A novel domain propulsion and adaptive modified inversion method for the inverse geometry heat conduction analysis of FGMs

Abstract

A novel domain propulsion and adaptive modified inversion method based on the least square error method and the precise integration finite element method is firstly proposed to identify the geometries of two-dimensional and three-dimensional models made of functional gradient materials. After introducing concept of virtual boundary, the inverse geometry problems can be solved only by the two processes, which are the domain propulsion process and the adaptive modified process. The first process is getting a better shape and position of virtual boundary through propulsion scheme. After that, the geometry can be identified by modifying the shape of virtual boundary and searching the isotherm or isothermal surface. To improve the ill-posedness of problems, the truncated singular value decomposition method and the coefficient expending scheme are adopted in inversing process. The results of some typical numerical examples show that the present method can obtain the great performance on both the inversing accuracy and the computing efficiency by discussing the influence of some factors such as the different approximation functions, the measurement errors, the number of measurement points and so on.

Additional information

Funding

The research was supported by the National Natural Science Foundation of China (Nos. 11872166, 11502063), the Natural Science Foundation of Anhui Province of China (No. 1608085QA07), the International Postdoctoral Exchange Fellowship Program of China (No. 20180096) and China Postdoctoral Science Foundation (No. 2016M592042).