syfi team mailing list archive

[Harish Narayanan <harish.mlists@xxxxxxxxx>]

kent-and@xxxxxxxxx wrote:
>> kent-and@xxxxxxxxx wrote:
>>> The nonlinear hyper-elasticity demos do not seem to produce
>>> the correct solution. I have been looking in particular on the Fung
>>> stuff.
>>>
>>> Newton seems to converge with quadratic convergence whenever
>>> it is close to the solution so I think the differentiation is correct.
>> OK. I have been trying a few things over the past week (compiling forms
>> with FFC instead) and here is what I see:
>>
>> 1. Nonlinear scalar Poisson works.
>> 2. Linear elasticity posed as a special case of a nonlinear problem
>> works. (Converges in one iteration).
>> 3. Nonlinear elasticity (hyperelasticity with the St. Venant-Kirchhoff
>> model) a. does not converge or b. the direct solvers complain about a
>> singular matrix.
>>
>> I didn't think to look into the boundary conditions for 3 because I used
>> the same setting as 2. I will look at them more closely.
>>
>> Harish
> 
> I don't think it is a problem with the bc. I tested some nonlinear variants
> of Poisson that come from convex functionals. In these cases Newton
> should work. Can we say the same about SVK or Fung or do we either
> need a relaxation scheme or start close to the solution ?

For the SVK or Fung (or any material model) that has been correctly
linearised, the Newton-Raphson scheme should converge quadratically as
long as one starts close to the solution. In practice, this is ensured
by not driving the problem too much in a given (time) step.

Harish