Non-Reflective Boundary Conditions for the Wave Equation

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Discussion Overview

The discussion revolves around implementing non-reflective boundary conditions for the 2-D wave equation in numerical simulations. Participants explore various approaches to prevent reflections that can distort the results of their simulations, including the use of Perfectly Matched Layer (PML) boundary conditions and other techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about implementing boundary conditions that prevent reflections in their numerical simulations of the wave equation.
  • Another participant suggests using Thompson-style boundary conditions, citing their physical relevance, and questions whether the original poster is experiencing issues with reflecting waves.
  • A participant proposes stretching the computational grid away from the area of interest as a potential solution to mitigate reflection issues.
  • One participant expresses interest in learning how to implement PML boundary conditions, noting difficulties in coding it into their simulation.

Areas of Agreement / Disagreement

There is no consensus on the best approach to implement non-reflective boundary conditions, as participants suggest different methods and express varying levels of familiarity with these techniques.

Contextual Notes

Participants mention limitations related to computational domain size and the challenges of implementing specific boundary conditions like PML, indicating a need for further exploration and clarification of these methods.

Who May Find This Useful

This discussion may be useful for researchers and practitioners involved in numerical simulations of wave phenomena, particularly those interested in boundary condition implementation and computational methods in physics and engineering.

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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