@Article{AAMM-10-6,
author = {Zhang, Aixia and Yan, Gu and Qingsong, Hua and Wen, Chen},
title = {A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {10},
number = {6},
pages = {1459--1477},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2018-0103},
url = {https://global-sci.com/article/73234/a-regularized-singular-boundary-method-for-inverse-cauchy-problem-in-three-dimensional-elastostatics}
}