syfi team mailing list archive

[Harish Narayanan <harish.mlists@xxxxxxxxx>]

kent-and@xxxxxxxxx wrote:
>> 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
> 
> The Newton-Raphson scheme should always converge quadratic as long as
> one starts close enough to the solution :)

I know :). Then I didn't understand what you meant by:

I tested some nonlinear variants of Poisson that come from convex
functionals. In these cases Newton should work.

Did you mean, a Newton solver should work from any starting point?

Harish