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Original Articles

A Dual Reciprocity Boundary Element Method for the Regularized Numerical Solution of the Inverse Source Problem Associated to the Poisson Equation

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Pages 123-139 | Published online: 18 Oct 2010

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Dinh Nho Hào, Le Thi Thu Giang & Nguyen Thi Ngoc Oanh. (2022) Determination of the right-hand side in elliptic equations. Optimization 0:0, pages 1-33.
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Jin Wen, Li-Ming Huang & Zhuan-Xia Liu. (2021) A modified quasi-reversibility method for inverse source problem of Poisson equation. Inverse Problems in Science and Engineering 29:12, pages 2098-2109.
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Michael Hinze, Bernd Hofmann & Tran Nhan Tam Quyen. (2019) A Regularization Approach for an Inverse Source Problem in Elliptic Systems from Single Cauchy Data. Numerical Functional Analysis and Optimization 40:9, pages 1080-1112.
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Jingjun Zhao & Songshu Liu. (2015) Two regularization methods for inverse source problem on the Poisson equation. Complex Variables and Elliptic Equations 60:10, pages 1374-1391.
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Jingjun Zhao & Songshu Liu. (2015) Central difference regularization method for inverse source problem on the Poisson equation. Complex Variables and Elliptic Equations 60:3, pages 405-415.
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M. Mierzwiczak & J.A. Kołodziej. (2011) The determination of heat sources in two dimensional inverse steady heat problems by means of the method of fundamental solutions. Inverse Problems in Science and Engineering 19:6, pages 777-792.
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Articles from other publishers (21)

Gopal Priyadarshi & Sila Ovgu Korkut. (2023) Comparative work for the source identification in parabolic inverse problem based on Taylor and Chebyshev wavelet methods. Mathematical Methods in the Applied Sciences 46:16, pages 16542-16561.
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Chein-Shan Liu & Chih-Wen Chang. (2023) Nonlinear Cauchy/Robin inverse problems solved by an optimal splitting-linearizing method. International Journal of Heat and Mass Transfer 213, pages 124329.
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Chein-Shan Liu & Lin Qiu. (2023) Solving Nonlinear Elliptic Inverse Source, Coefficient and Conductivity Problems by the Methods with Bases Satisfying the Boundary Conditions Automatically. Journal of Scientific Computing 95:2.
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Jun Lu, Lianpeng Shi, Chein-Shan Liu & C. S. Chen. (2022) Solving Inverse Conductivity Problems in Doubly Connected Domains by the Homogenization Functions of Two Parameters. Mathematics 10:13, pages 2256.
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Judy P. Yang & Hsiang-Ming Li. (2022) Recovering Heat Source from Fourth-Order Inverse Problems by Weighted Gradient Collocation. Mathematics 10:2, pages 241.
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Guillermo Federico Umbricht. (2021) IDENTIFICATION OF THE SOURCE FOR FULL PARABOLIC EQUATIONS. Mathematical Modelling and Analysis 26:3, pages 339-357.
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Abdellatif Ellabib & Abdessamad El Madkouri. (2020) A Discontinuous Dual Reciprocity Method in Conjunction with a Regularized Levenberg–Marquardt Method for Source Term Recovery in Inhomogeneous Anisotropic Materials. International Journal of Computational Methods 17:10, pages 2050002.
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Chein-Shan Liu. (2020) An energetic boundary functional method for solving the inverse source problems of 2D nonlinear elliptic equations. Engineering Analysis with Boundary Elements 118, pages 204-215.
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Abdessamad El Madkouri & Abdellatif Ellabib. (2020) A Preconditioned Krylov Subspace Iterative Methods for Inverse Source Problem by Virtue of a Regularizing LM-DRBEM. International Journal of Applied and Computational Mathematics 6:4.
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Michael Hinze & Tran Nhan Tam Quyen. (2019) Finite element approximation of source term identification with TV-regularization. Inverse Problems 35:12, pages 124004.
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Yan Gu, Lei Wang, Wen Chen, Chuanzeng Zhang & Xiaoqiao He. (2017) Application of the meshless generalized finite difference method to inverse heat source problems. International Journal of Heat and Mass Transfer 108, pages 721-729.
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Chein-Shan Liu. (2016) A BIEM using the Trefftz test functions for solving the inverse Cauchy and source recovery problems. Engineering Analysis with Boundary Elements 62, pages 177-185.
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Fan Yang, Miao Zhang & Xiao-Xiao Li. (2014) A quasi-boundary value regularization method for identifying an unknown source in the Poisson equation. Journal of Inequalities and Applications 2014:1.
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Fan Yang & Chu-Li Fu. (2012) The modified regularization method for identifying the unknown source on Poisson equation. Applied Mathematical Modelling 36:2, pages 756-763.
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Xiao-Xiao Li, Heng Zhen Guo, Shi Min Wan & Fan Yang. (2012) Inverse Source Identification by the Modified Regularization Method on Poisson Equation. Journal of Applied Mathematics 2012, pages 1-13.
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Magdalena Mierzwiczak & Jan Adam Kołodziej. (2010) Application of the method of fundamental solutions and radial basis functions for inverse transient heat source problem. Computer Physics Communications 181:12, pages 2035-2043.
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Thomas T. M. Onyango, Derek B. Ingham & Daniel Lesnic. (2007) Restoring boundary conditions in heat conduction. Journal of Engineering Mathematics 62:1, pages 85-101.
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Bangti Jin & Liviu Marin. (2007) The method of fundamental solutions for inverse source problems associated with the steady-state heat conduction. International Journal for Numerical Methods in Engineering 69:8, pages 1570-1589.
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C. W. Chen, D. L. Young, C. C. Tsai & K. Murugesan. (2005) The method of fundamental solutions for inverse 2D Stokes problems. Computational Mechanics 37:1, pages 2-14.
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S. A. Yang. (2004) An integral equation approach to three-dimensional acoustic radiation and scattering problems. The Journal of the Acoustical Society of America 116:3, pages 1372-1380.
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A. Farcas, L. Elliott, D.B. Ingham & D. Lesnic. (2004) An inverse dual reciprocity method for hydraulic conductivity identification in steady groundwater flow. Advances in Water Resources 27:3, pages 223-235.
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