Asymptotic Radiation Conditions for Reduced Wave Equation

Abstract

In this note the exact non-local radiation condition and its local approximations at finite artificial boundary for the exterior boundary value problem of the reduced wave equation in 2 and 3 dimensions are discussed. Based on the asymptotic expansion of Hankel functions for large arguments, an approach for the construction of local approximations is suggested and gives expression of the normal derivative at spherical artificial boundary in terms of linear combination of Laplace-Beltrami operator and its iterates, i.e. tangential derivatives of even order exclusively. The resulting formalism is compatible with the usual variational principle and the finite element methodology and thus seems to be convenient in practical implementation.