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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2013, Volume 16, Number 1, Pages 39–44 (Mi sjvm496)  
This article is cited in 9 scientific papers (total in 9 papers)

A numerical method for solving inverse thermoacoustic problem

S. I. Kabanikhinab, O. I. Krivorotkob, M. A. Shishleninc

a Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (508 kB) Citations (9)
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Abstract: In this paper, we consider the inverse problem of determining the initial condition of the initial boundary value problem for the wave equation with additional information about solving the direct initial boundary value problem that is measured at the boundary of the domain. The main objective of our research is to construct a numerical algorithm for solving the inverse problem based on the method of simple iteration (MSI) and to study the resolution of the inverse problem and its dependence on the number and location of measurement points. We consider three two-dimensional inverse problems. The results of numerical calculations are presented. We show that the MSI for each iteration step reduces the value of the object functional. However, due to the ill-posedness of an inverse problem the difference between the exact and the approximate solutions of the inverse problem decreases up to some fixed number kmin and then monotonically increases. This reflects the regularizing properties of the MSI, in which the iteration number is a regularization parameter.
Key words: thermoacoustic problem, inverse and ill-posed problems, wave equation, method of simple iteration.
Received: 06.10.2011
English version:
Numerical Analysis and Applications, 2013, Volume 6, Issue 1, Pages 34–39
DOI: https://doi.org/10.1134/S1995423913010047
Bibliographic databases:
Document Type: Article
UDC: 519.6+519.711.3
Language: Russian
Citation: S. I. Kabanikhin, O. I. Krivorotko, M. A. Shishlenin, “A numerical method for solving inverse thermoacoustic problem”, Sib. Zh. Vychisl. Mat., 16:1 (2013), 39–44; Num. Anal. Appl., 6:1 (2013), 34–39
Citation in format AMSBIB
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\pages 39--44
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\jour Num. Anal. Appl.
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  • https://www.mathnet.ru/eng/sjvm/v16/i1/p39
    • This publication is cited in the following 9 articles:
    1. H.K. Al-Mahdawi, Farah Hatem Khorsheed, Ali Subhi Alhumaima, Ali J. Ramadhan, Kilan M Hussien, Hussein Alkattan, N. Aldahan, A.J. Ramadhan, “Intelligent Particle Swarm Optimization Method for Parameter Selecting in Regularization Method for Integral Equation”, BIO Web Conf., 97 (2024), 00039  crossref
    2. Liyan Zhu, Yue Cui, Yanxia Du, Dong Wei, Youjun Deng, “Research on the multi-parameter identification of thermal-acoustic-solid coupling problem in an inhomogeneous medium”, Journal of Mathematical Analysis and Applications, 521:2 (2023), 126920  crossref
    3. Salam Abdulkhaleq Noaman, H.K. Al-Mahdawi, Bashar Talib Al-Nuaimi, A.I. Sidikova, “Iterative method for solving linear operator equation of the first kind”, MethodsX, 10 (2023), 102210  crossref
    4. Bashar Talib Al-Nuaimi, H.K. Al-Mahdawi, Zainalabideen Albadran, Hussein Alkattan, Mostafa Abotaleb, El-Sayed M. El-kenawy, “Solving of the Inverse Boundary Value Problem for the Heat Conduction Equation in Two Intervals of Time”, Algorithms, 16:1 (2023), 33  crossref
    5. Hassan K. Ibrahim Al-Mahdawi, Hussein Alkattan, Mostafa Abotaleb, Ammar Kadi, El-Sayed M. El-kenawy, “Updating the Landweber Iteration Method for Solving Inverse Problems”, Mathematics, 10:15 (2022), 2798  crossref
    6. H.K. Al-Mahdawi, A. I Sidikova, Hussein Alkattan, Mostafa Abotaleb, Ammar Kadi, El-Sayed M El-kenawy, “Parallel multigrid method for solving inverse problems”, MethodsX, 9 (2022), 101887  crossref
    7. Hassan K. Ibrahim Al-Mahdawi, Mostafa Abotaleb, Hussein Alkattan, Al-Mahdawi Zena Tareq, Amr Badr, Ammar Kadi, “Multigrid Method for Solving Inverse Problems for Heat Equation”, Mathematics, 10:15 (2022), 2802  crossref
    8. Bektemessov Maktagali, Temirbekova Laura, “Discretization of equations Gelfand-Levitan-Krein and regularization algorithms”, J. Phys.: Conf. Ser., 2092:1 (2021), 012015  crossref
    9. Aleksei Prikhodko, Maxim Shishlenin, “Comparative analysis of the numerical methods for 3D continuation problem for parabolic equation with data on the part of the boundary”, J. Phys.: Conf. Ser., 2092:1 (2021), 012010  crossref
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