弹性边界条件识别反问题的正则化间接边界元法

Regularized Boundary Element Method with Indirect Unknowns for Inverse Elasticity Problems

基于间接变量规则化边界元法,对弹性边界条件识别Cauchy反问题进行了研究。对于实施过程中出现的线性病态方程组,采用Tikhonov和TSVD两种正则化方法求解,通过广义交叉校验准则法(GCV法)确定正则化参数。数值算例表明:该算法稳定,数值解与精确解比较吻合。

The elasticity inverse identification boundary conditions Cauchy problem was investigated by using the indirect boundary element method（ IBEM）. Both the Tikhonov regularization method and the truncated singular value decomposition（ TSVD） were applied to solving the ill-conditioned linear system involved in the process of implementation,and the optimal parameter for the Tikhonov and the optimal truncation number for the TSVD were chosen according to the generalized cross validation（ GCV） method. A numerical example was given to verify the effectiveness of the proposed scheme,with numerical results being good agreement with the exact solutions.