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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 63, 2013 - Issue 4
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Original Articles

The Local Radial Basis Function Collocation Method for Solving Two-Dimensional Inverse Cauchy Problems

Hsin-Fang Chan Department of Harbor and River Engineering & Computation and Simulation Center, National Taiwan Ocean University, Keelung, Taiwan, Republic of China
&
Chia-Ming Fan Department of Harbor and River Engineering & Computation and Simulation Center, National Taiwan Ocean University, Keelung, Taiwan, Republic of ChinaCorrespondence[email protected]
Pages 284-303 | Received 15 Nov 2012, Accepted 15 Jan 2013, Published online: 15 Apr 2013

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Nikunja Bihari Barik & T. V. S. Sekhar. (2021) Mesh-free multilevel iterative algorithm for Navier–Stokes equations. Numerical Heat Transfer, Part B: Fundamentals 79:3, pages 150-164.
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Nikunja Bihari Barik & T. V. S. Sekhar. (2017) A novel RBF-FD meshless scheme in curvilinear geometry for unbounded flows. International Journal for Computational Methods in Engineering Science and Mechanics 18:4-5, pages 209-219.
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Jie Sun, Hong-Liang Yi & He-Ping Tan. (2016) Local RBF meshless scheme for coupled radiative and conductive heat transfer. Numerical Heat Transfer, Part A: Applications 69:12, pages 1390-1404.
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Ahmad Shirzadi & Fariba Takhtabnoos. (2016) A local meshless method for Cauchy problem of elliptic PDEs in annulus domains. Inverse Problems in Science and Engineering 24:5, pages 729-743.
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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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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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Wen-Hui Chu, Zhuo-Jia Fu, Zhuo-Chao Tang, Wen-Zhi Xu & Xiao-Ying Zhuang. (2023) A machine learning approach coupled with polar coordinate based localized collocation method for inner surface identification in heat conduction problem. Computers & Mathematics with Applications 148, pages 41-61.
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J. Thewlis, D. Stevens, H. Power, D. Giddings, P. Gowland & M. Vloeberghs. (2023) 4-dimensional local radial basis function interpolation of large, uniformly spaced datasets. Computer Methods and Programs in Biomedicine 228, pages 107235.
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Fajie Wang, Zengtao Chen & Yanpeng Gong. (2022) Local knot method for solving inverse Cauchy problems of Helmholtz equations on complicated two‐ and three‐dimensional domains. International Journal for Numerical Methods in Engineering 123:20, pages 4877-4892.
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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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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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Zengtao Chen, Fajie Wang, Suifu Cheng & Guozheng Wu. (2022) Localized MFS for three‐dimensional acoustic inverse problems on complicated domains. International Journal of Mechanical System Dynamics 2:1, pages 143-152.
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Marzieh Raei, Hadi Roohani Ghehsareh & Ardelio Galletti. (2020) An adaptive sparse kernel technique in greedy algorithm framework to simulate an anomalous solute transport model. Engineering Analysis with Boundary Elements 121, pages 243-254.
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Judy P. Yang & Yuan-Chia Chen. (2020) Gradient Enhanced Localized Radial Basis Collocation Method for Inverse Analysis of Cauchy Problems. International Journal of Applied Mechanics 12:09, pages 2050107.
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Judy P. Yang & Hon Fung Samuel Lam. (2020) Detecting Inverse Boundaries by Weighted High-Order Gradient Collocation Method. Mathematics 8:8, pages 1297.
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T. Tanbay & B. Ozgener. (2020) Fully meshless solution of the one-dimensional multigroup neutron transport equation with the radial basis function collocation method. Computers & Mathematics with Applications 79:5, pages 1266-1286.
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Ting Zhang, Zhen-Huan Lin, Guan-Yi Huang, Chia-Ming Fan & Po-Wei Li. (2020) Solving Boussinesq equations with a meshless finite difference method. Ocean Engineering 198, pages 106957.
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R.P. Niu, G.R. Liu & M. Li. (2019) The inverse methods based on S-FEMs with an adaptive SVD regularization technique for solving Cauchy inverse heat transfer problems. Engineering Analysis with Boundary Elements 107, pages 79-95.
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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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Ku, Xiao, Huang, Yeih & Liu. (2019) On Solving Two-Dimensional Inverse Heat Conduction Problems Using the Multiple Source Meshless Method. Applied Sciences 9:13, pages 2629.
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Chia-Ming Fan, Chi-Nan Chu, Božidar Šarler & Tsung-Han Li. (2019) Numerical solutions of waves-current interactions by generalized finite difference method. Engineering Analysis with Boundary Elements 100, pages 150-163.
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Yi-Ning Zhang, Hao-Chun Zhang, Xiu Zhang, Hong-Xing Yu & Guang-Bo Zhao. (2018) Block Radial Basis Function Collocation Meshless method applied to steady and transient neutronics problem solutions in multi-material reactor cores. Progress in Nuclear Energy 109, pages 83-96.
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Ting Zhang, Ying-Jie Huang, Lin Liang, Chia-Ming Fan & Po-Wei Li. (2018) Numerical solutions of mild slope equation by generalized finite difference method. Engineering Analysis with Boundary Elements 88, pages 1-13.
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Lihua Wang, Zhen Wang & Zhihao Qian. (2017) A meshfree method for inverse wave propagation using collocation and radial basis functions. Computer Methods in Applied Mechanics and Engineering 322, pages 311-350.
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Judy P. Yang, Pai-Chen Guan & Chia-Ming Fan. (2017) Solving Inverse Laplace Equation with Singularity by Weighted Reproducing Kernel Collocation Method. International Journal of Applied Mechanics 09:05, pages 1750065.
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Po-Wei Li & Chia-Ming Fan. (2017) Generalized finite difference method for two-dimensional shallow water equations. Engineering Analysis with Boundary Elements 80, pages 58-71.
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Elyas Shivanian & Ahmad Jafarabadi. (2016) Inverse Cauchy problem of annulus domains in the framework of spectral meshless radial point interpolation. Engineering with Computers 33:3, pages 431-442.
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Ting Zhang, Yu-Fei Ren, Zhi-Qiang Yang, Chia-Ming Fan & Po-Wei Li. (2016) Application of generalized finite difference method to propagation of nonlinear water waves in numerical wave flume. Ocean Engineering 123, pages 278-290.
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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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Jie Sun, Hong-Liang Yi & He-Ping Tan. (2016) Local radial basis function meshless scheme for vector radiative transfer in participating media with randomly oriented axisymmetric particles. Applied Optics 55:6, pages 1232.
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Judy P. Yang & Wan-Ting Su. (2016) Investigation of Radial Basis Collocation Method for Incremental-Iterative Analysis. International Journal of Applied Mechanics 08:01, pages 1650007.
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Ting Zhang, Yu-Fei Ren, Chia-Ming Fan & Po-Wei Li. (2016) Simulation of two-dimensional sloshing phenomenon by generalized finite difference method. Engineering Analysis with Boundary Elements 63, pages 82-91.
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Chia-Ming Fan, Chi-Hung Yang & Wei-Shiang Lai. (2015) Numerical solutions of two-dimensional flow fields by using the localized method of approximate particular solutions. Engineering Analysis with Boundary Elements 57, pages 47-57.
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Chia-Ming Fan, Chi-Hung Yang & Meng-Huang Gu. (2014) Applications of the Local RBF Collocation Method and the Fictitious Time Integration Method for Burgers? Equations. Procedia Engineering 79, pages 569-574.
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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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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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