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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 60, 2011 - Issue 1
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Original Articles

The Method of Fundamental Solutions for Solving the Backward Heat Conduction Problem with Conditioning by a New Post-Conditioner

Chein-Shan Liu Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, Republic of ChinaCorrespondence[email protected]
Pages 57-72 | Received 10 Dec 2010, Accepted 20 Apr 2011, Published online: 05 Jul 2011

Citations (29)

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Read on this site (11)

Chein-Shan Liu & Chih-Wen Chang. (2020) Analytic series solutions of 2D forward and backward heat conduction problems in rectangles and a new regularization. Inverse Problems in Science and Engineering 28:10, pages 1384-1406.
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Chein-Shan Liu, Yung-Wei Chen & Jiang-Ren Chang. (2018) A regularized Fourier sine series solution of a 3D backward heat conduction problem with extremal long time span. Numerical Heat Transfer, Part B: Fundamentals 74:6, pages 807-817.
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Jin Wen & Jun-Feng Cheng. (2018) The method of fundamental solution for the inverse source problem for the space-fractional diffusion equation. Inverse Problems in Science and Engineering 26:7, pages 925-941.
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Chein-Shan Liu, Wenzhen Qu & Yaoming Zhang. (2018) Numerically solving twofold ill-posed inverse problems of heat equation by the adjoint Trefftz method. Numerical Heat Transfer, Part B: Fundamentals 73:1, pages 48-61.
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Chein-Shan Liu. (2016) To recover heat source G(x) + H(t) by using the homogenized function and solving rectangular differencing equations. Numerical Heat Transfer, Part B: Fundamentals 69:4, pages 351-363.
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F.Z. Wang & K.H. Zheng. (2016) The method of fundamental solutions for steady-state groundwater flow problems. Journal of the Chinese Institute of Engineers 39:2, pages 236-242.
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Chein-Shan Liu. (2015) A double optimal descent algorithm for iteratively solving ill-posed linear inverse problems. Inverse Problems in Science and Engineering 23:1, pages 38-66.
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Chein-Shan Liu. (2014) A vector regularization method to solve linear inverse problems. Inverse Problems in Science and Engineering 22:5, pages 765-786.
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Chia-Ming Fan, Yu-Kai Huang, Po-Wei Li & Chia-Lin Chiu. (2014) Application of the Generalized Finite-Difference Method to Inverse Biharmonic Boundary-Value Problems. Numerical Heat Transfer, Part B: Fundamentals 65:2, pages 129-154.
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Hsin-Fang Chan & Chia-Ming Fan. (2013) The Local Radial Basis Function Collocation Method for Solving Two-Dimensional Inverse Cauchy Problems. Numerical Heat Transfer, Part B: Fundamentals 63:4, pages 284-303.
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Chein-Shan Liu. (2012) Reconstruction of moving boundary for one-dimensional heat conduction equation by using the Lie-group shooting method. Inverse Problems in Science and Engineering 20:3, pages 311-334.
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Articles from other publishers (18)

Juan Zhang, Rong-Juin Shuy, Chiung-Lin Chu & Chia-Ming Fan. (2022) Generalized finite difference method for three-dimensional eigenproblems of Helmholtz equation. Mathematics and Computers in Simulation 196, pages 45-67.
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L Zhang, FZ Wang, J Zhang, YY Wang, S Nadeem & TA Nofal. (2022) Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion Problems. Frontiers in Physics 10.
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Cheng-Yu Ku, Jing-En Xiao & Chih-Yu Liu. (2019) The Method of Fundamental Solutions for Three-Dimensional Nonlinear Free Surface Flows Using the Iterative Scheme. Applied Sciences 9:8, pages 1715.
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Chein-Shan Liu. (2016) Homogenized functions to recover / by solving a small scale linear system of differencing equations . International Journal of Heat and Mass Transfer 101, pages 1103-1110.
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Krzysztof Grysa & Artur Maciag. (2016) Temperature dependent thermal conductivity determination and source identification for nonlinear heat conduction by means of the Trefftz and homotopy perturbation methods. International Journal of Heat and Mass Transfer 100, pages 627-633.
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Ji Lin, C.S. Chen, Chein-Shan Liu & Jun Lu. (2016) Fast simulation of multi-dimensional wave problems by the sparse scheme of the method of fundamental solutions. Computers & Mathematics with Applications 72:3, pages 555-567.
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Chein-Shan Liu, Chung-Lun Kuo & Wun-Sin Jhao. (2016) The multiple-scale polynomial Trefftz method for solving inverse heat conduction problems. International Journal of Heat and Mass Transfer 95, pages 936-943.
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Chein-Shan Liu. (2016) A multiple/scale/direction polynomial Trefftz method for solving the BHCP in high-dimensional arbitrary simply-connected domains. International Journal of Heat and Mass Transfer 92, pages 970-978.
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Chein-Shan Liu & Chih-Wen Chang. (2016) A global boundary integral equation method for recovering space–time dependent heat source. International Journal of Heat and Mass Transfer 92, pages 1034-1040.
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F.F. Dou & Y.C. Hon. (2016) Fundamental kernel-based method for backward space–time fractional diffusion problem. Computers & Mathematics with Applications 71:1, pages 356-367.
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Chein-Shan Liu & Chih-Wen Chang. (2015) Nonlinear problems with unknown initial temperature and without final temperature, solved by the GL ( N , ) shooting method . International Journal of Heat and Mass Transfer 83, pages 665-678.
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Chein-Shan Liu. (2014) Optimal algorithms in a Krylov subspace for solving linear inverse problems by MFS. Engineering Analysis with Boundary Elements 44, pages 64-75.
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Chein-Shan Liu. (2014) A doubly optimized solution of linear equations system expressed in an affine Krylov subspace. Journal of Computational and Applied Mathematics 260, pages 375-394.
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Chein-Shan Liu. (2014) A globally optimal tri-vector method to solve an ill-posed linear system. Journal of Computational and Applied Mathematics 260, pages 18-35.
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F.F. Dou & Y.C. Hon. (2014) Numerical computation for backward time-fractional diffusion equation. Engineering Analysis with Boundary Elements 40, pages 138-146.
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Chein-Shan Liu. (2013) An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems. Journal of Applied Mathematics 2013, pages 1-15.
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Chein-Shan Liu. (2012) An equilibrated method of fundamental solutions to choose the best source points for the Laplace equation. Engineering Analysis with Boundary Elements 36:8, pages 1235-1245.
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Chein-Shan Liu. (2012) Optimally scaled vector regularization method to solve ill-posed linear problems. Applied Mathematics and Computation 218:21, pages 10602-10616.
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