A Virtual Boundary Element Method for Three-Dimensional Inverse Heat Conduction Problems in Orthotropic Media

作     者：Xu Liu Guojian Shao Xingxing Yue Qingbin Yang Jingbo Su 

作者机构：College of Mechanics and MaterialsHohai UniversityNanjing211100China School of Material Science and EngineeringNanjing University of Science&TechnologyNanjing210094China State Key Laboratory of Operation and Control of Renewable Energy&Storage SystemsChina Electric Power Research InstituteBeijing100192China College of HarbourCoastal and Offshore EngineeringHohai UniversityNanjing210098China. 

出 版 物：《Computer Modeling in Engineering & Sciences》 (工程与科学中的计算机建模（英文）)

年 卷 期：2018年第117卷第11期

页      面：189-211页

核心收录：

学科分类：07[理学] 0835[工学-软件工程] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：This study was supported by“the Fundamental Research Funds for the Central Universities”(Grant No.2015B37814) the Postgraduate Research and Practice Innovation Program of Jiangsu Province(Grant No.KYLX15_0489) the National Natural Science Foundation of China(Grant No.51679081) “the Fundamental Research Funds for the Central Universities”(Grant No.2018B48514). 

主　　题：Virtual boundary element method Tikhonov regularization threedimensional heat conduction inverse problem orthotropic media. 

摘      要：This paper aims to apply a virtual boundary element method(VBEM)to solve the inverse problems of three-dimensional heat conduction in orthotropic media.This method avoids the singular integrations in the conventional boundary element method,and can be treated as a potential approach for solving the inverse problems of the heat conduction owing to the boundary-only discretization and semi-analytical algorithm.When the VBEM is applied to the inverse problems,the numerical instability may occur if a virtual boundary is not properly chosen.The method encounters a highly illconditioned matrix for the larger distance between the physical boundary and the virtual boundary,and otherwise is hard to avoid the singularity of the source point.Thus,it must adopt an appropriate regularization method to deal with the ill-posed systems of inverse problems.In this study,the VBEM and different regularization techniques are combined to model the inverse problem of three-dimensional heat conduction in orthotropic media.The proper regularization techniques not only make the virtual boundary to be allocated freer,but also solve the ill-conditioned equation of the inverse problem.Numerical examples demonstrate that the proposed method is efficient,accurate and numerically stable for solving the inverse problems of three-dimensional heat conduction in orthotropic media.