[CIG-SHORT] Convergence problem with Neumann BCs

[Eric Lindsey]

Thanks very much for the help everyone.

Brad and Charles, thanks for pointing out the ill-posedness, I hadn't
thought this through properly. After adding back some Dirichlet BC the
solver does converge, in ~400 iterations. Thanks!

The initial stress field also works nicely. In this case I just want
uniform compression and shear stress, so I can impose it with a simple
spatialDB with just the 3 components; I believe this is compatible with the
Airy stress function. I had some confusion getting the other boundary
conditions to be compatible with this setup as you mentioned, but think
I've got it worked out -- the two sides with no Dirichlet BC need a Neumann
condition to maintain the initial normal stress.

Matt, I'm just using the linux binary package (1.9.0) -- but I grabbed a
clone from git, and tried out these solvers. They both converged in only
3-5 iterations, but run much slower (~2min instead of ~1sec). I'm not sure
what the metric is for a "better" solver I guess?

Thanks,
Eric


On Thu, Oct 31, 2013 at 1:12 PM, Charles Williams <willic3 at gmail.com> wrote:

> Hi Eric,
>
> Sorry to be slow in responding.  I just had a look at your problem, and it
> appears that you have changed all the BC to Neumann, which means that your
> displacements are completely unconstrained.  This is an ill-posed problem,
> and I wouldn't expect it to work.  I'm not quite sure what you're trying to
> represent, but I'm wondering whether initial stresses might be what you
> want.  Alternatively, you need to pin at least 3 DOF (to prevent
> translation/rotation).  Usually, with traction BC there is some sort of
> symmetry, so you could probably fix one of your boundaries.  I'm assuming
> your traction variations aren't that complicated, however, which means you
> could use an Airy stress function to describe the stresses within the
> domain (see, for example, the elasticity book by Timoshenko).  Your
> displacement BC would have to be compatible, though.
>
> Cheers,
> Charles
>
>
> On 31/10/2013, at 11:43 AM, Eric Lindsey wrote:
>
> Hi,
>
> I'd like to apply background stresses to a simple elastic 2D plane strain
> model in pylith, then add fault slip or other quasistatic deformation;
> later I'll modify the material properties etc. Of course the stresses also
> cause some deformation in the volume that I'd like to ignore. So I'm
> imposing the slip at the second time step, with the hopes of subtracting
> out the deformation from the first time step. (Is this the right way to do
> this?)
>
> However, I noticed that the effects from the boundary conditions continue
> to increase, and then oscillate, and don't stabilize until I let it run to
> the 8th step or so (ideally I'd only use 2 time steps, I think). I think
> the problem is with the solver's convergence; I see the message
>
> ...
> 499 KSP Residual norm 9.952574507238e-04
> 500 KSP Residual norm 9.952555275971e-04
> Linear solve did not converge due to DIVERGED_ITS iterations 500
>
> I've taken most of the configuration straight from
> examples/2d/greensfns/strikeslip, and just modified the boundary conditions
> from Dirichlet to Neumann. Config file is attached; any advice would be
> great.
>
> Thanks,
> Eric
>
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> Charles A. Williams
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