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

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

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