[petsc-users] Precision Problem in computing Eigenvalue

[Ajay Manwani]

Hello,

I am trying to solve Schroginger equation with open boundary conditions.
The problem boils down to a complex polynomial eigenvalue equation of order
two with A0,A1,A2 matrices of the size 300 x 300.
Here, A0 and A2 are tridiagonal matrices while A1 has only single element
at with imaginary value.
The complex eigenvalues are such that real part is around 1 while imaginary
part is in the range of 1e-12 to 1e-15.

 PEP solver gives out 600 complex eigenvalues having 300 complex conjugate
pairs.
However problem is that the real part of two states is same while complex
part of the eigenvalues differs by a order of one.( i mean ~e-14 and ~e-15)

The solver gives eigenvalues of the pair the same when the imaginary values
are more than 1e-10.

I tried with -pep_tol 1e-18. -pep_max_it 10000. However, answer does not
change for eigenvalues with imaginary part of the order of ~1e-15.

other options -pep_smallest imaginary and changing the solver types also
does not seem to work.

Is there some way one can improve answers I mean more precise value of very
small imaginary part of eigenvalue?

We have tried  -st_type sinvert -st_transform  as well as -pep_target and
-rg_type ellipse(region filtering) but there still the problem persists.
 Kindly suggest any way to improve precision for imaginary values below
(1e-10)

Regards,
Ajay Manwani
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