On the discretization of the time harmonic Maxwell equation

[Abbas]

This is not a dealii question per se but again, if it's someone who can answer this question it's going to be someone from here. 

The literature mostly refers to two approaches todiscretizing the time harmonic Maxwell equation. The first one is through the use of edge curl conforming Nedelec elements and the other being through the use of interior penalty DG. 

Any comments on the use of one approach over the other? 

[Jean-Paul Pelteret]

Hi Abbas,

I’m sorry that nobody has answered your question to date. It could be that there is no-one on the forum with the requisite knowledge to help you, or maybe those that have the knowledge just aren’t capable of responding at the moment. If you haven’t done so already, then perhaps you might choose to ask your question on another forum (StackOverflow might be a good one to start with) — hopefully you’d have better luck getting some advice or guidance there.

Best,

Jean-Paul 

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[Wolfgang Bangerth]

On 7/6/21 12:13 PM, Jean-Paul Pelteret wrote:
>
> The literature mostly refers to two approaches todiscretizing the time
> harmonic Maxwell equation. The first one is through the use of edge curl
> conforming Nedelec elements and the other being through the use of interior
> penalty DG.
>
> Any comments on the use of one approach over the other?

Abbas,
alternatively, I can try to scrape the bottom of my barrel and see what I know
about things. What specifically is your question? Which of the two methods is
better? Which is more accurate? Which is faster? Which is easier to implement?

The one using edge (Nedelec) elements is certainly more widely used today
because it is known to actually work. Using IP methods and the usual
continuous or discontinuous elements is newer, and so as a community we have
less experience on how well that works. I can't say that I've ever heard
anyone say "You should use method 1" or "2". If correctly implemented, both
will probably get you to your goal, and the difference in accuracy and speed
is probably not so large that it really matters one way or the other.

Best
W.

--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/