Bayliss–Turkel-like Radiation Conditions on Surfaces of Arbitrary Shape

Abstract

This paper addresses the extension of the Bayliss᎐Turkel second-order radiation condition to an arbitrarily shaped surface. The derivation is based mainly on the pseudo-differential calculus as well as on the introduction of a criterion providing a precise handling of the approximation process involved in the derivation of the radiation condition. The radiation condition then ranges among the most accurate of those of order two. As a by-product of the derivation, almost all known radiation conditions of order less than or equal to two are recovered and their respective accuracies are compared. ᮊ 1999 Academic Press

Stability estimates for a class of Helmholtz problems

“…Examples of pairs for (α, β) include (0, k) for the so-called Sommerfeld condition and, in two dimensions, the pair (ζ(x)/2, k) for the first order generalized Bayliss-GunzburgerTurkel condition [1,2], where ζ is the curvature on Γ r . Finally, we recall the existence result:…”

Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation

“…(τ 1 , τ 2 ) is an orthonormal basis of the tangent plane) and such that τ j is an eigenvector of the curvature tensor. Then, it can be shown (see for instance [7]) that in this principal basis, the Helmholtz equation reads…”

“…These formulations can be generalized as follows [6]. Let us assume that the exact Dirichlet-Neumann (DN) map Λ ex given by [7] Λ ex :…”

Hybrid Spectral Difference Methods for Elliptic Equations on Exterior Domains with the Discrete Radial Absorbing Boundary Condition

“…The subdomain 2 is a thin layer boundary region with single or double layers, on which the polar coordinate system is used. The width of the boundary layer region is of size h, the maximum diameter of a partition of 1 . Since our ABC is constructed based on the multipole expansion of a solution the layer boundary region with the polar coordinate and radial grid can be more efficient for implementing high order ABCs.…”

“…In 1 ∪ 2 the equation (1.1) can be reformulated as follows with a proper ABC: 12 is a polygon, and it is designed to change according to the mesh refinement in 1 . As a mesh becomes finer 12 converges to a circle.…”