Wave equation in temporal domain

[Alexander Kiselyov]

Dear deal.II users and developers,

I'm trying to solve inhomogeneous Maxwellian equations in 4-potential
form in 3D space. In terms of math it is equivalent to solving a system
of 4 independent scalar wave equations. I'm using "free space" b/c of
Neumann type, calculated via solving an integral boundary problem. The
initial state is stationary (i.e. no external wave sources), so the
"input data" are RHS functions. The EM spectrum is assumed to be quite
wide, so, in contrast to the usual approach to Maxwellian equations,
the problem is solved in the temporal domain.

This approach produces artifacts of wave reflection from the
computational domain borders. It seems that to combat the issue some
kind of PML or ABC has to be introduced, which are commonly formulated
in frequency domain.

What literature would you suggest that deals with PML-like boundaries
specifically in the temporal domain?

Best regards,
Alexander

[Wolfgang Bangerth]

I don't actually have much experience with PML-type boundary conditions
myself, but there are quite a number of papers on the topic:
https://scholar.google.com/scholar?hl=en&as_sdt=0%2C6&q=perfectly+matched+layer+time+domain&btnG=

There are of course also absorbing boundary conditions for time-domain
problems. These range for relatively simple "impedance" conditions that relate
Dirichlet to Neumann values (i.e., they are of Robin type) to much more
complex ones like those you can find in the works of Marcus Grote, Joe Keller,
and Tom Hagstrom.

Best
W.

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

[Alexander Kiselyov]

Thank you very much for the answer, Wolfgang! I'll try to search for
more literature on the topic.

Best regards,
Alexander