Re: [Libmesh-users] Store the finite element matrices for post-processing of stresses/strains?

[Yuxiang W. <yw...@vi...>]

Hi David,

Greetings again.

I found the answer from this link
<http://www.joinville.udesc.br/portal/professores/pablo/materiais/CIL26_0053.pdf>
and yes, we will get a globally smooth distribution at the cost of much
more computation.

Thank you,
Shawn

On Fri, Nov 2, 2018 at 10:01 PM Yuxiang Wang <yw...@vi...> wrote:

> Hi David,
>
> Thank you for your response! Yes I was indeed reading your example and
> thinking about it. Your insight helps a lot. Thank you so much!
>
> Since we are discussing on this topic, if you wouldn't mind, I'd like to
> ask one more question:
>
> During the L2 projection process, we solved the system per element. If we
> assemble the element mass matrices and the RHS to a global one with all
> elements, and similarly solve the global equation, would we be getting a
> globally smoothed stress distribution?
>
> I'd really love to hear your comment. Thanks in advance!
>
> Best,
> Shawn
>
> On Fri, Nov 2, 2018 at 7:27 PM David Knezevic <dav...@ak...>
> wrote:
>
>> On Fri, Nov 2, 2018 at 9:50 PM Yuxiang Wang <yw...@vi...> wrote:
>>
>>> Dear all,
>>>
>>> I have been using the matrix notation (following the Bathe textbook) with
>>> libmesh recently to code finite element solutions for basic continuum
>>> structural elements. I realized that I need to compute those matrices
>>> twice
>>> - once when I assemble the global stiffness matrix, and another time
>>> when I
>>> get the solutions and need to post-process to compute the
>>> stresses/strains.
>>> Being curious, do we have any best practices (or special considerations)
>>> to
>>> save those matrices so that we don't have to compute them twice? For
>>> example, should I just create a huge vector of DenseMatrix, and each
>>> matrix
>>> for each quadrature point? Or that libmesh has some tools for this book
>>> keeping?
>>>
>>> Explanation for what I meant by "matrix notation" and what are those
>>> finite
>>> element matrices: for example, for each quadrature point I have an
>>> interpolation matrix [H], a strain-displacement matrix [B] (constructed
>>> from derivatives of [H]). With the constitutive tensor matrix being [C],
>>> we
>>> can easily get the element stiffness matrix by [K] =
>>> integrate([B]^T[C][B]). After the solution [uhat] is obtained, we can
>>> also
>>> get the strain and stress by again [strain] = [B][uhat] or [stress] =
>>> [C][B][uhat].
>>>
>>> Just wondering whether anyone else has done this before and whether there
>>> would be a better practice to do it more elegantly. Thanks :)
>>>
>>> Best,
>>> Shawn
>>
>>
>> See systems_of_equations_ex6 for an example of computing stresses in
>> libMesh. In that case we do not store and re-use the per-element strain and
>> stress matrices (C and B in your notation) You could store and reuse that
>> data, but it's not clear to me whether it'd be worth it. You'd presumably
>> get some speedup in the evaluation of the stress at the cost of extra
>> storage, so you'd have to decide if you want that or not (in my experience
>> I would not want that since memory is usually more of a limiting factor
>> than speed).
>>
>> Best,
>> David
>>
>
>
> --
> Yuxiang "Shawn" Wang, PhD
> yw...@vi...
> +1 (434) 284-0836
>


-- 
Yuxiang "Shawn" Wang, PhD
yw...@vi...
+1 (434) 284-0836