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We discuss new approaches to compute numerically the Casimir interactionenergy for waveguides of arbitrary section, based on the boundary methodstraditionally used to compute eigenvalues of the 2D Helmholtz equation. Thesemethods are combined with the Cauchy's theorem in order to perform the sum overmodes. As an illustration, we describe a point-matching technique to computethe vacuum energy for waveguides containing media with differentpermittivities. We present explicit numerical evaluations for perfectconducting surfaces in the case of concentric corrugated cylinders and acircular cylinder inside an elliptic one.

Using boundary methods to compute the Casimir energy