Localized Method of Fundamental Solutions for Two-Dimensional Inhomogeneous Inverse Cauchy Problems

Junli Zhang, Hui Zheng, Chia-Ming Fan and Ming-Fu Fu
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Junli Zhang: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China
Hui Zheng: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China
Chia-Ming Fan: Department of Harbor and River Engineering & Computation and Simulation Center, National Taiwan Ocean University, Keelung 20224, Taiwan
Ming-Fu Fu: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China

Mathematics, 2022, vol. 10, issue 9, 1-22

Abstract: Due to the fundamental solutions are employed as basis functions, the localized method of fundamental solution can obtain more accurate numerical results than other localized methods in the homogeneous problems. Since the inverse Cauchy problem is ill posed, a small disturbance will lead to great errors in the numerical simulations. More accurate numerical methods are needed in the inverse Cauchy problem. In this work, the LMFS is firstly proposed to analyze the inhomogeneous inverse Cauchy problem. The recursive composite multiple reciprocity method (RC-MRM) is adopted to change original inhomogeneous problem into a higher-order homogeneous problem. Then, the high-order homogeneous problem can be solved directly by the LMFS. Several numerical experiments are carried out to demonstrate the efficiency of the LMFS for the inhomogeneous inverse Cauchy problems.

Keywords: localized method of fundamental solutions; meshless method; recursive composite multiple reciprocity method; inhomogeneous problems; inverse Cauchy problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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