Method of interior boundaries for the impedance problem in scattering theory.
type: Item
instance of: scholarly article
title: Method of interior boundaries for the impedance problem in scattering theory.
zbMATH Open document ID: 1055.35034
DOI: 10.1016/S0096-3003(01)00320-4
author: P. A. Krutitskii
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The author proposes yet another scheme for obtaining a solution \(W\) to the third boundary value problem for Helmholtz' equation in an exterior domain \(D := \mathbb R^m \setminus \overline{{\bigcup_n}\Omega_n}\) , \(\Omega_n\) (bounded domains) \(\subset \mathbb R^m\) : Extend \(W\) by solutions \(u_n\) of Helmholtz' equation in \(\Omega_n \setminus B_n,\) \(B_n := B(x_n,\rho)\) subject to the boundary conditions \(u_n = W\) on \(\partial \Omega_n\) and \(\frac{\partial}{\partial n} u_n - i \cdot u_n = 0\) on \(\partial B_n\). The extended solution may then be found by solving an integral equation.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 1861332
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: exterior boundary value problem
reviewed by: Norbert Weck
MaRDI profile type: Publication
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full work available at URL: s0096-3003(01)00320-4
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description: scientific article; zbMATH DE number 1861332