1 #include <../src/snes/impls/ngmres/snesngmres.h> /*I "petscsnes.h" I*/ 2 3 static PetscErrorCode SNESSetFromOptions_Anderson(SNES snes, PetscOptionItems *PetscOptionsObject) 4 { 5 SNES_NGMRES *ngmres = (SNES_NGMRES *)snes->data; 6 PetscBool monitor = PETSC_FALSE; 7 8 PetscFunctionBegin; 9 PetscOptionsHeadBegin(PetscOptionsObject, "SNES NGMRES options"); 10 PetscCall(PetscOptionsInt("-snes_anderson_m", "Number of directions", "SNES", ngmres->msize, &ngmres->msize, NULL)); 11 PetscCall(PetscOptionsReal("-snes_anderson_beta", "Mixing parameter", "SNES", ngmres->andersonBeta, &ngmres->andersonBeta, NULL)); 12 PetscCall(PetscOptionsInt("-snes_anderson_restart", "Iterations before forced restart", "SNES", ngmres->restart_periodic, &ngmres->restart_periodic, NULL)); 13 PetscCall(PetscOptionsInt("-snes_anderson_restart_it", "Tolerance iterations before restart", "SNES", ngmres->restart_it, &ngmres->restart_it, NULL)); 14 PetscCall(PetscOptionsEnum("-snes_anderson_restart_type", "Restart type", "SNESNGMRESSetRestartType", SNESNGMRESRestartTypes, (PetscEnum)ngmres->restart_type, (PetscEnum *)&ngmres->restart_type, NULL)); 15 PetscCall(PetscOptionsBool("-snes_anderson_monitor", "Monitor steps of Anderson Mixing", "SNES", ngmres->monitor ? PETSC_TRUE : PETSC_FALSE, &monitor, NULL)); 16 if (monitor) ngmres->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes)); 17 PetscOptionsHeadEnd(); 18 PetscFunctionReturn(PETSC_SUCCESS); 19 } 20 21 static PetscErrorCode SNESSolve_Anderson(SNES snes) 22 { 23 SNES_NGMRES *ngmres = (SNES_NGMRES *)snes->data; 24 /* present solution, residual, and preconditioned residual */ 25 Vec X, F, B, D; 26 /* candidate linear combination answers */ 27 Vec XA, FA, XM, FM; 28 29 /* coefficients and RHS to the minimization problem */ 30 PetscReal fnorm, fMnorm, fAnorm; 31 PetscReal xnorm, ynorm; 32 PetscReal dnorm, dminnorm = 0.0, fminnorm; 33 PetscInt restart_count = 0; 34 PetscInt k, k_restart, l, ivec; 35 PetscBool selectRestart; 36 SNESConvergedReason reason; 37 38 PetscFunctionBegin; 39 PetscCheck(!snes->xl && !snes->xu && !snes->ops->computevariablebounds, PetscObjectComm((PetscObject)snes), PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name); 40 41 PetscCall(PetscCitationsRegister(SNESCitation, &SNEScite)); 42 /* variable initialization */ 43 snes->reason = SNES_CONVERGED_ITERATING; 44 X = snes->vec_sol; 45 F = snes->vec_func; 46 B = snes->vec_rhs; 47 XA = snes->vec_sol_update; 48 FA = snes->work[0]; 49 D = snes->work[1]; 50 51 /* work for the line search */ 52 XM = snes->work[3]; 53 FM = snes->work[4]; 54 55 PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes)); 56 snes->iter = 0; 57 snes->norm = 0.; 58 PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes)); 59 60 /* initialization */ 61 62 /* r = F(x) */ 63 64 if (snes->npc && snes->npcside == PC_LEFT) { 65 PetscCall(SNESApplyNPC(snes, X, NULL, F)); 66 PetscCall(SNESGetConvergedReason(snes->npc, &reason)); 67 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 68 snes->reason = SNES_DIVERGED_INNER; 69 PetscFunctionReturn(PETSC_SUCCESS); 70 } 71 PetscCall(VecNorm(F, NORM_2, &fnorm)); 72 } else { 73 if (!snes->vec_func_init_set) { 74 PetscCall(SNESComputeFunction(snes, X, F)); 75 } else snes->vec_func_init_set = PETSC_FALSE; 76 77 PetscCall(VecNorm(F, NORM_2, &fnorm)); 78 SNESCheckFunctionNorm(snes, fnorm); 79 } 80 fminnorm = fnorm; 81 82 PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes)); 83 snes->norm = fnorm; 84 PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes)); 85 PetscCall(SNESLogConvergenceHistory(snes, fnorm, 0)); 86 PetscCall(SNESConverged(snes, 0, 0.0, 0.0, fnorm)); 87 PetscCall(SNESMonitor(snes, 0, fnorm)); 88 if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS); 89 PetscCall(SNESNGMRESUpdateSubspace_Private(snes, 0, 0, F, fnorm, X)); 90 91 k_restart = 0; 92 l = 0; 93 ivec = 0; 94 for (k = 1; k < snes->max_its + 1; k++) { 95 /* select which vector of the stored subspace will be updated */ 96 if (snes->npc && snes->npcside == PC_RIGHT) { 97 PetscCall(VecCopy(X, XM)); 98 PetscCall(SNESSetInitialFunction(snes->npc, F)); 99 100 PetscCall(PetscLogEventBegin(SNES_NPCSolve, snes->npc, XM, B, 0)); 101 PetscCall(SNESSolve(snes->npc, B, XM)); 102 PetscCall(PetscLogEventEnd(SNES_NPCSolve, snes->npc, XM, B, 0)); 103 104 PetscCall(SNESGetConvergedReason(snes->npc, &reason)); 105 if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) { 106 snes->reason = SNES_DIVERGED_INNER; 107 PetscFunctionReturn(PETSC_SUCCESS); 108 } 109 PetscCall(SNESGetNPCFunction(snes, FM, &fMnorm)); 110 if (ngmres->andersonBeta != 1.0) PetscCall(VecAXPBY(XM, (1.0 - ngmres->andersonBeta), ngmres->andersonBeta, X)); 111 } else { 112 PetscCall(VecCopy(F, FM)); 113 PetscCall(VecCopy(X, XM)); 114 PetscCall(VecAXPY(XM, -ngmres->andersonBeta, FM)); 115 fMnorm = fnorm; 116 } 117 118 PetscCall(SNESNGMRESFormCombinedSolution_Private(snes, ivec, l, XM, FM, fMnorm, X, XA, FA)); 119 ivec = k_restart % ngmres->msize; 120 if (ngmres->restart_type == SNES_NGMRES_RESTART_DIFFERENCE) { 121 PetscCall(SNESNGMRESNorms_Private(snes, l, X, F, XM, FM, XA, FA, D, &dnorm, &dminnorm, NULL, NULL, NULL, &xnorm, &fAnorm, &ynorm)); 122 PetscCall(SNESNGMRESSelectRestart_Private(snes, l, fMnorm, fnorm, dnorm, fminnorm, dminnorm, &selectRestart)); 123 /* if the restart conditions persist for more than restart_it iterations, restart. */ 124 if (selectRestart) restart_count++; 125 else restart_count = 0; 126 } else if (ngmres->restart_type == SNES_NGMRES_RESTART_PERIODIC) { 127 PetscCall(SNESNGMRESNorms_Private(snes, l, X, F, XM, FM, XA, FA, D, NULL, NULL, NULL, NULL, NULL, &xnorm, &fAnorm, &ynorm)); 128 if (k_restart > ngmres->restart_periodic) { 129 if (ngmres->monitor) PetscCall(PetscViewerASCIIPrintf(ngmres->monitor, "periodic restart after %" PetscInt_FMT " iterations\n", k_restart)); 130 restart_count = ngmres->restart_it; 131 } 132 } else { 133 PetscCall(SNESNGMRESNorms_Private(snes, l, X, F, XM, FM, XA, FA, D, NULL, NULL, NULL, NULL, NULL, &xnorm, &fAnorm, &ynorm)); 134 } 135 /* restart after restart conditions have persisted for a fixed number of iterations */ 136 if (restart_count >= ngmres->restart_it) { 137 if (ngmres->monitor) PetscCall(PetscViewerASCIIPrintf(ngmres->monitor, "Restarted at iteration %" PetscInt_FMT "\n", k_restart)); 138 restart_count = 0; 139 k_restart = 0; 140 l = 0; 141 ivec = 0; 142 } else { 143 if (l < ngmres->msize) l++; 144 k_restart++; 145 PetscCall(SNESNGMRESUpdateSubspace_Private(snes, ivec, l, FM, fnorm, XM)); 146 } 147 148 fnorm = fAnorm; 149 if (fminnorm > fnorm) fminnorm = fnorm; 150 151 PetscCall(VecCopy(XA, X)); 152 PetscCall(VecCopy(FA, F)); 153 154 PetscCall(PetscObjectSAWsTakeAccess((PetscObject)snes)); 155 snes->iter = k; 156 snes->norm = fnorm; 157 snes->xnorm = xnorm; 158 snes->ynorm = ynorm; 159 PetscCall(PetscObjectSAWsGrantAccess((PetscObject)snes)); 160 PetscCall(SNESLogConvergenceHistory(snes, snes->norm, snes->iter)); 161 PetscCall(SNESConverged(snes, snes->iter, xnorm, ynorm, fnorm)); 162 PetscCall(SNESMonitor(snes, snes->iter, snes->norm)); 163 if (snes->reason) PetscFunctionReturn(PETSC_SUCCESS); 164 } 165 snes->reason = SNES_DIVERGED_MAX_IT; 166 PetscFunctionReturn(PETSC_SUCCESS); 167 } 168 169 /*MC 170 SNESANDERSON - Anderson Mixing nonlinear solver 171 172 Level: beginner 173 174 Options Database Keys: 175 + -snes_anderson_m - Number of stored previous solutions and residuals 176 . -snes_anderson_beta - Anderson mixing parameter 177 . -snes_anderson_restart_type - Type of restart (see SNESNGMRES) 178 . -snes_anderson_restart_it - Number of iterations of restart conditions before restart 179 . -snes_anderson_restart - Number of iterations before periodic restart 180 - -snes_anderson_monitor - Prints relevant information about the ngmres iteration 181 182 Notes: 183 The Anderson Mixing method combines m previous solutions into a minimum-residual solution by solving a small linearized 184 optimization problem at each iteration. 185 186 Very similar to the `SNESNGMRES` algorithm. 187 188 References: 189 + * - D. G. Anderson. Iterative procedures for nonlinear integral equations. 190 J. Assoc. Comput. Mach., 12, 1965." 191 - * - Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers", 192 SIAM Review, 57(4), 2015 193 194 .seealso: `SNESNGMRES`, `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESType` 195 M*/ 196 197 PETSC_EXTERN PetscErrorCode SNESCreate_Anderson(SNES snes) 198 { 199 SNES_NGMRES *ngmres; 200 SNESLineSearch linesearch; 201 202 PetscFunctionBegin; 203 snes->ops->destroy = SNESDestroy_NGMRES; 204 snes->ops->setup = SNESSetUp_NGMRES; 205 snes->ops->setfromoptions = SNESSetFromOptions_Anderson; 206 snes->ops->view = SNESView_NGMRES; 207 snes->ops->solve = SNESSolve_Anderson; 208 snes->ops->reset = SNESReset_NGMRES; 209 210 snes->usesnpc = PETSC_TRUE; 211 snes->usesksp = PETSC_FALSE; 212 snes->npcside = PC_RIGHT; 213 214 snes->alwayscomputesfinalresidual = PETSC_TRUE; 215 216 PetscCall(PetscNew(&ngmres)); 217 snes->data = (void *)ngmres; 218 ngmres->msize = 30; 219 220 if (!snes->tolerancesset) { 221 snes->max_funcs = 30000; 222 snes->max_its = 10000; 223 } 224 225 PetscCall(SNESGetLineSearch(snes, &linesearch)); 226 if (!((PetscObject)linesearch)->type_name) PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHBASIC)); 227 228 ngmres->additive_linesearch = NULL; 229 ngmres->approxfunc = PETSC_FALSE; 230 ngmres->restart_type = SNES_NGMRES_RESTART_NONE; 231 ngmres->restart_it = 2; 232 ngmres->restart_periodic = 30; 233 ngmres->gammaA = 2.0; 234 ngmres->gammaC = 2.0; 235 ngmres->deltaB = 0.9; 236 ngmres->epsilonB = 0.1; 237 238 ngmres->andersonBeta = 1.0; 239 PetscFunctionReturn(PETSC_SUCCESS); 240 } 241