An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions
type: Item
instance of: scholarly article
title: An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions
zbMATH Open document ID: 1180.35545
author: B. Tomas Johansson
author: R. S. Chapko
published in: Inverse Problems and Imaging
publication date: 2008-11-06T00:00:00Z
review text: The authors extend the alternating method to the Cauchy problem for the Laplace equation in semi-infinite regions, that is the region is the intersection between a half-plane and the exterior of a bounded closed curved contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim of the authors is to construct the solution on the boundary of the inclusion. The authors describe the well-posedness of the corresponding mixed problems using a boundary integral equations method and present convergence of the alternating procedure. Moreover, they show how to solve the mixed problems numerically and how to discretize the suitable boundary integrals. The approach of the authors involves Green's function techniques and numerical schemes for the calculations of integrals on the real line with various singularities, and can easily be adjusted to the three-dimensional case. Finally, the reconstruction of the solution on the inclusion boundary is accurately found in the case of exact data. In the case of noisy data, the authors employ a discrepancy principle to stop the iteration.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35R25
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 5362899
zbMATH Keywords: Laplace equation
zbMATH Keywords: Cauchy problem
zbMATH Keywords: semi-infinite region
zbMATH Keywords: alternating method
zbMATH Keywords: Green's functions
zbMATH Keywords: integral equation of the first kind
zbMATH Keywords: quadrature method
zbMATH Keywords: trigonometric- and sinc- quadrature rules
MaRDI profile type: Publication
full work available at URL: ipi.2008.2.317
OpenAlex ID: W1994254061
DOI: 10.3934/IPI.2008.2.317
description: scientific article; zbMATH DE number 5362899