On an approximate solution of a class of boundary integral equations of the first kind
type: Item
instance of: scholarly article
title: On an approximate solution of a class of boundary integral equations of the first kind
zbMATH Open document ID: 1359.65279
DOI: 10.1134/S0012266116090147
author: Elnur H. Khalilov
published in: Differential Equations
publication date: 2017-02-07T00:00:00Z
review text: The paper proposes a collocation-like method for solving the first kind boundary integral equation associated with the Dirichlet problem for the Helmholtz equation in \(\mathbb R^3\). The method is based on the representation of the inverse of the single layer operator as the product of two inverses of second kind Fredholm integral operators and the corresponding hypersingular integral operator. Then an approximate solution can be obtained by applying a cubature of the hypersingular operator to the right hand side and the approximate solution of two Fredholm integral equations of the second kind. The author discusses cubature formulas for the double layer potential and the hypersingular integral on closed smooth surfaces, which leads to error estimates of the method.
reviewed by: Gunther Schmidt
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 6681164
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: first kind boundary integral equation
zbMATH Keywords: cubature estimates
zbMATH Keywords: collocation
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: second kind Fredholm integral operators
zbMATH Keywords: hypersingular integral operator
zbMATH Keywords: error estimates
MaRDI profile type: Publication
cites work: Q3672341
cites work: Numerical Solution of an Exterior Neumann Problem Using a Double Layer Potential
cites work: Curved finite element methods for the solution of singular integral equations on surfaces in \(R^3\)
cites work: A finite element method for some integral equations of the first kind
cites work: Potential-based numerical solution of Dirichlet problems for the Helmholtz equation
cites work: Some properties of the operators generated by a derivative of the acoustic double layer potential
cites work: Q3463935
cites work: Q3964940
cites work: Cubic formula for class of weakly singular surface integrals
description: scientific article; zbMATH DE number 6681164