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

[Mark Adams]

> 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).
>

I agree with the other responses and let me add that 1) you kinda do
want to reduce your tolerance as you refine, but nobody does, and 2) a
properly working MG reduces the entire spectrum of the error pretty
uniformly, whereas (damped) Jacobi reduces the high frequency error
fast and is slow on the low frequency error. So you could find that,
with a constant rtol, your solution goes bad as you refine, whereas MG
will stay good.