[petsc-users] How to determine a reasonable relative tolerance to iteratively solve a linear system of equations?

[Fangbo Wang]

Hi,

I know this is not a problem specific to PETSc, but I have this doubt for a
long time and want to ask the experts here.

Suppose I have a very large linear system of equations with 1.5 million
unkowns. It is common to use relative tolerance as a stopping criteria.

For a small linear system, I usually use 1e-6, or 1e-8, or 1e-10, etc. But
for a very large linear system, do I need to use a relative tolerance much
smaller than the previous I use? (Theoretically I think the relative
tolerance has nothing related to system size).

However, something very weird happens. I used 1e-7 as my relative tolerance
for my linear system  with 1.5 million unknows using conjugate gradient
method with jacobi preconditioner, the solver can not converge to 1e-7 with
10,000 iterations. I can use a larger tolerance but the solution is not
good.

Any one have some  advices? Thank you very much!

Best regards,

Fangbo Wang

-- 
Fangbo Wang, PhD student
Stochastic Geomechanics Research Group
Department of Civil, Structural and Environmental Engineering
University at Buffalo
Email: *fangbowa at buffalo.edu <fangbowa at buffalo.edu>*
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