Approximating Open Boundary

[phillip mobley]

Hello everyone,

I have another question regarding approximating open boundary conditions.

In many electromagnetic problems, I will need to approximate the Vector Potential (A) to be 0 at r = infinite. I can do this a number of different ways. One being that I can create an air mesh that is 5x greater in radius then my problem. For me, this is the simplest to do but there is an increase in the computational time. There are a few others such as applying an asymptotic boundary Condition or performing a Kelvin Transform.

In deal.II, what is the best method that I can take that will approximate an open boundary problem?

[Wolfgang Bangerth]

I don't think people have come to a consensus as to which approach is
best. All of them (Perfectly Matches Layer, approximate absorbing
boundary conditions, exact absorbing boundary conditions, maybe even
infinite elements) have been implemented with deal.II at one point or
other by various people. It's your choice what you want.

Best
W.

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

[phillip mobley]

I apologize, need to reword a question.

Is there any particular one the works better in deal.II or are they pretty much the same? From what it sounds like they all perform equally well.

Is there a tutorial that goes over implementing one of these?

[Wolfgang Bangerth]

> Is there any particular one the works better in deal.II or are they pretty
> much the same? From what it sounds like they all perform equally well.

You're starting at the wrong end if you choose a method based on how easy it
is to implement. You should choose the method that is appropriate for the
problem you want to solve. Then you wonder how to implement it.

> Is there a tutorial that goes over implementing one of these?

Unfortunately not.

Best
WB

[Jean-Paul Pelteret]

There's also the boundary element method that could be used if you really don't want to model the surrounding free space. There are a number of papers listed here that illustrate its application to nonlinear electro-elastostatics.

[phillip mobley]

Hello Jean,

Thank you for the link, I will have to take a look at them later. Just to confirm, I was redirected to a staff page of PD Dr.-Ing. habil. Duc-Khoi Vu. Is this the correct link?

@Wolfgang

I apologize fir my question. I was looking at it as does deal.II prefer one method over the other?

I thinking about the asymptotic boundary Condition simply because this is the one COMSOL uses. And from what I have heard from a number of different engineers, this is one of the industry standard programs. I will look into others as I go along but I think that learning how to implement this first would be beneficial.

[Jean-Paul Pelteret]

Yes, that is correct. You will see the titles of a number of papers related to the boundary element method (BEM) at the bottom of the page.

Jean-Paul

[phillip mobley]

Hello Jean,

I was taking a look through the papers and all of the journals require a subscription. Which my school does not provide :(

I would say that I could tap into funds by my professor does not have funding. We are currently working to resolve this issue this semester.

Looking into BEM a little bit, this maybe a good solution for the problem. I still need to spend some more time researching it though to confirm that his the direction that I should take.

In the meantime, do you know of anyone who has implemented a BEM-FEM hybrid in deal.II? This could be the direction that I ultimately take since I still would like to use deal.II

[Ross Kynch]

Hi Phillip,

A lot of authors (e.g. Wolfgang tends to put a lot of his on his site) put a copy of their papers on their own personal pages. I'd suggest just googling for the title and looking for pdf files, sometimes you get lucky :)

For example: http://perso.ensta-paristech.fr/~mbonnet/vu_steinmann_12.pdf is one of the papers which pops up - maybe this is useful to you?

R

[phillip mobley]

Hello Ross,

Yes, I did not think about that! Sometimes, I try to do that with textbooks. I get lucky every once in awhile. Thank you for pointing this out. I can look a little more into the artickes.

Also, thanks for getting this one. I have been reading through it and there is a lot to digest. I am new to the computational science so there will be a bit of a learning curve which is fine. I have the time. In the spring, I my master's will upgrade to a PhD. So I have 4+ years to learn this. Please, for everyone, I apologize if I ask seemingly stupid questions! I am in the process of learning. I will try my best to tag all posts that I make so that others who may be new to computational science will be able to sift through these.

So, reading the article a bit, it looks like he accounted for the BEM within the systems of equations. He specifically states that "Equations (33), (46) and (47) form a coupled BEM–FEM system of equations with nodal unknowns of the motion map u, the electric potential and the electric flux qt. This system of equations is solved in this work by using the Newton–Raphson scheme"

Is this a correct understanding that I am to apply the BEM into the PDE that I need to solve then solve these using deal.II?