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Complete radiation boundary conditions for the Helmholtz equation. I: Waveguides. (English) Zbl 1412.65187

Summary: We consider the use of complete radiation boundary conditions for the solution of the Helmholtz equation in waveguides. A general analysis of well-posedness, convergence, and finite element approximation is given. In addition, methods for the optimization of the boundary condition parameters are considered. The theoretical results are illustrated by some simple numerical experiments.

MSC:

65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A50 Antennas, waveguides in optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory

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