Discussion on the assembly of the element matrix

[huangyb2]

In Palace, when assembling the element matrix, the element matrix is first computed without considering the material coefficients. After the element matrix is calculated, the material coefficients are then added to the element matrix. Doesn't this significantly increase the computational cost? Is this approach beneficial for parallel computing in some way?

[hughcars]

Hi @huangyb2,

I'm not 100% sure what you mean by your question, but if you are referring to computing the element transformation pieces separately before the coefficient terms, then this is an optimization. See #122 and #166. The rough idea was that extra computation on the fly was worth it to reduce the size of the data needed to be stored. Does that answer your question? If not if you point me at the particular lines of code you are confused by, maybe I can be of more help.

[huangyb2]

Hi@hughcars
Thank you for your reply, and I apologize for the delay in my response. My focus is on understanding how the relative permeability is incorporated into the assembly process of the unit matrix, such as the curlcurl unit matrix, in Palace. I have gone through the code implementation of each function layer by layer, but still cannot find the answer. Could you please tell me where the bottom-level implementation of this function is located?My trace process is as follows:
1

2

3

and so on.......

[hughcars]

I think what you're looking for are the integrators and qfunctions. If you look at CurlCurlIntegrator::Assemble you will find that a QFunction is being assembled, which contains all the data that will be evaluated at each quadrature point. If you trace further, you'll eventually end up in the libceed functions, where the geometry data (things like jacobians, jacobian determinants etc. are computed) and the physical data (material properties) are combined. You need to go a long way further than BilinearForm::PartialAssemble, as the process to assemble efficiently in parallel is fairly involved.

The geometry data is computed once and then reused in any relevant integrands, whereas the physical data is specific to each integrand. This process is key to the partial assembly approach taken within Palace, that is explained by MFEM, https://mfem.org/performance/.