A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics
Year: 2018
Author: Aixia Zhang, Yan Gu, Qingsong Hua, Wen Chen
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1459–1477
Abstract
The application of the singular boundary method (SBM), a relatively new meshless boundary collocation method, to the inverse Cauchy problem in three-dimensional (3D) linear elasticity is investigated. The SBM involves a coupling between the non-singular boundary element method (BEM) and the method of fundamental solutions (MFS). The main idea is to fully inherit the dimensionality advantages of the BEM and the meshless and integration-free attributes of the MFS. Due to the boundary-only discretizations and its semi-analytical nature, the method can be viewed as an ideal candidate for the solution of inverse problems. The resulting ill-conditioned algebraic equations is regularized here by employing the first-order Tikhonov regularization technique, while the optimal regularization parameter is determined by the $L$-curve criterion. Numerical results with both smooth and piecewise smooth geometries show that accurate and stable solution can be obtained with a comparatively large level of noise added into the input data.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0103
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1459–1477
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Meshless method singular boundary method method of fundamental solutions elastostatics inverse problem.
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