[petsc-users] Select a preconditioner for SLEPc eigenvalue solver Jacobi-Davidson

[Fande Kong]

Thanks Jose,

I think I understand now. Another question: what is the right way to setup
a linear preconditioning matrix for the inner linear solver of JD?

I was trying to do something like this:

  /*
     Create eigensolver context
  */
  ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr);

  /*
     Set operators. In this case, it is a standard eigenvalue problem
  */
  ierr = EPSSetOperators(eps,A,NULL);CHKERRQ(ierr);
  ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr);
  ierr = EPSGetST(eps,&st);CHKERRQ(ierr);
  ierr = STPrecondSetMatForPC(st,B);CHKERRQ(ierr);

  /*
     Set solver parameters at runtime
  */
  ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve the eigensystem
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = EPSSolve(eps);CHKERRQ(ierr);


But did not work. A complete example is attached.  I could try to dig into
the code, but you may already know the answer.


On Wed, Oct 23, 2019 at 3:58 AM Jose E. Roman <jroman at dsic.upv.es> wrote:

> Yes, it is confusing. Here is the explanation: when you use a target, the
> preconditioner is built from matrix A-sigma*B. By default, instead of
> TARGET_MAGNITUDE we set LARGEST_MAGNITUDE, and in Jacobi-Davidson we treat
> this case by setting sigma=PETSC_MAX_REAL. In this case, the preconditioner
> is built from matrix B. The thing is that in a standard eigenproblem we
> have B=I, and hence there is no point in using a preconditioner, that is
> why we set PCNONE.
>
> Jose
>
>
> > El 22 oct 2019, a las 19:57, Fande Kong via petsc-users <
> petsc-users at mcs.anl.gov> escribió:
> >
> > Hi All,
> >
> > It looks like the preconditioner is hard-coded in the Jacobi-Davidson
> solver. I could not select a preconditioner rather than the default setting.
> >
> > For example, I was trying to select LU, but PC NONE was still used.  I
> ran standard example 2 in slepc/src/eps/examples/tutorials, and had the
> following results.
> >
> >
> > Thanks,
> >
> > Fande
> >
> >
> > ./ex2 -eps_type jd -st_ksp_type gmres  -st_pc_type lu   -eps_view
> >
> > 2-D Laplacian Eigenproblem, N=100 (10x10 grid)
> >
> > EPS Object: 1 MPI processes
> >   type: jd
> >     search subspace is orthogonalized
> >     block size=1
> >     type of the initial subspace: non-Krylov
> >     size of the subspace after restarting: 6
> >     number of vectors after restarting from the previous iteration: 1
> >     threshold for changing the target in the correction equation (fix):
> 0.01
> >   problem type: symmetric eigenvalue problem
> >   selected portion of the spectrum: largest eigenvalues in magnitude
> >   number of eigenvalues (nev): 1
> >   number of column vectors (ncv): 17
> >   maximum dimension of projected problem (mpd): 17
> >   maximum number of iterations: 1700
> >   tolerance: 1e-08
> >   convergence test: relative to the eigenvalue
> > BV Object: 1 MPI processes
> >   type: svec
> >   17 columns of global length 100
> >   vector orthogonalization method: classical Gram-Schmidt
> >   orthogonalization refinement: if needed (eta: 0.7071)
> >   block orthogonalization method: GS
> >   doing matmult as a single matrix-matrix product
> > DS Object: 1 MPI processes
> >   type: hep
> >   solving the problem with: Implicit QR method (_steqr)
> > ST Object: 1 MPI processes
> >   type: precond
> >   shift: 1.79769e+308
> >   number of matrices: 1
> >   KSP Object: (st_) 1 MPI processes
> >     type: gmres
> >       restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> >       happy breakdown tolerance 1e-30
> >     maximum iterations=90, initial guess is zero
> >     tolerances:  relative=0.0001, absolute=1e-50, divergence=10000.
> >     left preconditioning
> >     using PRECONDITIONED norm type for convergence test
> >   PC Object: (st_) 1 MPI processes
> >     type: none
> >     linear system matrix = precond matrix:
> >     Mat Object: 1 MPI processes
> >       type: shell
> >       rows=100, cols=100
> >  Solution method: jd
> >
> >  Number of requested eigenvalues: 1
> >  Linear eigensolve converged (1 eigenpair) due to CONVERGED_TOL;
> iterations 20
> >  ---------------------- --------------------
> >             k             ||Ax-kx||/||kx||
> >  ---------------------- --------------------
> >         7.837972            7.71944e-10
> >  ---------------------- --------------------
> >
> >
> >
>
>
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