A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation-Reference-Cited by-同舟云学术

A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation

Published:2012 Issue: Volume:2012 Page:1-13
ISSN:1024-123X
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Gao Jinghuai¹,Wang Dehua¹,Peng Jigen²

Affiliation:

1. Institute of Wave and Information, National Engineering Laboratory for Offshore Oil Exploration, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Abstract

An inverse source problem in the modified Helmholtz equation is considered. We give a Tikhonov-type regularization method and set up a theoretical frame to analyze the convergence of such method. A priori and a posteriori choice rules to find the regularization parameter are given. Numerical tests are presented to illustrate the effectiveness and stability of our proposed method.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2012/878109.pdf

Reference31 articles.

1. An Integral Equation Approach to the Incompressible Navier--Stokes Equations in Two Dimensions

2. Recovery of cracks using a point-source reciprocity gap function

3. Identification of planar cracks by complete overdetermined data: inversion formulae