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 and Chuanzeng Zhang


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

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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.

  • History

Published online: 2018-09

  • AMS Subject Headings

62P30, 65M32, 65K05

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