Radiation boundary conditions for acoustic and elastic wave calculations

Abstract

In situations where the computed solution approximates a steady solution which possesses a regular far field asymptotic expansion, coordinate transformations are a traditional and an effective way to eliminate the difficulties with computational boundaries. This is certainly the case for many of the steady state problems in transonic flow. On the other hand, when highly oscillatory transient solutions are computed or when the computed solution has an asymptotic expansion with essential singularities near infinity, coordinate mapping techniques are ineffective and alternate approaches must be developed for treating the computational boundaries. These circumstances are typical for most calculations in seismology and some of the calculations in unsteady transonic flow and meterology.

Non-reflecting regions for finite difference methods in modeling of elastic wave propagation in plates

“…Boundary Conditions --Absorbing boundary conditions for elastic waves have been developed by Clayton and Engquist [4], analyzed by Engquist and Majda [5], and improved by Higdon [7] who used the general absorbing boundary condition:…”

Transparent Boundary Conditions for Wave Propagation on Unbounded Domains

“…One class of conditions is given by local differential operators [2], [3], including conditions that perfectly annihilate impinging waves at a finite number of selected angles of incidence [4], whilst a different approach is based on absorbing layers [5]. There are cases, where some of the difficulties with boundary conditions may be avoided partially by using a momentum space approach [6].…”

On the stability analysis of boundary conditions for the wave equation by energy methods. I. The homogeneous case

“…The study of the stability of the wave equation associated with various boundary conditions has a very important practical interest if one thinks, for instance, of absorbing boundary conditions. In their second paper on the subject, Engquist and Majda [1] applied the theory of Kreiss to show the strong stability of their boundary conditions. More recently, Trefethen and Halpern [ 15] considered a completely general class of boundary conditions for the wave equation and, applying the Kreiss theory, obtained explicit necessary and sufficient criteria (concerning the coefficients of the differential operator appearing in the boundary condition) for the strong well-posedness of the corresponding initial boundary value problem.…”