Finite part representations of hypersingular integral equation of acoustic scattering and radiation by open smooth surfaces
type: Item
instance of: scholarly article
title: Finite part representations of hypersingular integral equation of acoustic scattering and radiation by open smooth surfaces
zbMATH Open document ID: 0862.45004
DOI: 10.1007/BF02867435
author: Sujit K. Bose
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1997-05-25T00:00:00Z
review text: The use of the Green function method for the solution of the Helmholtz equation for both acoustic scattering by hard surfaces or radiation by vibrating surfaces is shown to lead to hypersingular surface boundary integral equations. For a general open surface a simple proof is given that the integral term should be interpreted as the Hadamard finite part of a divergent integral in one variable. The problem is reformulated as a Cauchy principal value integral equation which also contains the potential at the control point. This is then amenable to numerial treatment by conventional methods. An alternative formulation is given in the better known form containing the tangential derivative of the potential. The simpler two-dimensional problem for an open arc is treated separately.
reviewed by: D. Kershaw
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45H05
Mathematics Subject Classification ID: 76Q05
zbMATH DE Number: 955210
zbMATH Keywords: Green function method
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: acoustic scattering
zbMATH Keywords: radiation
zbMATH Keywords: hypersingular surface boundary integral equations
zbMATH Keywords: Hadamard finite part of a divergent integral
zbMATH Keywords: Cauchy principal value integral equation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 955210