Reproducing Kernel Enhanced Local Radial Basis Collocation Method for Solving Inverse Problems

• Main Authors: Chen, Yuan-Chia, 陳原嘉
• Other Authors: Yang, Judy P.
• Format: Others
• Language: zh-TW
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/2558uh

碩士 === 國立交通大學 === 土木工程系所 === 107 === As inverse problems have been known for the incomplete boundary conditions, how to solve it effectively remains a challenging task in the field of computational mechanics. Although the radial basis collocation method has exponential convergence rate, the resulting discrete systems are full matrices and thus have ill-conditioned systems. In contrast, the reproducing kernel collocation method has algebraic convergence rate, but the resulting systems are more stable compared to the ones obtained by the global approximation. As such, this work introduces the localized radial basis collocation method to solve inverse problems in order to get rid of ill-conditioned systems. In particular, different types of inverse problems are provided to demonstrate the accuracy of approximation and efficiency of calculation by using the localized radial basis collocation method.