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Perfectly Matched Layer for a Standard Wave Equation

version 1.0.1 (396 KB) by oreoman
Absorbing boundary conditions, not for solving Maxwell's Equations, but for a standard wave equation, e.g. for use with potentials.

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Updated 30 Jun 2020

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How do you add decent absorbing boundary conditions so that you can pretend you're simulating real electromagnetic phenomenon except inside of a computer? How do you do this when you're not solving Maxwell's equations, but wave equations for potentials and not fields? Well look no further: this does just that by using a, "standard," analytic continuation of spatial coordinates into the complex domain, and then discretized and solved using a few different techniques:

1. A fully explicit finite difference method using first order equations via an auxiliary differential equation,
2. A fully explicit finite difference method using second order equations,
3. A semi-implicit finite difference method using first order equations via an auxiliary differential equation.

The nice thing about these methods is that the exact same files should work exactly the same in 3D (albeit quite slow and memory intensive) because MATLAB is rad like that. The included PDF discusses some of the theory behind this work, with a very good reference to start with being:

http://math.mit.edu/~stevenj/18.369/pml.pdf

With the exception of setupPML.m each of these files is a standalone file that you should be able to run to see how things play out for a standard oscillating source charge distribution.

Cite As

oreoman (2020). Perfectly Matched Layer for a Standard Wave Equation (https://github.com/michael-nix/MATLAB-Perfectly-Matched-Layer), GitHub. Retrieved .

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Updates

1.0.1

Fixed some typos.

MATLAB Release Compatibility
Created with R2020a
Compatible with any release
Platform Compatibility
Windows macOS Linux
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