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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 59, 2011 - Issue 1
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Original Articles

Modified Collocation Trefftz Method for the Geometry Boundary Identification Problem of Heat Conduction

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Pages 58-75 | Received 09 Sep 2010, Accepted 13 Oct 2010, Published online: 28 Jan 2011

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Read on this site (13)

Fajie Wang, Chein-Shan Liu & Wenzhen Qu. (2018) Numerical analysis of heat transfer in arbitrary plane domains using a novel Trefftz energy method. Numerical Heat Transfer, Part B: Fundamentals 73:3, pages 146-154.
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Bo Yu, Huan-Lin Zhou, Qiang Gao & Jun Yan. (2016) Geometry boundary identification of the furnace inner wall by BEM without iteration. Numerical Heat Transfer, Part A: Applications 69:11, pages 1253-1262.
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Cheng-Yu Ku, Jing-En Xiao, Chih-Yu Liu & Weichung Yeih. (2016) On the accuracy of the collocation Trefftz method for solving two- and three-dimensional heat equations. Numerical Heat Transfer, Part B: Fundamentals 69:4, pages 334-350.
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Wenyu Zhang, Fuming Ma & Yao Sun. (2016) The homotopy method for identifying the radiative source term in the heat conduction problem. Applicable Analysis 95:4, pages 842-859.
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Chia-Ming Fan & Po-Wei Li. (2015) Numerical Solutions of Direct and Inverse Stokes Problems by the Method of Fundamental Solutions and the Laplacian Decomposition. Numerical Heat Transfer, Part B: Fundamentals 68:3, pages 204-223.
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Chia-Ming Fan, Po-Wei Li & Weichung Yeih. (2015) Generalized finite difference method for solving two-dimensional inverse Cauchy problems. Inverse Problems in Science and Engineering 23:5, pages 737-759.
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A. Karageorghis, D. Lesnic & L. Marin. (2014) Regularized collocation Trefftz method for void detection in two-dimensional steady-state heat conduction problems. Inverse Problems in Science and Engineering 22:3, pages 395-418.
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C.M. Fan, Y.C. Liu, H.F. Chan & S.S. Hsiao. (2014) Solutions of boundary detection problem for modified Helmholtz equation by Trefftz method. Inverse Problems in Science and Engineering 22:2, pages 267-281.
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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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Tien-Mo Shih, Yingbin Zheng, Martinus Arie & Jin-Cheng Zheng. (2013) Literature Survey of Numerical Heat Transfer (2010–2011). Numerical Heat Transfer, Part A: Applications 64:6, pages 435-525.
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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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Edyta Hetmaniok, Iwona Nowak, Damian Słota & Adam Zielonka. (2012) Determination of Optimal Parameters for the Immune Algorithm Used for Solving Inverse Heat Conduction Problems with and without a Phase Change. Numerical Heat Transfer, Part B: Fundamentals 62:6, pages 462-478.
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Chein-Shan Liu. (2011) A Lie-Group Adaptive Method to Identify Spatial-Dependence Heat Conductivity Coefficients. Numerical Heat Transfer, Part B: Fundamentals 60:4, pages 305-323.
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Yang Wu, Junli Zhang, Shuang Ding & Yan-Cheng Liu. (2022) Localized Boundary Knot Method for Solving Two-Dimensional Inverse Cauchy Problems. Mathematics 10:8, pages 1324.
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Ke Sun, Shuang Ding, Junli Zhang & Yan-Cheng Liu. (2022) Solving the Eigenfrequencies Problem of Waveguides by Localized Method of Fundamental Solutions with External Source. Mathematics 10:7, pages 1128.
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Leszek Hożejowski. (2019) A boundary determination problem in steady-state heat conduction – a solution and sensitivity analysis. International Journal of Numerical Methods for Heat & Fluid Flow 30:5, pages 2351-2362.
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Po-Wei Li, Zhuo-Jia Fu, Yan Gu & Lina Song. (2019) The generalized finite difference method for the inverse Cauchy problem in two-dimensional isotropic linear elasticity. International Journal of Solids and Structures 174-175, pages 69-84.
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Judy P. Yang & Wen-Chims Hsin. (2019) Weighted reproducing kernel collocation method based on error analysis for solving inverse elasticity problems. Acta Mechanica 230:10, pages 3477-3497.
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Lin Qiu, Wen Chen, Fajie Wang, Chein-Shan Liu & Qingsong Hua. (2019) Boundary function method for boundary identification in two-dimensional steady-state nonlinear heat conduction problems. Engineering Analysis with Boundary Elements 103, pages 101-108.
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Po-Wei Li, Wen Chen, Zhuo-Jia Fu & Chia-Ming Fan. (2018) Generalized finite difference method for solving the double-diffusive natural convection in fluid-saturated porous media. Engineering Analysis with Boundary Elements 95, pages 175-186.
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Fajie Wang, Qingsong Hua & Chein-Shan Liu. (2018) Boundary function method for inverse geometry problem in two-dimensional anisotropic heat conduction equation. Applied Mathematics Letters 84, pages 130-136.
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Leszek Hożejowski. (2018) An inverse geometric problem in steady state heat conduction – the solution and stability analysis. MATEC Web of Conferences 240, pages 01013.
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Chein-Shan Liu, Wen Chen & Zhuojia Fu. (2016) A multiple-scale MQ-RBF for solving the inverse Cauchy problems in arbitrary plane domain. Engineering Analysis with Boundary Elements 68, pages 11-16.
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Judy P. Yang, Pai-Chen Guan & Chia-Ming Fan. (2016) Weighted Reproducing Kernel Collocation Method and Error Analysis for Inverse Cauchy Problems. International Journal of Applied Mechanics 08:03, pages 1650030.
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Chia-Ming Fan, Hong-Huei Li, Chuan-Yen Hsu & Chun-Hung Lin. (2014) Solving inverse Stokes problems by modified collocation Trefftz method. Journal of Computational and Applied Mathematics 268, pages 68-81.
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Chia-Ming Fan & Po-Wei Li. (2014) Generalized Finite Difference Method for Solving Two-dimensional Burgers’ Equations. Procedia Engineering 79, pages 55-60.
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A. Karageorghis. (2012) Efficient Trefftz collocation algorithms for elliptic problems in circular domains. Numerical Algorithms 64:3, pages 427-453.
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Hsin-Fang Chan, Chia-Ming Fan & Chia-Wen Kuo. (2013) Generalized finite difference method for solving two-dimensional non-linear obstacle problems. Engineering Analysis with Boundary Elements 37:9, pages 1189-1196.
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H.-F. Chan & C.-M. Fan. (2013) The Modified Collocation Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm for the Inverse Boundary Determination Problem for the Biharmonic Equation. Journal of Mechanics 29:2, pages 363-372.
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Chia-Ming Fan, Chih-Shuan Chien, Hsin-Fang Chan & Chia-Lin Chiu. (2013) The local RBF collocation method for solving the double-diffusive natural convection in fluid-saturated porous media. International Journal of Heat and Mass Transfer 57:2, pages 500-503.
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Bogdan Căruntu & Constantin Bota. (2012) Approximate polynomial solutions for nonlinear heat transfer problems using the squared remainder minimization method. International Communications in Heat and Mass Transfer 39:9, pages 1336-1341.
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Chia-Ming Fan, Hsin-Fang Chan, Chung-Lun Kuo & Weichung Yeih. (2012) Numerical solutions of boundary detection problems using modified collocation Trefftz method and exponentially convergent scalar homotopy algorithm. Engineering Analysis with Boundary Elements 36:1, pages 2-8.
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