On the Engquist Majda absorbing boundary conditions for hyperbolic systems

Abstract

In their classical paper [2], the authors presented a methodology for the derivation of far field boundary conditions for the absorption of waves that are almost perpendicular to the boundary. In this paper we derive a general order absorbing boundary conditions of the type suggested by Engquist and Majda. The derivation utilizes a different methodology which is more general and simpler. This methodology is applied to the two and three dimensional wave equation, to the three dimensional Maxwell's equations and to the equations of advective acoustics in two dimensions.

The Work of David Gottlieb: A Success Story

“…The parameter ε must be kept small to keep the absorption of waves complete, while at the same time it must be large enough to keep the solution bounded. David had also an interesting article [14] together with Adi Ditkowski on the classical Engquist-Majda absorbing boundary conditions. They derived the same type of boundary conditions for the wave equation by using a different technique.…”

High‐order Higdon‐like boundary conditions for exterior transient wave problems

“…Thus, the Higdon NRBCs can be viewed as generalization of rationalapproximation NRBCs. See also the recent paper by Ditkowski and Gottlieb [36] on this subject.…”

A sequence of absorbing boundary conditions for Maxwell’s equations

“…The vanishing of B at s ¼ 0, which is recognized as a generalized eigenvalue of the problem, is found to imply that nonzero data at the outer boundary can lead to polynomial growth in the interior. Ditkowski and Gottlieb [16] construct an explicit example of this behavior for their form of the absorbing boundary conditions. However, in [18] Gustafsson also shows that implementing an integrated form of the boundary conditions can ameliorate the effect of the instability.…”

“…Recently, Ditkowski and Gottlieb [16] have derived a particularly simple form for the mth-order absorbing boundary condition for MaxwellÕs equations in terms of normal derivatives at the boundary. In our notation their result is ðo=ot þ o=oxÞ m p ¼ 0;…”