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Signs of Intelligent Life

Over time, Slashdot has sunk to your standard level of Internet discussion, i.e.

One of the worst parts was Ask Slashdot, where the editor put up obvious questions where answers can be found on Google in 10 seconds, or obvious flaimbait questions designed more to raise comment counts (refer to Internet Arguments above) than to provide enlightenment. So my curiosity was piqued when someone asked how to numerically approximate the wave equation. It wasn't the standard-issue second-order partial differential equation either. The wave velocity ν was a function of position, and not necessarily smooth. There are irregular boundary conditions and no model-massaging so no assumptions about scale, either.

Of course, the question is still mental masturbation put forward to get someone else to do his research project for him. The real surprise was the number of helpful answers provided by different people. Who knew there were so many applied mathematicians and computational physicists lurking on Slashdot?

Seems like this is a pretty good summary of how to go about it.

• Green's function techniques (see, e.g. Martin et. al. for an accessible start point).
• Transfer matrix methods (see, e.g. Barns and Pendry)
• Discrete dipole scattering (see, e.g. Bruce Draine's DDSCAT)
• Multiple multipole methods (see, e.g. C. Hafner)
• Finite Difference Time Domain (e.g. see the excellent MEEP from MIT)
• Basis expansions and stratified media (similar to transfer matrix) see. Chew for details

Well, there you go, then.