object: 1 MPI process 979 type: newtonls 980 maximum iterations=50, maximum function evaluations=10000 981 tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 982 total number of linear solver iterations=8 983 total number of function evaluations=2 984 norm schedule ALWAYS 985 SNESLineSearch Object: 1 MPI process 986 type: bt 987 interpolation: cubic 988 alpha=1.000000e-04 989 maxlambda=1.000000e+00, minlambda=1.000000e-12 990 tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08 991 maximum iterations=40 992 KSP Object: 1 MPI process 993 type: fgmres 994 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 995 happy breakdown tolerance=1e-30 996 maximum iterations=10000, initial guess is zero 997 tolerances: relative=1e-09, absolute=1e-50, divergence=10000. 998 right preconditioning 999 using UNPRECONDITIONED norm type for convergence test 1000 PC Object: 1 MPI process 1001 type: mg 1002 type is MULTIPLICATIVE, levels=2 cycles=v 1003 Cycles per PCApply=1 1004 Not using Galerkin computed coarse grid matrices 1005 Coarse grid solver -- level 0 ------------------------------- 1006 KSP Object: (mg_coarse_) 1 MPI process 1007 type: preonly 1008 maximum iterations=10000, initial guess is zero 1009 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 1010 left preconditioning 1011 not checking for convergence 1012 PC Object: (mg_coarse_) 1 MPI process 1013 type: lu 1014 out-of-place factorization 1015 tolerance for zero pivot 2.22045e-14 1016 using diagonal shift on blocks to prevent zero pivot [INBLOCKS] 1017 matrix ordering: nd 1018 factor fill ratio given 1., needed 1. 1019 Factored matrix: 1020 Mat Object: (mg_coarse_) 1 MPI process 1021 type: seqaij 1022 rows=1, cols=1 1023 package used to perform factorization: petsc 1024 total: nonzeros=1, allocated nonzeros=1 1025 not using I-node routines 1026 linear system matrix, which is also used to construct the preconditioner: 1027 Mat Object: 1 MPI process 1028 type: seqaij 1029 rows=1, cols=1 1030 total: nonzeros=1, allocated nonzeros=1 1031 total number of mallocs used during MatSetValues calls=0 1032 not using I-node routines 1033 Down solver (pre-smoother) on level 1 ------------------------------- 1034 KSP Object: (mg_levels_1_) 1 MPI process 1035 type: chebyshev 1036 Chebyshev polynomial of first kind 1037 eigenvalue targets used: min 0.151841, max 1.67025 1038 eigenvalues estimated via gmres: min 0.994613, max 1.51841 1039 eigenvalues estimated using gmres with transform: [0. 0.1; 0. 1.1] 1040 KSP Object: (mg_levels_1_esteig_) 1 MPI process 1041 type: gmres 1042 restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement 1043 happy breakdown tolerance=1e-30 1044 maximum iterations=10, initial guess is zero 1045 tolerances: relative=1e-12, absolute=1e-50, divergence=10000. 1046 left preconditioning 1047 using PRECONDITIONED norm type for convergence test 1048 estimating eigenvalues using a noisy random number generated right-hand side 1049 maximum iterations=2, nonzero initial guess 1050 tolerances: relative=1e-05, absolute=1e-50, divergence=10000. 1051 left preconditioning 1052 not checking for convergence 1053 PC Object: (mg_levels_1_) 1 MPI process 1054 type: sor 1055 type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. 1056 linear system matrix, which is also used to construct the preconditioner: 1057 Mat Object: 1 MPI process 1058 type: seqaij 1059 rows=9, cols=9 1060 total: nonzeros=41, allocated nonzeros=41 1061 total number of mallocs used during MatSetValues calls=0 1062 not using I-node routines 1063 Up solver (post-smoother) same as down solver (pre-smoother) 1064 linear system matrix, which is also used to construct the preconditioner: 1065 Mat Object: 1 MPI process 1066 type: seqaij 1067 rows=9, cols=9 1068 total: nonzeros=41, allocated nonzeros=41 1069 total number of mallocs used during MatSetValues calls=0 1070 not using I-node routines 1071Timestep: 0010 time = 1 L_2 Error: 0.41293 107210 TS dt 0.1 time 1. 1073