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

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

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 a...

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Main Authors: Jinghuai Gao, Dehua Wang, Jigen Peng
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2012/878109
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spelling doaj-ffa6f93d41d744ccbfe30243942fd8d52020-11-24T22:56:07ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472012-01-01201210.1155/2012/878109878109A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz EquationJinghuai Gao0Dehua Wang1Jigen Peng2Institute 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, ChinaInstitute 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, ChinaSchool of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, ChinaAn 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.http://dx.doi.org/10.1155/2012/878109
collection DOAJ
language English
format Article
sources DOAJ
author Jinghuai Gao
Dehua Wang
Jigen Peng
spellingShingle Jinghuai Gao
Dehua Wang
Jigen Peng
A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation
Mathematical Problems in Engineering
author_facet Jinghuai Gao
Dehua Wang
Jigen Peng
author_sort Jinghuai Gao
title A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation
title_short A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation
title_full A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation
title_fullStr A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation
title_full_unstemmed A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation
title_sort tikhonov-type regularization method for identifying the unknown source in the modified helmholtz equation
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2012-01-01
description 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.
url http://dx.doi.org/10.1155/2012/878109
work_keys_str_mv AT jinghuaigao atikhonovtyperegularizationmethodforidentifyingtheunknownsourceinthemodifiedhelmholtzequation
AT dehuawang atikhonovtyperegularizationmethodforidentifyingtheunknownsourceinthemodifiedhelmholtzequation
AT jigenpeng atikhonovtyperegularizationmethodforidentifyingtheunknownsourceinthemodifiedhelmholtzequation
AT jinghuaigao tikhonovtyperegularizationmethodforidentifyingtheunknownsourceinthemodifiedhelmholtzequation
AT dehuawang tikhonovtyperegularizationmethodforidentifyingtheunknownsourceinthemodifiedhelmholtzequation
AT jigenpeng tikhonovtyperegularizationmethodforidentifyingtheunknownsourceinthemodifiedhelmholtzequation
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