finite differenc eproblem

Dear group!

I'm attempting to solve a reaction-diffusion type partial differential
equation by finite differences for a geometry that is composed from a
cylinder subscribing a sphere. The domain of interest is the volume
between the sphere and the cylinder, the latter having an infinite
extension. Naturally, my first thought was to use cylindrical
coordinates (with the sphere located at its origin), however, that
would require the implementation of an irregular boundary at the
sphere, where its normal derivative is given (Neumann boundary
conditions). Hence, I'm looking for some coordinate transformation that
would allow an easy implementation of the boundary condition. Could I
for example use instead of z, r, \theta,

R = \sqrt{ z^2 + r^2 }, r and \theta
( R = \sqrt{ x^2 + y^2 + z^2 }, r = \sqrt{ x^2 + y^2 } and \theta =
\tan^{-1}(y/x) )

with r running from 0 to R. Actually, I more than suspicious about
that.
Do you have any other ideas of how to implement this problem or
references to similar problems?

Thanks,
Daniel

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