[petsc-users] Convergence of different fields/equations

[Carles Bona]

Hi all,

I am currently running petsc to solve a time-dependent nonlinear system
with default options (NewtonLS, etc.). I have a question regarding
convergence. My application evolves different fields and equations, which
might be in different units (like temperature and velocity) and might not
involve the same order of derivatives (for example second derivatives,
scaling as ~1/dx^2 or first derivatives, scaling as ~1/dx). My application
also has a handicap: the tangent matrix is cumbersome to calculate.

>From what I understand and I see in the source code, convergence norms are
performed on the whole residual, that is, including all fields/equations.
Am I wrong?

My concern is, if I am using a relative convergence criteria for the
residual norm, it might happen that I am solving one of my equations very
nicely and another equation shouldn't be converging yet... But just because
it's dealing with a much smaller residual than the other equation from the
very beginning, the residual norm is not caring about it and it's showing
convergence too early (specially if I don't run with the default parameters
anymore and I ask for a relative convergence of 10^-3, for example).

I have been looking at the documentation and mailing list and I haven't
been able to find if there is a specific petsc option to prevent this from
happening (other than setting a very restrictive relative convergence,
which is painful for me as I don't have a nice tangent matrix) or if I
should implement a convergence criteria myself, probably something like
what has been suggested here:
http://lists.mcs.anl.gov/pipermail/petsc-users/2014-August/022577.html

Thanks in advance,

Carles
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