Far-Field Filtering Operators for Suppression of Reflection From Artificial Boundaries

Abstract

The concern of this paper is the treatment of far-field artificial boundaries for first order hyperbolic systems, where the aim is to suppress nonphysical reflections of outgoing waves. We construct far-field filtering operators of two types: (1) slowing-down operators and (2) damping operators. The operators are activated in anarrow sponge layer near the far-field boundary and have the following properties: (a) the operators act only on the outgoing part of the solution leaving the incoming part unharmed, (b) the passage of waves across the modified layer is reflection-free, and (c) the implementation of the operators amounts to a small modification of the governing equations in the far-field. In either case, the treatment of the boundary itself is greatly simplified, since the outgoing waves either do not reach the boundary or have practically zero strength when they do. Well-posedness of the modified equations and stability of the discretization scheme are established. We also show that such reflection-free operators do not exist for the second order scalar wave equation. Numerical results in one and two space dimensions are shown.