Radiation boundary conditions for wave‐like equations

Abstract

In the numerical computation of hyperbolic equations it is not practical to use infinite domains. Instead, one truncates the domain with an artificial boundary. In this study we construct a sequence of radiating boundary conditions for wave-like equations. We prove that as the artificial boundary is moved to infinity the solution approaches the solution of the infinite domain as O(r-"'-"2) for the m-th boundary condition. Numerical experiments with problems in jet acoustics verify the practical nature and utility of the boundary conditions.

An optimized Schwarz method with two‐sided Robin transmission conditions for the Helmholtz equation

“…The parameters s j are complex numbers and correspond to approximations of the radiation condition, of the form −iω + a j , a j > 0, see [3]. The other parameters s 12 and s 21 will be used to optimize the performance of the algorithm.…”

A multiple scales approach to sound generation by vibrating bodies

“…For example, the rather simple form of our final results allows us to express the far field behavior of the waves in a concise form. This expression, when used with some of the ideas of Bayliss and Turkel (1980), for example, may allow us to derive the required boundary conditions. Investigations along these lines are continuing.…”

Perturbation Method for the Calculation of Losses Inside Conductors in Microwave Structures

“…The constants α and β are related to the second order radiation conditions set on the boundary C of the disk that partially defines ∂Ω 2 (remember that the core of the plate is not described because of the skin effect); these constants depend on the radius of the disk and on the wavenumber k 0 [14]. τ is the unit tangent on C .…”