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