MatrixFree support for Nedelec element in deal.II

[yy.wayne]

Hi deal.II community,

I'm working on MatrixFree electromagnetic problems with deal.II. For 2d TE waves FE_Q element works good, but for cases like in step-81 and in 3d, Nedelec element in the appropriate one for EM.

I posted a discussion about this 3 months ago. May I ask what's the current state for MatriFree support of Nedelec elements in deal.II? Implementing MatrixFree Nedelec is quite difficult for me. Currently I plan to solve 3d EM problem with FE_Q elements with some penalty terms, but of course that's not a nice policy because of spurious solution and singularity when solving EM numerically with nodal elements.

[Abbas]

Maybe you can look into using DG for discritizing the problem? You're already using penalty terms so might as well. 
One thing I am afraid of is that Nedelec elements inherently satisfy the div free condition, while DG might need careful treatment or your preconditioner would fail at high frequency. 
Just my 2 cents. Maybe you know someone else who can help you with this.   

[yy.wayne]

Thanks Abbas,

I considered about DG method, because DG allows discontinuity and implements boundary condition easier than FE_Q. 

However DG requires more DoF than continuous finite element, especially in frequency-domain. 

Best,

Wayne

[Abbas]

Nedelec elements aren't cheap either. If I recall correctly you'd need 108 dofs for the 6 EM components per element to achieve first order convergence. (I hope someone would correct me on this if I am wrong) 
With AMR and hanging nodes this can get expensive fairly quickly.  The only thing that worries me about DG is if they could handle the div free condition well, and if they are robust for high frequency problems. 
Just my 2 cents. Hope it helps in some way even if you don't chose this path. 

best, 
Abbas