Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation-Reference-Cited by-同舟云学术

Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation

Published:2014 Issue: Volume:2014 Page:1-7
ISSN:1110-757X
Container-title:Journal of Applied Mathematics
language:en
Short-container-title:Journal of Applied Mathematics

Author:

Kabanikhin Sergey Igorevich¹²,Shishlenin M. A.²³,Nurseitov D. B.⁴,Nurseitova A. T.⁵,Kasenov S. E.⁴

Affiliation:

1. Institute of Computational Mathematics and Mathematical Geophysics, Akademika Lavrentjeva, No. 6, Novosibirsk 630090, Russia

2. Novosibirsk State University, Pirogova Street 2, Novosibirsk 630090, Russia

3. Sobolev Institute of Mathematics, 4 Academy Koptyug Avenue, Novosibirsk 630090, Russia

4. National Open Research Laboratory of Information and Space Technologies, Kazakh National Technical University after K.I. Satpaev, Seifullin Street 122/22, Almaty 050013, Kazakhstan

5. Kazakh National Pedagogical University Abai, 13 Dostyk Avenue, Almaty 050010, Kazakhstan

Abstract

We consider an ill-posed initial boundary value problem for the Helmholtz equation. This problem is reduced to the inverse continuation problem for the Helmholtz equation. We prove the well-posedness of the direct problem and obtain a stability estimate of its solution. We solve numerically the inverse problem using the Tikhonov regularization, Godunov approach, and the Landweber iteration. Comparative analysis of these methods is presented.

Funder

Ministry of Education and Science of the Russian Federation

Publisher

Hindawi Limited

Subject

Applied Mathematics

Link

http://downloads.hindawi.com/journals/jam/2014/786326.pdf

Reference23 articles.

1. The Detection of the Source of Acoustical Noise in Two Dimensions

2. The detection of surface vibrations from interior acoustical pressure

3. A boundary element investigation of irregular frequencies in electromagnetic scattering