syfi team mailing list archive

[kent-and@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

The Newton-Raphson scheme should always converge quadratic as long as
one starts close enough to the solution :)

Kent