? solving outgoing Helmholtz eqn using fft

Cheng Cosine · science forum Guru Wannabe Joined: 26 May 2005 Posts: 168

Hi:

Given a Helmholtz eqn with constant coefficients, assuming solution in
negative

z-dir is neglegible, i.e., no reflecting wave in negative z-dir, one can
then use 2d FFT

in xy-plane to solve the eqn. What I don't understand are: 1) phys books
say this assumption

is equilvent to assume wave solution is a plane wave going in z-dir, but
don't quit see that

correlate to math eqn. Or say in this way, if a plnae wave goes only in
positive z-dir is equivalent

to neglect negative z-dir, then when applying the same argument applies to
x- and y-dir, one

can argue that wave still propogate in positive and negative x- and y-dir
since no simplifications

are made in those directions; 2) when one has some point sources in space,
can one still solve

Helmholtz eqn in this way? Or when one place a finite wall in space facing
positive z-dir and then

that wall has many point sources on it, can one still solve Helmholtz eqn in
this way? What if that

finite wall is curved?

Thanks,
by Cheng Cosine
Jun/15/2k6 NC

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