Influence of the Discretizing Method on the Identified Results in Boundary Value Inverse Analysis by the Boundary Element Method

Abstract

In this study, the influence of the discretizing method, such as a constant element or a linear element, on the accuracy of the identified results is investigated in the boundary value inverse analysis by the Boundary Element Method. For the regularization of the inverse analysis, the combination method is used; the one that the fundamental solution in B.E.M. is selected adequately and the one that the rank of the coefficient matrix is reduced. The optimum condition for solving the inverse problem is found by two performance indexes which are the condition number of the coefficient matrix and the residual norm caused by the rank reduction of the matrix. In a numerical example, the inverse problem governed by two-dimensional Laplace equation is treated. As a result, the identified result obtained using the linear element has almost the same accuracy as the one using the constant element while the accuracy using the constant element is often better, and the selection method of an adequate fundamental solution is very effective for the inverse analysis. Thus, the inverse analysis may be carried out using the constant element and the adequate fundamental solution selected.