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We study theoretical aspects of the Hagstrom-Warburton (H-W) ABC for time domain simulations of wave propagation on unbounded spatial domains. Here we investigate the H-W ABC applied to an artificial half-plane boundary, considering the basic models in wave propagation: the wave equation and first-order systems. The Hagstrom-Warburton formulation is an improved, equivalent version of the well known Higdon formulation. For the wave equation, much of the theory on the Higdon´s BC is well known, and here we collect results concerning well-posedness and convergence of such BCs. A main issue is how to minimize the error through optimal parameter selection. We present some theoretical results as well as computational tests addressing this problem. Concerning first-order systems, we present a general outline of the theory concerning well-posedness, convergence and parameter selection. When considering Maxwell´s equations, we were able to demonstrate strong well-posedness, convergence and some suggestive results on parameter selection.

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Manuela L. de Castro joined Universidade Federal do Rio Grande do Sul (Brazil) in 2005 as a Professor of Analysis, shortly after receiving her Doctor degree in Mathematics from the University of New Mexico. Her current research interests include Numerical Analysis, Differential Equations and Ecological Modelling.

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