1:  #include <petsc/private/snesimpl.h>
  2:  #include <petscdm.h>

  4: PetscErrorCode MatMultASPIN(Mat m,Vec X,Vec Y)
  5: {
  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;

 21:   MatShellGetContext(m,&ctx);
 22:   snes = (SNES)ctx;
 23:   SNESGetNPC(snes,&npc);
 24:   SNESGetFunction(npc,&W,NULL,NULL);
 25:   PetscObjectTypeCompare((PetscObject)npc,SNESNASM,&match);
 26:   if (!match) {
 27:     PetscObjectGetComm((PetscObject)snes,&comm);
 28:     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"MatMultASPIN requires that the nonlinear preconditioner be Nonlinear additive Schwarz");
 29:   }
 30:   SNESNASMGetSubdomains(npc,&n,&subsnes,NULL,&oscatter,NULL);
 31:   SNESNASMGetSubdomainVecs(npc,&n,&x,&b,NULL,NULL);

 33:   VecSet(Y,0);
 34:   MatMult(npc->jacobian_pre,X,W);

 36:   for (i=0;i<n;i++) {
 37:     VecScatterBegin(oscatter[i],W,b[i],INSERT_VALUES,SCATTER_FORWARD);
 38:   }
 39:   for (i=0;i<n;i++) {
 40:     VecScatterEnd(oscatter[i],W,b[i],INSERT_VALUES,SCATTER_FORWARD);
 41:     VecSet(x[i],0.);
 42:     SNESGetJacobian(subsnes[i],&subJ,&subpJ,NULL,NULL);
 43:     SNESGetKSP(subsnes[i],&ksp);
 44:     KSPSetOperators(ksp,subJ,subpJ);
 45:     KSPSolve(ksp,b[i],x[i]);
 46:     VecScatterBegin(oscatter[i],x[i],Y,ADD_VALUES,SCATTER_REVERSE);
 47:   }
 48:   for (i=0;i<n;i++) {
 49:     VecScatterEnd(oscatter[i],x[i],Y,ADD_VALUES,SCATTER_REVERSE);
 50:   }
 51:   return(0);
 52: }

 54: static PetscErrorCode SNESDestroy_ASPIN(SNES snes)
 55: {

 59:   SNESDestroy(&snes->npc);
 60:   /* reset NEWTONLS and free the data */
 61:   SNESReset(snes);
 62:   PetscFree(snes->data);
 63:   return(0);
 64: }

 66: /* -------------------------------------------------------------------------- */
 67: /*MC
 68:       SNESASPIN - Helper SNES type for Additive-Schwarz Preconditioned Inexact Newton

 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

 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

 80:     \sum_{i=0}^{N_b}J_b({X^b_{converged}})^{-1}J(X + \sum_{i=0}^{N_b}(X^b_{converged} - X^b))

 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}.

 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()

 96:    Level: intermediate

 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

103: .seealso:  SNESCreate(), SNES, SNESSetType(), SNESNEWTONLS, SNESNASM, SNESGetNPC(), SNESGetNPCSide()

105: M*/
106: PETSC_EXTERN PetscErrorCode SNESCreate_ASPIN(SNES snes)
107: {
109:   SNES           npc;
110:   KSP            ksp;
111:   PC             pc;
112:   Mat            aspinmat;
113:   Vec            F;
114:   PetscInt       n;
115:   SNESLineSearch linesearch;

118:   /* set up the solver */
119:   SNESSetType(snes,SNESNEWTONLS);
120:   SNESSetNPCSide(snes,PC_LEFT);
121:   SNESSetFunctionType(snes,SNES_FUNCTION_PRECONDITIONED);
122:   SNESGetNPC(snes,&npc);
123:   SNESSetType(npc,SNESNASM);
124:   SNESNASMSetType(npc,PC_ASM_BASIC);
125:   SNESNASMSetComputeFinalJacobian(npc,PETSC_TRUE);
126:   SNESGetKSP(snes,&ksp);
127:   KSPGetPC(ksp,&pc);
128:   PCSetType(pc,PCNONE);
129:   SNESGetLineSearch(snes,&linesearch);
130:   SNESLineSearchSetType(linesearch,SNESLINESEARCHBT);

132:   /* set up the shell matrix */
133:   SNESGetFunction(snes,&F,NULL,NULL);
134:   VecGetLocalSize(F,&n);
135:   MatCreateShell(PetscObjectComm((PetscObject)snes),n,n,PETSC_DECIDE,PETSC_DECIDE,snes,&aspinmat);
136:   MatSetType(aspinmat,MATSHELL);
137:   MatShellSetOperation(aspinmat,MATOP_MULT,(void(*)(void))MatMultASPIN);
138:   SNESSetJacobian(snes,aspinmat,NULL,NULL,NULL);
139:   MatDestroy(&aspinmat);

141:   snes->ops->destroy = SNESDestroy_ASPIN;

143:   return(0);
144: }