Hi Anna,

I believe I have found your problem. The test and trial functions for the 3rd block are v_4 and mu_t respectively. The relevant term is:

amu = v4*(mu_bar*lambda_t + lambda_bar*mu_t)*dx

i.e. the diagonal block is:

v4*lambda_bar*mu_t*dx.

However, if I plot lambda_bar, I find that it is zero over most of the domain. Most rows of this block are therefore zero with the result that the solver fails on this block.

Now it can be that the diagonal blocks are supposed to be zero and that the problem is still well-posed (as with mixed Poisson, for example). However that situation needs to be dealt with in the right way in a field split preconditioner. Before we get there, what is the argument in this case that this problem is in fact well-posed?

Regards,

David

On Fri, 2 Dec 2016 at 16:20 David Ham <David.Ham@imperial.ac.uk> wrote:

On Fri, 2 Dec 2016 at 16:12 Mitchell, Lawrence <lawrence.mitchell@imperial.ac.uk> wrote:

> On 2 Dec 2016, at 16:01, Anna Kalogirou <a.kalogirou@leeds.ac.uk> wrote:
>
> Linear firedrake_0_fieldsplit_3_ solve did not converge due to DIVERGED_DTOL iterations 35
>
> The option
>
> "fieldsplit_3_pc_factor_shift_type": "nonzero"

Given that LU with pivoting ought to invert the block unless it is singular, I think something funky is going on.

Can you additionally run with:

"fieldsplit_3_ksp_monitor_true_residual": True

(In passing, if you're using LU you should probably be setting the ksp_type of these sub solves to "preonly", so you don't bother iterating).

The function space is CG1. I believe that has diagonally dominant mass matrices so we shouldn't actually need pivotting.

Lawrence
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