PetscErrorCode MatMultASPIN(Mat m,Vec X,Vec Y)
{
PetscErrorCode ierr;
void *ctx;
SNES snes;
PetscInt n,i;
VecScatter *oscatter;
SNES *subsnes;
PetscBool match;
MPI_Comm comm;
KSP ksp;
PC pc;
Vec *x,*b;
Vec W;
SNES npc;
PetscFunctionBegin;
ierr = MatShellGetContext(m,&ctx);CHKERRQ(ierr);
snes = (SNES)ctx;
ierr = SNESGetPC(snes,&npc);CHKERRQ(ierr);
ierr = SNESGetFunction(npc,&W,NULL,NULL);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)npc,SNESNASM,&match);CHKERRQ(ierr);
if (!match) {
ierr = PetscObjectGetComm((PetscObject)snes,&comm);
SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"MatMultASPIN requires that the nonlinear preconditioner be Nonlinear additive Schwarz");
}
ierr = SNESNASMGetSubdomains(npc,&n,&subsnes,NULL,&oscatter,NULL);CHKERRQ(ierr);
ierr = SNESNASMGetSubdomainVecs(npc,&n,&x,&b,NULL,NULL);CHKERRQ(ierr);
ierr = VecSet(Y,0);CHKERRQ(ierr);
ierr = MatMult(npc->jacobian_pre,X,W);CHKERRQ(ierr);
for (i=0;i<n;i++) {
ierr = VecScatterBegin(oscatter[i],W,b[i],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
}
for (i=0;i<n;i++) {
ierr = VecScatterEnd(oscatter[i],W,b[i],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecSet(x[i],0.);CHKERRQ(ierr);
ierr = SNESGetKSP(subsnes[i],&ksp);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCApply(pc,b[i],x[i]);CHKERRQ(ierr);
ierr = VecScatterBegin(oscatter[i],x[i],Y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
}
for (i=0;i<n;i++) {
ierr = VecScatterEnd(oscatter[i],x[i],Y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*MC
SNESASPIN - Helper SNES type for Additive-Schwarz Preconditioned Inexact Newton
Options Database:
+ -npc_snes_ - options prefix of the nonlinear subdomain solver (must be of type NASM)
. -npc_sub_snes_ - options prefix of the subdomain nonlinear solves
. -npc_sub_ksp_ - options prefix of the subdomain Krylov solver
- -npc_sub_pc_ - options prefix of the subdomain preconditioner
Notes: This routine sets up an instance of NETWONLS with nonlinear left preconditioning. It differs from other
similar functionality in SNES as it creates a linear shell matrix that corresponds to the product:
\sum_{i=0}^{N_b}J_b({X^b_{converged}})^{-1}J(X + \sum_{i=0}^{N_b}(X^b_{converged} - X^b))
which is the ASPIN preconditioned matrix. Similar solvers may be constructed by having matrix-free differencing of
nonlinear solves per linear iteration, but this is far more efficient when subdomain sparse-direct preconditioner
factorizations are reused on each application of J_b^{-1}.
Level: intermediate
.seealso: SNESCreate(), SNES, SNESSetType(), SNESNEWTONLS, SNESNASM, SNESGetPC(), SNESGetPCSide()
M*/
PETSC_EXTERN PetscErrorCode SNESCreate_ASPIN(SNES snes)
{
PetscErrorCode ierr;
SNES npc;
KSP ksp;
PC pc;
Mat aspinmat;
MPI_Comm comm;
Vec F;
PetscInt n;
SNESLineSearch linesearch;
PetscFunctionBegin;
/* set up the solver */
ierr = SNESSetType(snes,SNESNEWTONLS);CHKERRQ(ierr);
ierr = SNESSetPCSide(snes,PC_LEFT);CHKERRQ(ierr);
ierr = SNESGetPC(snes,&npc);CHKERRQ(ierr);
ierr = SNESSetType(npc,SNESNASM);CHKERRQ(ierr);
ierr = SNESNASMSetComputeFinalJacobian(npc,PETSC_TRUE);CHKERRQ(ierr);
ierr = SNESGetKSP(snes,&ksp);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr);
ierr = SNESGetLineSearch(snes,&linesearch);CHKERRQ(ierr);
ierr = SNESLineSearchSetType(linesearch,SNESLINESEARCHBT);CHKERRQ(ierr);
/* set up the shell matrix */
ierr = SNESGetFunction(snes,&F,NULL,NULL);CHKERRQ(ierr);
ierr = VecGetLocalSize(F,&n);CHKERRQ(ierr);
ierr = MatCreateShell(comm,n,n,PETSC_DECIDE,PETSC_DECIDE,snes,&aspinmat);CHKERRQ(ierr);
ierr = MatSetType(aspinmat,MATSHELL);CHKERRQ(ierr);
ierr = MatShellSetOperation(aspinmat,MATOP_MULT,(void(*)(void))MatMultASPIN);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes,aspinmat,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = MatDestroy(&aspinmat);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
SNES snes; /* nonlinear solver */
SNES psnes; /* nonlinear Gauss-Seidel approximate solver */
Vec x,b; /* solution vector */
PetscInt its; /* iterations for convergence */
PetscErrorCode ierr;
DM da;
PetscBool use_ngs = PETSC_FALSE; /* use the nonlinear Gauss-Seidel approximate solver */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
PetscInitialize(&argc,&argv,(char *)0,help);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create nonlinear solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(PETSC_NULL,"-use_ngs",&use_ngs,0);CHKERRQ(ierr);
if (use_ngs) {
ierr = SNESGetPC(snes,&psnes);CHKERRQ(ierr);
ierr = SNESSetType(psnes,SNESSHELL);CHKERRQ(ierr);
ierr = SNESShellSetSolve(psnes,NonlinearGS);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1,PETSC_NULL,PETSC_NULL,&da);CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);CHKERRQ(ierr);
ierr = SNESSetDM(snes,da);CHKERRQ(ierr);
if (use_ngs) {
ierr = SNESShellSetContext(psnes,da);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DMDA; then duplicate for remaining
vectors that are the same types
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&b);CHKERRQ(ierr);
ierr = VecSetRandom(b,PETSC_NULL);CHKERRQ(ierr);
ierr = SNESSetFunction(snes,PETSC_NULL,MyComputeFunction,PETSC_NULL);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes,PETSC_NULL,PETSC_NULL,MyComputeJacobian,PETSC_NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Customize nonlinear solver; set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = SNESSolve(snes,b,x);CHKERRQ(ierr);
ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}