Point matching computation of transverse resonances

Point matching (collocation) methods are reviewed and the conditions under which they break down are examined. The detailed treatment applies to complex-valued solutions of the two-dimensional Helmholtz equation with either Neumann or Dirichlet boundary conditions. Point matching methods (when they are valid) can have very real computational advantages. It is shown, by a combination of analysis and computational example, how to estimate whether the cross-section of any particular resonant system is suitable for the application of an existing point matching method. An extended point matching method is introduced to handle cases for which previous methods fail. The method is illustrated with several computational examples. The discussion is specifically concerned with electromagnetic wave guides, but the results can be applied to a wide range of physical systems.

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