1 #include <petsc/private/snesimpl.h> /*I "petscsnes.h" I*/
2 #include <petscdm.h>
3
MatMultASPIN(Mat m,Vec X,Vec Y)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
SNESDestroy_ASPIN(SNES snes)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 {cite}`ck02`, {cite}`bruneknepleysmithtu15`
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 Level: intermediate
69
70 Notes:
71 This solver transform the given nonlinear problem to a new form and then runs matrix-free Newton-Krylov with no
72 preconditioner on that transformed problem.
73
74 This routine sets up an instance of `SNESNETWONLS` with nonlinear left preconditioning. It differs from other
75 similar functionality in `SNES` as it creates a linear shell matrix that corresponds to the product
76
77 $$
78 \sum_{i=0}^{N_b}J_b({X^b_{converged}})^{-1}J(X + \sum_{i=0}^{N_b}(X^b_{converged} - X^b))
79 $$
80
81 which is the ASPIN preconditioned matrix. Similar solvers may be constructed by having matrix-free differencing of
82 nonlinear solves per linear iteration, but this is far more efficient when subdomain sparse-direct preconditioner
83 factorizations are reused on each application of $J_b^{-1}$.
84
85 The Krylov method used in this nonlinear solver is run with NO preconditioner, because the preconditioning is done
86 at the nonlinear level, but the Jacobian for the original function must be provided (or calculated via coloring and
87 finite differences automatically) in the Pmat location of `SNESSetJacobian()` because the action of the original Jacobian
88 is needed by the shell matrix used to apply the Jacobian of the nonlinear preconditioned problem (see above).
89 Note that since the Pmat is not used to construct a preconditioner it could be provided in a matrix-free form.
90 The code for this implementation is a bit confusing because the Amat of `SNESSetJacobian()` applies the Jacobian of the
91 nonlinearly preconditioned function Jacobian while the Pmat provides the Jacobian of the original user provided function.
92 Note that the original `SNES` and nonlinear preconditioner (see `SNESGetNPC()`), in this case `SNESNASM`, share
93 the same Jacobian matrices. `SNESNASM` computes the needed Jacobian in `SNESNASMComputeFinalJacobian_Private()`.
94
95 .seealso: [](ch_snes), `SNESCreate()`, `SNES`, `SNESSetType()`, `SNESNEWTONLS`, `SNESNASM`, `SNESGetNPC()`, `SNESGetNPCSide()`
96 M*/
SNESCreate_ASPIN(SNES snes)97 PETSC_EXTERN PetscErrorCode SNESCreate_ASPIN(SNES snes)
98 {
99 SNES npc;
100 KSP ksp;
101 PC pc;
102 Mat aspinmat;
103 Vec F;
104 PetscInt n;
105 SNESLineSearch linesearch;
106
107 PetscFunctionBegin;
108 /* set up the solver */
109 PetscCall(SNESSetType(snes, SNESNEWTONLS));
110 PetscCall(SNESSetNPCSide(snes, PC_LEFT));
111 PetscCall(SNESSetFunctionType(snes, SNES_FUNCTION_PRECONDITIONED));
112 PetscCall(SNESGetNPC(snes, &npc));
113 PetscCall(SNESSetType(npc, SNESNASM));
114 PetscCall(SNESNASMSetType(npc, PC_ASM_BASIC));
115 PetscCall(SNESNASMSetComputeFinalJacobian(npc, PETSC_TRUE));
116 PetscCall(SNESGetKSP(snes, &ksp));
117 PetscCall(KSPGetPC(ksp, &pc));
118 PetscCall(PCSetType(pc, PCNONE));
119 PetscCall(SNESGetLineSearch(snes, &linesearch));
120 if (!((PetscObject)linesearch)->type_name) PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHBT));
121
122 /* set up the shell matrix */
123 PetscCall(SNESGetFunction(snes, &F, NULL, NULL));
124 PetscCall(VecGetLocalSize(F, &n));
125 PetscCall(MatCreateShell(PetscObjectComm((PetscObject)snes), n, n, PETSC_DECIDE, PETSC_DECIDE, snes, &aspinmat));
126 PetscCall(MatSetType(aspinmat, MATSHELL));
127 PetscCall(MatShellSetOperation(aspinmat, MATOP_MULT, (PetscErrorCodeFn *)MatMultASPIN));
128 PetscCall(SNESSetJacobian(snes, aspinmat, NULL, NULL, NULL));
129 PetscCall(MatDestroy(&aspinmat));
130
131 snes->ops->destroy = SNESDestroy_ASPIN;
132 PetscCall(PetscObjectChangeTypeName((PetscObject)snes, SNESASPIN));
133 PetscFunctionReturn(PETSC_SUCCESS);
134 }
135