@Article{AAMM-10-1459, author = {Zhang , AixiaGu , YanHua , Qingsong and Chen , Wen}, 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 = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0103}, url = {http://global-sci.org/intro/article_detail/aamm/12722.html} }