[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)



-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20180807/a9f8d0c1/attachment-0001.html>


More information about the petsc-users mailing list