>
> sinvert should give you more that 2 eigenvalues if you set eps_nev > 2. You
> may need to increase the number of iterations with eps_max_it
i would expect that it should, but it is not the case. I tried setting number
of iterations 10 times the number of DoFs, and no change.
It does not seem to be related. Here is an output without shift-and-invert
EPS Object: 1 MPI processes
type: krylovschur
Krylov-Schur: 50% of basis vectors kept after restart
problem type: generalized symmetric eigenvalue problem
selected portion of the spectrum: smallest real parts
computing true residuals explicitly
number of eigenvalues (nev): 5
number of column vectors (ncv): 20
maximum dimension of projected problem (mpd): 20
maximum number of iterations: 2890
tolerance: 1e-07
convergence test: absolute
BV Object: 1 MPI processes
type: svec
21 columns of global length 289
orthogonalization method: classical Gram-Schmidt
orthogonalization refinement: if needed (eta: 0.7071)
non-standard inner product
Mat Object: 1 MPI processes
type: seqaij
rows=289, cols=289
total: nonzeros=1913, allocated nonzeros=5491
total number of mallocs used during MatSetValues calls =0
not using I-node routines
DS Object: 1 MPI processes
type: hep
solving the problem with: Implicit QR method (_steqr)
ST Object: 1 MPI processes
type: shift
shift: 0
number of matrices: 2
all matrices have different nonzero pattern
KSP Object: (st_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-08, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (st_) 1 MPI processes
type: redundant
Redundant preconditioner: First (color=0) of 1 PCs follows
KSP Object: (st_redundant_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (st_redundant_) 1 MPI processes
type: lu
LU: out-of-place factorization
tolerance for zero pivot 2.22045e-14
matrix ordering: nd
factor fill ratio given 5, needed 2.99686
Factored matrix follows:
Mat Object: 1 MPI processes
type: seqaij
rows=289, cols=289
package used to perform factorization: petsc
total: nonzeros=5733, allocated nonzeros=5733
total number of mallocs used during MatSetValues calls =0
not using I-node routines
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqaij
rows=289, cols=289
total: nonzeros=1913, allocated nonzeros=5491
total number of mallocs used during MatSetValues calls =0
not using I-node routines
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqaij
rows=289, cols=289
total: nonzeros=1913, allocated nonzeros=5491
total number of mallocs used during MatSetValues calls =0
not using I-node routines
>
>>
>> 2) Another peculiarity is that `-eps_smallest_real` and `-eps_target 0
>> -st_type sinvert` return different sets of eigenvalues.
>
> The matrix from the 2D Laplace operator is positive definite, so both should
> give the same eigenvalues.
>
>> In the latter case there are degenerate eigenvalues.
>> Those are consistent with the results given by ARPACK with shift and invert
>> around 0.
>> The matrices I sent you originally correspond to the eigenvalues of the 2D
>> Laplace operator on a uniform mesh with 256 cells.
>> If more refined mesh is used (1024 cells instead of 256), same set with
>> degenerate eigenvalues is returned in both cases.
>> This is not directly related to SLEPc and is a question out of curiosity.
>
> Some eigenvalues of the 2D Laplacian have multiplicity 2. The default SLEPc
> solver may not return the two copies of the eigenvalue, because the second
> copy appears much later and the iteration stops as soon as nev eigenvalues
> have been computed.
i see…
so technically, one could try asking for more eigenvectors to resolve those
degenerate eigenvalues?
>
>>
>> 3) It is not stated in the documentation explicitly, but I suppose the
>> residual discussed in ‘SolverControl’ section
>> always corresponds to the direct problem (even in case when, say,
>> shift-and-invert is applied) and so
>> EPSComputeRelativeError and EPSComputeResidualNorm?
>
> The convergence criterion is applied to the transformed problem
> (shift-and-invert).
understood, thanks.
Regards,
Denis.
