Volume 10, Issue 6
A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics

Aixia Zhang, Yan Gu, Qingsong Hua, Wen Chen & Chuanzeng Zhang

Adv. Appl. Math. Mech., 10 (2018), pp. 1459-1477.

Published online: 2018-09

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  • Abstract

The application of the singular boundary method (SBM), a relatively new meshless boundary collocation method, to the inverse Cauchy problem in threedimensional (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.

  • Keywords

Meshless method singular boundary method method of fundamental solutions elastostatics inverse problem.

  • AMS Subject Headings

62P30 65M32 65K05

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COPYRIGHT: © Global Science Press

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@Article{AAMM-10-1459, author = {Aixia Zhang, Yan Gu, Qingsong Hua, Wen Chen and Chuanzeng Zhang}, 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 threedimensional (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} }
TY - JOUR T1 - A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics AU - Aixia Zhang, Yan Gu, Qingsong Hua, Wen Chen & Chuanzeng Zhang JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1459 EP - 1477 PY - 2018 DA - 2018/09 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2018-0103 UR - https://global-sci.org/intro/aamm/12722.html KW - Meshless method KW - singular boundary method KW - method of fundamental solutions KW - elastostatics KW - inverse problem. AB -

The application of the singular boundary method (SBM), a relatively new meshless boundary collocation method, to the inverse Cauchy problem in threedimensional (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.

Aixia Zhang, Yan Gu, Qingsong Hua, Wen Chen & Chuanzeng Zhang. (1970). A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics. Advances in Applied Mathematics and Mechanics. 10 (6). 1459-1477. doi:10.4208/aamm.OA-2018-0103
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