Selection of Satisfactory Fundamental Solution in Boundary Value Inverse Analysis by B.E.M.

Abstract

In this study, a method for the regularization of the boundary value inverse analysis is proposed. The method is that the fundamental solution in B.E.M.is selected satisfactorily according to the prolem to be solved and the rank of the coefficient matrix constructed using the satisfactory fundamental solution is reduced for the regularization. The optimum condition for solving the boundary value inverse problem is found by using the objective function which consists of the condition number of the coefficient matrix and the error norm caused by the rank reduction of the matrix. In a numerical example, the optimum conditions to the inverse problems governed by the two-dimensional Laplace equation and the plate bending eqation are found. It is shown that the optimum condition obtained by the proposed method is more adequate than that obtained by the conventional method, from the viewpoint of the objective function. The proposed method is therefore proved to be effective for the inverse analysis in B.E.M.