Method of integral equations in the scalar problem of diffraction on a system consisting of a ``soft'' and a ``hard'' screen and an inhomogeneous body
type: Item
instance of: scholarly article
title: Method of integral equations in the scalar problem of diffraction on a system consisting of a ``soft'' and a ``hard'' screen and an inhomogeneous body
zbMATH Open document ID: 1312.65203
DOI: 10.1134/S0012266114090031
author: Yong-Cai Geng
author: Sumit K. Garg
published in: Differential Equations
publication date: 2015-01-15T00:00:00Z
review text: The authors study the scalar problem on the diffraction of a plane wave on a system that consists of a ``soft'' and a ``hard'' screen and a solid inhomogeneous body. The boundary value problem consists of the Helmholtz equation with Dirichlet, respectively Neumann conditions on the surfaces of the screens and transmission conditions on the boundary of the body. The differential statement of the problem is reduced to an equivalent system of singular integral equations over the body domain and the screen surfaces. The solvability of the system of integral equations in Sobolev spaces and the smoothness of the solutions are demonstrated. Approximate solutions of the system of integral equations are found by the Bubnov-Galerkin method. Piecewise constant basis functions in the body domain and on the ``soft'' screen surface and piecewise linear basis functions on the ``hard'' screen are used. The consistency property and the convergence theorem for the numerical method are proved.
reviewed by: Adrian Carabineanu
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 6386867
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: singular integral equations
zbMATH Keywords: existence and smoothness of solution
zbMATH Keywords: Galerkin method
zbMATH Keywords: integral equation method
zbMATH Keywords: diffraction
zbMATH Keywords: consistency
zbMATH Keywords: convergence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6386867