[petsc-dev] Strange behaviour from TSARKIMEX

[Stefano Zampini]

I came across this thing recently, and I couldn't figure out where the
issue could be.

The problem I'm solving is a simple DG advection, the ode is M*udot =
K*u+b, M is diagonal.

Attached is a MWE that reproduces the problem.

The problem is formed in two different cases depending on the command line
option -m_lhs

a) -m_lhs 1 : F(u,udot,t) = M*udot, G(u,t) = K*u+b
b) -m_lhs 0 : F(u,udot,t) = udot, G(u,t) = M^-1(K*u+b)

Using option b) and RK4, the solution is ok.
If run with any implicit TS method except arkimex, no matter if I'm
choosing option a) or b), the solution is always very close (say, final
error < 0.05) to the expected one (computed with BDF).

When using ARKIMEX, case b) gives a good solution, but not case a). In
fact, the solution does not seem to be advected at all in this case.

I was wondering if I'm doing something wrong or there's a bug in the
ARKIMEX implementation.

I also noticed that, using  -ts_arkimex_fully_implicit does not produce the
same output for case a) and b). Shouldn't they produce the same method with
this option?

Thanks,
-- 
Stefano
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