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manpreet Best Answer 3 years ago

If I wanted to figure out how to do a simulation with the Helmholtz equation, how would I do it? Or, what kinds of techniques would I have to learn in order to figure it out?

Background: 1st year Aero Engineering student (this isn't on our syllabus, just general interest)

Thanks!

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manpreet 3 years ago

One way to solve the Helmholtz equation rather directly in free space (i.e. the wave speed is constant) is to use a double or single layer potential. So we have

Δ u + k 2 u = 0 in R 3

For example, given a smooth boundary $\partial D \subset R^{3}$ and a function $ϕ \in L^{2} (\partial D)$ , let

D ϕ (x) : = \int \partial D ϕ (y) \partial Φ ( x , y ) \partial ν y d S y

where

Φ (x, y) = \frac{e^{i k | x - y |}}{4 π | x - y |}

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Solving the Helmholtz equation

Manpreet Singh

Answers (2)

manpreet Best Answer 3 years ago

manpreet 3 years ago

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