Dirichlet-to-Neumann boundary condition for time-dependent dispersive waves in three-dimensional guides
type: Item
instance of: scholarly article
title: Dirichlet-to-Neumann boundary condition for time-dependent dispersive waves in three-dimensional guides
zbMATH Open document ID: 1061.78006
author: Dan Givoli
author: Igor Patlashenko
published in: Journal of Computational Physics
publication date: 2004-10-01T00:00:00Z
review text: The dispersive Klein-Gordon equation is considered in a three-dimensional semi-infinite cylindrical domain (in a waveguide). The dependence between the boundary values of solutions and their normal derivatives on the cross-section of a waveguide is derived, this dependence is called as Dirichlet-to-Neumann (DtN) boundary condition. The DtN boundary condition is nonlocal in space but is local in time. An arbitrary unbounded part of the waveguide can be truncated and replaced by the DtN condition on the auxiliary artifical section. Thus, the boundary value problem in semi-infinite domain is reduced to the problem in the bounded domain which contains all irregularities of the waveguide. The truncated condition is incorporated in a finite element scheme to solve the problem in the finite domain. The complete set of semi-discrete equations is described. Some numerical examples are given and discussed.
reviewed by: Nikolai Pleshchinskii
Mathematics Subject Classification ID: 78A50
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 65M60
zbMATH DE Number: 2104500
zbMATH Keywords: waveguide
zbMATH Keywords: dispersion
zbMATH Keywords: artificial boundary
zbMATH Keywords: Dirichlet and Neumann condition
zbMATH Keywords: finite elements
zbMATH Keywords: Klein-Gordon equation
MaRDI profile type: Publication
full work available at URL: j.jcp.2004.02.011
OpenAlex ID: W2019135187
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DOI: 10.1016/J.JCP.2004.02.011
description: scientific article; zbMATH DE number 2104500