Asymptotic Boundary Conditions for Dissipative Waves: General Theory

An outstanding issue in the computational analysis of time-dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. In this work we develop accurate conditions based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descent, we identify dominant wave groups and consider simple approximations to the dispersion relation in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.