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Anonymous
Closed Form Solution to the Wave Equation 2017-03-01 10:35:56 Post No. 8714321
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Closed Form Solution to the Wave Equation 2017-03-01 10:35:56 Post No. 8714321
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I've done some reading and it seems that while we have a solution to the 2D wave equation bounded by a rectangle, I can't find any information regarding closed solutions on different domains.
Do we have closed solutions for different geometries? Circles? Triangles? Something more exotic? I ask so that I can do propagation simulation without having to incur the numerical error that a time-domain finite difference method would yield.
Thanks you for any help.
https://en.wikipedia.org/wiki/Wave_equation
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Surely someone here has experience with this class of problem?
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>>8714528
Peepee poopoo
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>>8714321
IIRC we have them for circles, using Bessel functions. I'm not too sure about triangles. I doubt it, but you're better off looking for solutions through Google.
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>>8714321
Have you taken a Math Methods course before? If not I suggest picking up a book on this. I recall learning about vibrations on a drum >>8714528 but I can't really remember if there was a closed solution. I'd imagine that as long as there is enough symmetry in the boundary conditions, you would be able to use a familiar coordinate system and use some math tricks to find a solution.
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