1 #include <petsc/private/snesimpl.h> /*I "petscsnes.h" I*/ 2 #include <petscdm.h> 3 4 PetscErrorCode MatMultASPIN(Mat m,Vec X,Vec Y) 5 { 6 PetscErrorCode ierr; 7 void *ctx; 8 SNES snes; 9 PetscInt n,i; 10 VecScatter *oscatter; 11 SNES *subsnes; 12 PetscBool match; 13 MPI_Comm comm; 14 KSP ksp; 15 Vec *x,*b; 16 Vec W; 17 SNES npc; 18 Mat subJ,subpJ; 19 20 PetscFunctionBegin; 21 ierr = MatShellGetContext(m,&ctx);CHKERRQ(ierr); 22 snes = (SNES)ctx; 23 ierr = SNESGetNPC(snes,&npc);CHKERRQ(ierr); 24 ierr = SNESGetFunction(npc,&W,NULL,NULL);CHKERRQ(ierr); 25 ierr = PetscObjectTypeCompare((PetscObject)npc,SNESNASM,&match);CHKERRQ(ierr); 26 if (!match) { 27 ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr); 28 SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"MatMultASPIN requires that the nonlinear preconditioner be Nonlinear additive Schwarz"); 29 } 30 ierr = SNESNASMGetSubdomains(npc,&n,&subsnes,NULL,&oscatter,NULL);CHKERRQ(ierr); 31 ierr = SNESNASMGetSubdomainVecs(npc,&n,&x,&b,NULL,NULL);CHKERRQ(ierr); 32 33 ierr = VecSet(Y,0);CHKERRQ(ierr); 34 ierr = MatMult(npc->jacobian_pre,X,W);CHKERRQ(ierr); 35 36 for (i=0;i<n;i++) { 37 ierr = VecScatterBegin(oscatter[i],W,b[i],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr); 38 } 39 for (i=0;i<n;i++) { 40 ierr = VecScatterEnd(oscatter[i],W,b[i],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr); 41 ierr = VecSet(x[i],0.);CHKERRQ(ierr); 42 ierr = SNESGetJacobian(subsnes[i],&subJ,&subpJ,NULL,NULL);CHKERRQ(ierr); 43 ierr = SNESGetKSP(subsnes[i],&ksp);CHKERRQ(ierr); 44 ierr = KSPSetOperators(ksp,subJ,subpJ);CHKERRQ(ierr); 45 ierr = KSPSolve(ksp,b[i],x[i]);CHKERRQ(ierr); 46 ierr = VecScatterBegin(oscatter[i],x[i],Y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr); 47 } 48 for (i=0;i<n;i++) { 49 ierr = VecScatterEnd(oscatter[i],x[i],Y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr); 50 } 51 PetscFunctionReturn(0); 52 } 53 54 static PetscErrorCode SNESDestroy_ASPIN(SNES snes) 55 { 56 PetscErrorCode ierr; 57 58 PetscFunctionBegin; 59 ierr = SNESDestroy(&snes->npc);CHKERRQ(ierr); 60 /* reset NEWTONLS and free the data */ 61 ierr = SNESReset(snes);CHKERRQ(ierr); 62 ierr = PetscFree(snes->data);CHKERRQ(ierr); 63 PetscFunctionReturn(0); 64 } 65 66 /* -------------------------------------------------------------------------- */ 67 /*MC 68 SNESASPIN - Helper SNES type for Additive-Schwarz Preconditioned Inexact Newton 69 70 Options Database: 71 + -npc_snes_ - options prefix of the nonlinear subdomain solver (must be of type NASM) 72 . -npc_sub_snes_ - options prefix of the subdomain nonlinear solves 73 . -npc_sub_ksp_ - options prefix of the subdomain Krylov solver 74 - -npc_sub_pc_ - options prefix of the subdomain preconditioner 75 76 Notes: 77 This routine sets up an instance of NETWONLS with nonlinear left preconditioning. It differs from other 78 similar functionality in SNES as it creates a linear shell matrix that corresponds to the product 79 80 \sum_{i=0}^{N_b}J_b({X^b_{converged}})^{-1}J(X + \sum_{i=0}^{N_b}(X^b_{converged} - X^b)) 81 82 which is the ASPIN preconditioned matrix. Similar solvers may be constructed by having matrix-free differencing of 83 nonlinear solves per linear iteration, but this is far more efficient when subdomain sparse-direct preconditioner 84 factorizations are reused on each application of J_b^{-1}. 85 86 The Krylov method used in this nonlinear solver is run with NO preconditioner, because the preconditioning is done 87 at the nonlinear level, but the Jacobian for the original function must be provided (or calculated via coloring and 88 finite differences automatically) in the Pmat location of SNESSetJacobian() because the action of the original Jacobian 89 is needed by the shell matrix used to apply the Jacobian of the nonlinear preconditioned problem (see above). 90 Note that since the Pmat is not used to construct a preconditioner it could be provided in a matrix-free form. 91 The code for this implementation is a bit confusing because the Amat of SNESSetJacobian() applies the Jacobian of the 92 nonlinearly preconditioned function Jacobian while the Pmat provides the Jacobian of the original user provided function. 93 Note that the original SNES and nonlinear preconditioner preconditioner (see SNESGetNPC()), in this case NASM, share 94 the same Jacobian matrices. SNESNASM computes the need Jacobian in SNESNASMComputeFinalJacobian_Private() 95 96 Level: intermediate 97 98 References: 99 + 1. - X. C. Cai and D. E. Keyes, "Nonlinearly preconditioned inexact Newton algorithms", SIAM J. Sci. Comput., 24, 2002. 100 - 2. - Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu, "Composing Scalable Nonlinear Algebraic Solvers", 101 SIAM Review, 57(4), 2015 102 103 .seealso: SNESCreate(), SNES, SNESSetType(), SNESNEWTONLS, SNESNASM, SNESGetNPC(), SNESGetNPCSide() 104 105 M*/ 106 PETSC_EXTERN PetscErrorCode SNESCreate_ASPIN(SNES snes) 107 { 108 PetscErrorCode ierr; 109 SNES npc; 110 KSP ksp; 111 PC pc; 112 Mat aspinmat; 113 Vec F; 114 PetscInt n; 115 SNESLineSearch linesearch; 116 117 PetscFunctionBegin; 118 /* set up the solver */ 119 ierr = SNESSetType(snes,SNESNEWTONLS);CHKERRQ(ierr); 120 ierr = SNESSetNPCSide(snes,PC_LEFT);CHKERRQ(ierr); 121 ierr = SNESSetFunctionType(snes,SNES_FUNCTION_PRECONDITIONED);CHKERRQ(ierr); 122 ierr = SNESGetNPC(snes,&npc);CHKERRQ(ierr); 123 ierr = SNESSetType(npc,SNESNASM);CHKERRQ(ierr); 124 ierr = SNESNASMSetType(npc,PC_ASM_BASIC);CHKERRQ(ierr); 125 ierr = SNESNASMSetComputeFinalJacobian(npc,PETSC_TRUE);CHKERRQ(ierr); 126 ierr = SNESGetKSP(snes,&ksp);CHKERRQ(ierr); 127 ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr); 128 ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr); 129 ierr = SNESGetLineSearch(snes,&linesearch);CHKERRQ(ierr); 130 ierr = SNESLineSearchSetType(linesearch,SNESLINESEARCHBT);CHKERRQ(ierr); 131 132 /* set up the shell matrix */ 133 ierr = SNESGetFunction(snes,&F,NULL,NULL);CHKERRQ(ierr); 134 ierr = VecGetLocalSize(F,&n);CHKERRQ(ierr); 135 ierr = MatCreateShell(PetscObjectComm((PetscObject)snes),n,n,PETSC_DECIDE,PETSC_DECIDE,snes,&aspinmat);CHKERRQ(ierr); 136 ierr = MatSetType(aspinmat,MATSHELL);CHKERRQ(ierr); 137 ierr = MatShellSetOperation(aspinmat,MATOP_MULT,(void(*)(void))MatMultASPIN);CHKERRQ(ierr); 138 ierr = SNESSetJacobian(snes,aspinmat,NULL,NULL,NULL);CHKERRQ(ierr); 139 ierr = MatDestroy(&aspinmat);CHKERRQ(ierr); 140 141 snes->ops->destroy = SNESDestroy_ASPIN; 142 143 PetscFunctionReturn(0); 144 } 145