[petsc-users] Convergence of iterative linear solver

[Mark Adams]

On Tue, Jun 2, 2015 at 6:00 PM, Jed Brown <jed at jedbrown.org> wrote:

> Eduardo <erocha.ssa at gmail.com> writes:
>
> > I am solving a FEM solid mechanics linear elasticity model, for now the
> > only problem is the mesh that has needle-shaped and very flat elements.
>
> Why does it have such elements?  Is the material highly anisotropic
> (e.g., fiber)?  Is the geometry anisotropic (shell structures
> discretized using volumes)?  Is it just a low-quality mesh?
>
> As Mark says, thresholding is important for AMG to solve anisotropic
> problems, but many of the discretizations used in solid mechanics will
> obscure the anisotropy from the usual strength of connection measures.
>

Yes, but the main point of thresholding is that it governs the rate of
coarsening.  If you coarsen "too" fast convergence rates deteriorate, if
you coarsen "too" slow the cost if each iterations gets (very) high.  This
is problem dependant and the defaults can be very bad for some problems.
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