🚀 go-pugleaf

Hi,
   I am attempting to solve the electromagnetic vector wave equation in an 
optical fibre using a finite difference technique. The problem reduces to
an eigenvalue problem with analytic representation thus:

1-d^2/dy^2   d^2/dxdy           -id/dx           e_x

d^2/dxdy     1-d^2/dx^2         -id/dy           e_y  = W^2 n^2 E

-id/dx         -id/dy     -(d^2/dx^2 + d^2/dy^2) e_z


Where on the LHS I have explicitly shown the field components. n^2 is the
inhomogenous, lossy, anisotropic permitivity distribution.

These equations are then scaled using a non-linear scaling functions:
x = f(rho), y = g(xi) where, in general, f and g are the same.
I map all of the real plane onto the square (-.5, .5) x (-.5,.5).

I then make numerical replacements for all the derivatives leading to a 
large sparse algebraic eigenvalue problem. It turns out that the eigenvalues
I need are 1/3 of the way up from the bottom of the spectrum (this is not
a problem - I can successfully pull out eigenvalues).

The problem is as follows: On any mesh that includes the origin (even mesh) the 
eigenfunctions I obtain have ripples at the mesh period on them. On any
mesh that doesn't include the origin (odd mesh) there is no ripple on the
eigenfunctions. Any tests I do indicate that the differential operator has
been discretized correctly (e.g. supply known functions, apply operator and
compare with known analytic result). Can anyone think of a test that
will home in on this problem? seen it before? Anything?

Email is preferable because I'll probably  have to supply more detail.

Thanks in advance,
	Glenn

--
___________________________________________________________________________
Glenn Geers                       | "So when it's over, 
                                  |  we're back to people.
Department of Theoretical Physics |  Just to prove that human touch
The University of Sydney          |  can have no equal."
Sydney NSW 2006 Australia         |  - Basia Trzetrzelewska, 'Prime Time TV'
                                  |
Phone: +61 2 692-3241 (voice)     |_________________________________________
       +61 2 660-2903 (fax)       |
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glenn@physics.su.oz.au            | #include <standard_disclaimer.h>
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