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Neumann boundary value problem for the Helmholtz equation: 2D arbitrary boundary

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posted on 28.03.2022, 13:00 authored by Cheong Ho Seng
This thesis is aimed at presenting the mathematically rigorous analytical-numerical method for solving the Neumann boundary-value problem for Helmholtz equation. It is consistently realised that the idea of analytical regularisation of ill-conditioned integral, integral-dierential and series equations of the first kind resulted in the efficient technique and numerical algorithm which allows accurate numerical solution. the presented regularisation technique is successfully used studies of two-dimensional wave scattering by closed and unclosed screens. The thesis concentrates on the screens in the form of infinitely long cylinders with circular and arbitrary cross sections. When the boundary of the cross section is opened (or unclosed) we get a slotted cylinder.


Table of Contents

1. Introduction -- 2. Preliminaries -- 3. The Neumann BVP for a circular cylinder -- The Neumann BVP for an open cylinder of arbitrary profile -- 5. The analytical regularisation of the solution.


Empirical thesis. Bibliography: pages 51-52

Awarding Institution

Macquarie University

Degree Type

Thesis MRes


MRes, Macquarie University, Faculty of Science and Engineering, Department of Mathematics

Department, Centre or School

Department of Mathematics

Year of Award


Principal Supervisor

Elena Vynogradova


Copyright Cheong Ho Seng 2014. Copyright disclaimer: http://www.copyright.mq.edu.au




1 online resource (viii, 52 pages)

Former Identifiers

mq:42181 http://hdl.handle.net/1959.14/1051152