[petsc-users] Preconditioning with SLEPc
Kenneth Hall, SC.D.
kenneth.c.hall at duke.edu
Tue Aug 7 11:31:36 CDT 2018
Jose,
Thank you very much for the quick response. I will try the approach for the Krylov solver.
Kenneth.
_________________________________________________________________
Kenneth C. Hall
On Aug 7, 2018, at 11:13 AM, Jose E. Roman <jroman at dsic.upv.es<mailto:jroman at dsic.upv.es>> wrote:
Currently there is no straightforward way to do this in SLEPc. For a preconditioned eigensolver such as JD you could use this:
https://urldefense.proofpoint.com/v2/url?u=http-3A__slepc.upv.es_documentation_current_docs_manualpages_ST_STPrecondSetMatForPC.html&d=DwIFaQ&c=imBPVzF25OnBgGmVOlcsiEgHoG1i6YHLR0Sj_gZ4adc&r=HM_IVChvU7XXVyLZB9xFCbw5_4LZNuzGEpVw5dUCyyo&m=L-kD1fTipDH_5BEC-T3FTfZKFQBUO6_ymvkpAiFfe38&s=kZTO6rmsUygc5qVZm5IkYMfjEMPVXloxoE0xi16ccUQ&e=
in combination with pc=PCMAT.
For a Krylov solver you will have to do something like this:
call EPSSetWhichEigenpairs(eps,EPS_TARGET_REAL,ierr);CHKERRA(ierr)
call EPSSetTarget(eps,sigma,ierr);CHKERRA(ierr)
call EPSGetST(eps,st,ierr);CHKERRA(ierr)
call STSetType(st,STSINVERT,ierr);CHKERRA(ierr)
call STGetKSP(st,ksp,ierr);CHKERRA(ierr)
call KSPGetPC(ksp,pc,ierr);CHKERRA(ierr)
call KSPSetType(ksp,KSPBCGS,ierr);CHKERRA(ierr)
call PCSetType(pc,PCNONE,ierr);CHKERRA(ierr) ! dummy preconditioner
! provide the preconditioner matrix after setup
call EPSSetUp(eps,ierr);CHKERRA(ierr)
call PCSetOperators(pc,PETSC_NULL_MAT,my_matmul_K,ierr);CHKERRA(ierr)
call PCSetType(pc,PCMAT,ierr);CHKERRA(ierr)
We may change the interface in future versions so that this can be done in a more natural way.
Jose
El 7 ago 2018, a las 16:42, Kenneth Hall, SC.D. <kenneth.c.hall at duke.edu> escribió:
Hello,
I am new to SLEPc and Petsc, so I would appreciate any help I can get with my question. I have a large eigenvalue problem I am solving, based on the linearization of a nonlinear code. The eigenvalue problem takes the form
A.x = lambda.B.x
I can generate the matrix B explicitly, but I can only form products of A.x, and not A itself, so I use a shell matrix. I also have an iterative solver I could potentially use as a preconditioner. That is, I have an operator K^-1 where
K^-1 \approx (A - sigma.B)^-1
But again, I don’t have K^-1 explicitly, rather I can form products of K^-1 with a vector, so I would need to use a shell matrix.
I have had success with the un-preconditioned case, but can’t figure out how to do the preconditioned case. Any suggestions would be greatly appreciated. I work with Fortran. A code snippet with the un-preconditioned set-up follows.
Thanks in advance.
Kenneth Hall
===============================================================
!
!.... initialize slepc
call SlepcInitialize(PETSC_NULL_CHARACTER,ierr) ; if (ierr .ne. 0) then ; stop 'SlepcInitialize failed' ; end if
!
!.... get size and rank of MPI process
call MPI_Comm_size(PETSC_COMM_WORLD,sz ,ierr) ; CHKERRA(ierr)
call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr) ; CHKERRA(ierr)
!
if (sz .ne. 1) then ; SETERRA(PETSC_COMM_SELF,1,'This is a uniprocessor example only!'); endif
!
!.... get user options
call PetscOptionsGetInt (PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n' ,n ,flg,ierr) ; CHKERRA(ierr)
call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-terse',terse,ierr) ; CHKERRA(ierr)
!
!.... write out option list
if (rank .eq. 0 ) then
write(*,*) 'n = ',n
end if
!
!.... Register the matrix-vector subroutine for the operator that defines the eigensystem, Ax=kBx
call MatCreateShell(PETSC_COMM_WORLD,n,n,n,n,PETSC_NULL_INTEGER,A,ierr) ; CHKERRA(ierr)
call MatShellSetOperation(A,MATOP_MULT,my_matmul_A,ierr) ; CHKERRA(ierr)
!
!.... set up B matrix
call MatCreate(PETSC_COMM_WORLD,B,ierr) ; CHKERRA(ierr)
call MatSetSizes(B,n,n,n,n,ierr) ; CHKERRA(ierr)
call MatSetFromOptions(B,ierr) ; CHKERRA(ierr)
call MatSetUp(B,ierr) ; CHKERRA(ierr)
call My_Matrix_B(B,n)
!
!.... set up eigenvectors
call VecCreate(PETSC_COMM_WORLD,xr,ierr) ; CHKERRA(ierr)
call VecSetSizes(xr,n,n,ierr) ; CHKERRA(ierr)
call VecSetFromOptions(xr,ierr) ; CHKERRA(ierr)
call VecSetUp(xr,ierr) ; CHKERRA(ierr)
!
call VecCreate(PETSC_COMM_WORLD,xi,ierr) ; CHKERRA(ierr)
call VecSetSizes(xi,n,n,ierr) ; CHKERRA(ierr)
call VecSetFromOptions(xi,ierr) ; CHKERRA(ierr)
call VecSetUp(xi,ierr) ; CHKERRA(ierr)
!
!.... Create eigensolver context
call EPSCreate(PETSC_COMM_WORLD,eps,ierr) ; CHKERRA(ierr)
!
!.... Set operators. In this case, it is a generalized eigenvalue problem
call EPSSetOperators(eps,A,B,ierr) ; CHKERRA(ierr)
call EPSSetProblemType(eps,EPS_GNHEP,ierr) ; CHKERRA(ierr)
!
!.... set default options
call EPSSetType(eps,EPSKRYLOVSCHUR,ierr) ; CHKERRA(ierr)
!
!.... set default eigenvalues to find
call EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL,ierr) ; CHKERRA(ierr)
!
!.... number of requested eigenvalues
call EPSSetDimensions(eps,nev,PETSC_DEFAULT_INTEGER,PETSC_DEFAULT_INTEGER,ierr) ; CHKERRA(ierr)
!
!.... set stopping criteria
call EPSSetTolerances(eps,tol,maxit,ierr) ; CHKERRA(ierr)
!
!.... set up monitors
call PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,vf,ierr) ; CHKERRA(ierr)
call EPSMonitorSet(eps,EPSMONITORFIRST,vf,PetscViewerAndFormatDestroy,ierr) ; CHKERRA(ierr)
call SlepcConvMonitorCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,ctx,ierr) ; CHKERRA(ierr)
call EPSMonitorSet(eps,EPSMONITORCONVERGED,ctx,SlepcConvMonitorDestroy,ierr) ; CHKERRA(ierr)
!
!.... Set solver parameters at runtime
call EPSSetFromOptions(eps,ierr) ; CHKERRA(ierr)
!
!.... Solve the eigensystem
call EPSSolve(eps,ierr) ; CHKERRA(ierr)
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