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P. Amodio, T. Levitina, G. Settanni, E. Weinmüller:
"Whispering gallery modes in oblate spheroidal cavities: calculations with a variable stepsize";
in: "ASC Report 37/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 4.

We propose an efficient and reliable technique to calculate highly localized Whispering Gallery Modes (WGMs)inside an oblate spheroidal cavity. The idea is to first separate variables in spheroidal coordinates and then to deal with two ODEs, related to the angular and radial coordinates solved using high order finite difference schemes. It turns out that, due to solution structure, the efficiency of the calculation is greatly enhanced by using variable stepsizes to better reflect the behaviour of the evaluated functions. We illustrate the approach by numerical experiments.

Multiparameter spectral problems; Prüfer angle; finite difference schemes; variable stepsize

http://www.asc.tuwien.ac.at/preprint/2014/asc37x2014.pdf