A new inverse analysis approach for multi-region heat conduction BEM using complex-variable-differentiation method

This paper presents a new inverse analysis approach for identifying material properties and unknown geometries for multi-region problems using the Boundary Element Method (BEM). In this approach, the material properties and coordinates of an unknown region boundary are taken as the optimization variables, and the sensitivity coefficients are computed by the Complex-Variable-Differentiation Method (CVDM). Due to the use of CVDM, the sensitivity coefficients can be accurately determined in a way that is as simple to use as the Finite Difference Method (FDM) and an inverse analysis for a complex composite structure can be easily performed through a similar procedure to the direct computation. Although basic integral equations are presented for heat conduction problems, the application of the proposed algorithm to other problems, such as elastic problems, is straightforward. Two numerical examples are given to demonstrate the potential of the proposed approach.