[petsc-users] Preconditioning with SLEPc

[Kenneth Hall, SC.D.]

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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