[petsc-users] [SLEPc] Krylov-Schur convergence

[Ale Foggia]

Hello,

I'm using SLEPc to get the smallest real eigenvalue (EPS_SMALLEST_REAL) of
a Hermitian problem (EPS_HEP). The linear size of the matrices I'm solving
is around 10**9 elements and they are sparse. I've asked a few questions
before regarding the same problem setting and you suggested me to use
Krylov-Schur (because I was using Lanczos). I tried KS and up to a certain
matrix size the convergence (relative to the eigenvalue) is good, it's
around 10**-9, like with Lanczos, but when I increase the size I start
getting the eigenvalue with only 3 correct digits. I've used the options:
-eps_tol 1e-9 -eps_mpd 100 (16 was the default), but the only thing I got
is one more eigenvalue with the same big error, and the iterations
performed were only 2. Why didn't it do more in order to reach the
convergence? Should I set other parameters? I don't know how to work out
this problem, can you help me with this please? I send the -eps_view output
and the eigenvalues with its errors:

EPS Object: 2048 MPI processes
  type: krylovschur
    50% of basis vectors kept after restart
    using the locking variant
  problem type: symmetric eigenvalue problem
  selected portion of the spectrum: smallest real parts
  number of eigenvalues (nev): 1
  number of column vectors (ncv): 101
  maximum dimension of projected problem (mpd): 100
  maximum number of iterations: 46210024
  tolerance: 1e-09
  convergence test: relative to the eigenvalue
BV Object: 2048 MPI processes
  type: svec
  102 columns of global length 2333606220
  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: 2048 MPI processes
  type: hep
  parallel operation mode: REDUNDANT
  solving the problem with: Implicit QR method (_steqr)
ST Object: 2048 MPI processes
  type: shift
  shift: 0.
  number of matrices: 1

              k                ||Ax-kx||/||kx||
   -----------------        ------------------
     -15.093051         0.00323917 (with KS)
     -15.087320         0.00265215 (with KS)
     -15.048025         8.67204e-09 (with Lanczos)
Iterations performed 2

Ale
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