A new investigation into regularization techniques for the method of fundamental solutions |
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Authors: | Ji Lin Wen Chen Fuzhang Wang |
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Affiliation: | a Center for Numerical Simulation Software in Engineering and Sciences, Department of Engineering Mechanics, Hohai University, Box 102, No. 1 XiKang Road, Nanjing, Jiangsu 210098, China b State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China |
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Abstract: | This study examines different regularization approaches to investigate the solution stability of the method of fundamental solutions (MFS). We compare three regularization methods in conjunction with two different regularization parameters to find the optimal stable MFS scheme. Meanwhile, we have investigated the relationship among the condition number, the effective condition number, and the MFS solution accuracy. Numerical results show that the damped singular value decomposition under the parameter choice of the generalized cross-validation performs the best in terms of the MFS stability analysis. We also find that the condition number is a superior criterion to the effective condition number. |
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Keywords: | Method of fundamental solutions Regularization technique Regularization parameter Effective condition number |
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