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

[Jose E. Roman]

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
>  ---------------------- --------------------
> 
> 
>