[petsc-users] Fieldsplit with LSC for constrained elasticity/poroelasticity?

[Jed Brown]

Tabrez Ali <stali at geology.wisc.edu> writes:

> Jed
>
> You're right and it is precisely what I am trying to understand as well. 
> I am attaching the comparison to the analytical solution. As you can see 
> the agreement is almost perfect, except at the discontinuity (y=0 in the 
> analytical solution).
>
> So why am I getting the correct solution when according to true 
> residuals I should not?

Assuming (I'm not convinced) that the solution is "correct", your system
is sufficiently ill-conditioned that the residual is huge.  Take any
system A and add a single row and column that are all zero except an
entry on the diagonal.  Augment the right-hand side with a corresponding
0.  The solution is obviously the solution of A x = b with an extra 0
regardless of what the diagonal entry is.

If the diagonal entry is 1e20, then [x; 1e-10] has a huge residual even
though it is pretty accurate.  If the diagonal entry is 1e-20, then [x;
1e10] is a nonsensical solution with a tiny residual.  This is
ill-conditioning.  You should nondimensionalize your problem to avoid
this spurious ill-conditioning, otherwise you should assume your results
are nonsense any any case where you don't already know the answer.
Sorry.
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