syfi team mailing list archive

[kent-and@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

Yes,  for an equation like
-Delta u + u**p

where p is odd.

Kent