Year: 2012
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 2 : pp. 157–176
Abstract
This paper is concerned with the reconstruction of the radiation wave field in the exterior of a bounded two- or three-dimensional domain from the knowledge of Cauchy data on a part of the boundary of the aforementioned domain. It is described by the Cauchy problem for the Helmholtz equation. By using the Dirichlet-to-Neumann map, this problem is transformed into an operator equation with compact operator. We rigorously justify the asymptotic behaviors of singular values of the compact operator. Then a projection method with regularization is applied to solve the operator equation, and the convergence of the regularization method is discussed. Finally, several numerical examples are presented to illustrate the approach. The results demonstrate that the algorithm is effective.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1109-m3491
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 2 : pp. 157–176
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Helmholtz equation Cauchy Problem Projection method Regularization.