Actual source code: aspin.c

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

  4: 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;

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

 31:   VecSet(Y,0);
 32:   MatMult(npc->jacobian_pre,X,W);

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

 50: static PetscErrorCode SNESDestroy_ASPIN(SNES snes)
 51: {
 52:   SNESDestroy(&snes->npc);
 53:   /* reset NEWTONLS and free the data */
 54:   SNESReset(snes);
 55:   PetscFree(snes->data);
 56:   return 0;
 57: }

 59: /* -------------------------------------------------------------------------- */
 60: /*MC
 61:       SNESASPIN - Helper SNES type for Additive-Schwarz Preconditioned Inexact Newton

 63:    Options Database:
 64: +  -npc_snes_ - options prefix of the nonlinear subdomain solver (must be of type NASM)
 65: .  -npc_sub_snes_ - options prefix of the subdomain nonlinear solves
 66: .  -npc_sub_ksp_ - options prefix of the subdomain Krylov solver
 67: -  -npc_sub_pc_ - options prefix of the subdomain preconditioner

 69:     Notes:
 70:     This routine sets up an instance of NETWONLS with nonlinear left preconditioning.  It differs from other
 71:     similar functionality in SNES as it creates a linear shell matrix that corresponds to the product

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

 75:     which is the ASPIN preconditioned matrix. Similar solvers may be constructed by having matrix-free differencing of
 76:     nonlinear solves per linear iteration, but this is far more efficient when subdomain sparse-direct preconditioner
 77:     factorizations are reused on each application of J_b^{-1}.

 79:     The Krylov method used in this nonlinear solver is run with NO preconditioner, because the preconditioning is done
 80:     at the nonlinear level, but the Jacobian for the original function must be provided (or calculated via coloring and
 81:     finite differences automatically) in the Pmat location of SNESSetJacobian() because the action of the original Jacobian
 82:     is needed by the shell matrix used to apply the Jacobian of the nonlinear preconditioned problem (see above).
 83:     Note that since the Pmat is not used to construct a preconditioner it could be provided in a matrix-free form.
 84:     The code for this implementation is a bit confusing because the Amat of SNESSetJacobian() applies the Jacobian of the
 85:     nonlinearly preconditioned function Jacobian while the Pmat provides the Jacobian of the original user provided function.
 86:     Note that the original SNES and nonlinear preconditioner preconditioner (see SNESGetNPC()), in this case NASM, share
 87:     the same Jacobian matrices. SNESNASM computes the needed Jacobian in SNESNASMComputeFinalJacobian_Private().

 89:    Level: intermediate

 91:    References:
 92: +  * - X. C. Cai and D. E. Keyes, "Nonlinearly preconditioned inexact Newton algorithms",  SIAM J. Sci. Comput., 24, 2002.
 93: -  * - Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu, "Composing Scalable Nonlinear Algebraic Solvers",
 94:    SIAM Review, 57(4), 2015

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

 98: M*/
 99: PETSC_EXTERN PetscErrorCode SNESCreate_ASPIN(SNES snes)
100: {
101:   SNES           npc;
102:   KSP            ksp;
103:   PC             pc;
104:   Mat            aspinmat;
105:   Vec            F;
106:   PetscInt       n;
107:   SNESLineSearch linesearch;

109:   /* set up the solver */
110:   SNESSetType(snes,SNESNEWTONLS);
111:   SNESSetNPCSide(snes,PC_LEFT);
112:   SNESSetFunctionType(snes,SNES_FUNCTION_PRECONDITIONED);
113:   SNESGetNPC(snes,&npc);
114:   SNESSetType(npc,SNESNASM);
115:   SNESNASMSetType(npc,PC_ASM_BASIC);
116:   SNESNASMSetComputeFinalJacobian(npc,PETSC_TRUE);
117:   SNESGetKSP(snes,&ksp);
118:   KSPGetPC(ksp,&pc);
119:   PCSetType(pc,PCNONE);
120:   SNESGetLineSearch(snes,&linesearch);
121:   if (!((PetscObject)linesearch)->type_name) {
122:     SNESLineSearchSetType(linesearch,SNESLINESEARCHBT);
123:   }

125:   /* set up the shell matrix */
126:   SNESGetFunction(snes,&F,NULL,NULL);
127:   VecGetLocalSize(F,&n);
128:   MatCreateShell(PetscObjectComm((PetscObject)snes),n,n,PETSC_DECIDE,PETSC_DECIDE,snes,&aspinmat);
129:   MatSetType(aspinmat,MATSHELL);
130:   MatShellSetOperation(aspinmat,MATOP_MULT,(void(*)(void))MatMultASPIN);
131:   SNESSetJacobian(snes,aspinmat,NULL,NULL,NULL);
132:   MatDestroy(&aspinmat);

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

136:   return 0;
137: }