Abstract
Wave propagation problems with radiation boundary conditions are non‐hermitian and therefore typically cannot be solved by expanding in terms of eigenfunctions that correspond to real eigenvalues. We present a method for solving such problems entirely in terms of a superposition of normal modes, using the "shifted eigenvalue" method outlined by Lanczos. In effect, the desired system with an outgoing radiation boundary condition is coupled to a system which is identical, but has an incoming radiation boundary condition. The combined system is hermitian, and thus has real eigenvalues. We present numerical computations for a one‐dimensional, semi‐infinite, homogeneous continuum.
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