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jackhamel16 / Acoustics

Acoustic integral equation solver
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Add frequency derivative of scattering matrix #57

Closed jackhamel16 closed 3 years ago

jackhamel16 commented 3 years ago

Follow derivations in write up.

Test by approximating derivative with finite difference

jackhamel16 commented 3 years ago

There was a slight hold up in the final expression for computing the scattering matrix. It relies on trans(Vs) * inv(Z) = trans(Js) which is only true when Z is symmetric. Z is symmetric only when doing full galerkin (i.e. same bases and quadrature rules for test and source integrals). Even though Z isn't perfectly symmetric under full Galerkin (maybe just due to numerical error?) we can assume the relation above is true because the derivative of the S matrix is about just as accurate under that assumption as when not. So in the end, we can assume Z is symmetric under full galerkin testing.

jackhamel16 commented 3 years ago

All is added but I am going to quickly code in the direct and indirect ways of computing the WS matrix, Q, as an additional check.