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

• Published in: Engineering analysis with boundary elements Vol. 29; no. 8; pp. 788 - 795
• Main Authors: Gao, Xiao-Wei, He, Man-Chao
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.08.2005; Elsevier
• Subjects: Analytical and numerical techniques; Boundary element method; Complex-Variable-Differentiation; Computation; Conduction; Damage identification; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Inverse; Inverse analysis; Mathematical analysis; Mathematical models; Measurement and testing methods; Multi-region BEM; Physics; Sensitivity coefficients; Shape optimization; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Inverse analysis; Heat conduction; Complex-Variable-Differentiation; Shape optimization; Multi-region BEM; Damage identification; Sensitivity coefficients; Geometrical shape; Heat equation; Optimization; Complex variable method; Inverse problems; Integral equations; Modelling; System identification; Differentiation; Boundary element method; Heat transfer; Thermal conduction; Finite difference method
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2005.03.001

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.