Non-Reflective Boundary Conditions for the Wave Equation

AI Thread Summary
The discussion centers on implementing non-reflective boundary conditions for numerical simulations of the 2-D wave equation. Participants suggest using Thompson-style boundary conditions, which are considered physically realistic, and discuss the issue of reflecting waves that can distort the solution. One participant recommends stretching the computational grid away from the area of interest to mitigate reflections, while another expresses the need to implement Perfectly Matched Layer (PML) boundary conditions for better performance on larger domains. There is a request for guidance on how to start coding PML, indicating a need for practical advice on implementation. Overall, the conversation highlights the challenges of managing boundary conditions in wave simulations and the desire for effective solutions.
NeoDevin
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I wasn't completely sure where to put this (programming or Diff.E.'s), so if there's a better place, maybe the mentors could move it for me.

I'm doing some numerical simulations involving the (2-D) wave equation, and was wondering if anyone could tell me (or give a reference to a paper which would tell me) how to implement a boundary condition which will prevent reflections?

For now I'm just doing a straightforward centered difference, I may implement a higher order method later, depending how much time I have.
 
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Anybody? Could we move this to the programming forum and try there?
THanks
 
What is the particular problem of interest, and why do you wish to use non-reflective BCs? I've typically used Thompson-style boundary conditions as they seem the most "physical." Are you having problems with reflecting waves growing and ruining the solution?

If so, you might just want to stretch the grid away from the area of interest. The old way of doing things is that if the waves don't make it to the boundary (by way of damping), then you don't have to worry about the boundaries ;).
 
minger said:
What is the particular problem of interest, and why do you wish to use non-reflective BCs? I've typically used Thompson-style boundary conditions as they seem the most "physical." Are you having problems with reflecting waves growing and ruining the solution?

If so, you might just want to stretch the grid away from the area of interest. The old way of doing things is that if the waves don't make it to the boundary (by way of damping), then you don't have to worry about the boundaries ;).

Yes, you are so right minger. I am also extending the computational domain as your idea...
However, since I need to compute on a large domain in a proper computed time, so I have to learn how to make my code better with PML boundary condition...

I've heard about PML, but it's not easy for me to implement it into my code...

Anyone can help us out? How should I start with coding PML?

Thank you so much !
 

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