syfi team mailing list archive

[Harish Narayanan <harish.mlists@xxxxxxxxx>]

kent-and@xxxxxxxxx wrote:
>> kent-and@xxxxxxxxx wrote:
>>>> 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.
>> OK, and by "work" do you mean will head in the right direction (not
>> necessarily at a quadratic rate)? If that is what you meant, then this
>> is true of these hyperelastic materials as well. The strain energy is a
>> convex function of the deformation measure.
>>
>> Harish
> 
> 
> For the above equation I think there should be only one minimum and so
> it will head in the right direction. I'm not sure whether it should be
> quadratic.

That was what I was trying to clarify in an earlier e-mail. It will
always work, but converge quadratically only if close.

> If it is convex it can have several minium and it may therefore head
> towards different minima at different times but I didn't think it could head
> off to infinity (or creating a singular matrix) ?

It should not. There is something else going on. I need to look at
things more carefully.

Harish