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Title of Journal: J Eng Math

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Abbravation: Journal of Engineering Mathematics

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Springer Netherlands

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DOI

10.1007/s11368-014-1009-y

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1573-2703

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The analytic form of Green’s function in elliptic

Authors: Ioannis K Chatjigeorgiou Spyros A Mavrakos
Publish Date: 2011/03/22
Volume: 72, Issue: 1, Pages: 87-105
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Abstract

The purpose of this study is the derivation of a closedform formula for Green’s function in elliptic coordinates that could be used for achieving an analytic solution for the secondorder diffraction problem by elliptical cylinders subjected to monochromatic incident waves In fact Green’s function represents the solution of the socalled locked wave component of the secondorder velocity potential The mathematical analysis starts with a proper analytic formulation of the secondorder diffraction potential that results in the inhomogeneous Helmholtz equation The associated boundaryvalue problem is treated by applying Green’s theorem to obtain a closedform solution for Green’s function Green’s function is initially expressed in polar coordinates while its final elliptic form is produced through the proper employment of addition theorems

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