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# Subdivision Surface-Based Isogeometric Boundary Element Method for Steady Heat Conduction Problems with Variable Coefficient

Xiuyun Chen1, Xiaomeng Yin2, Kunpeng Li3, Ruhui Cheng1, Yanming Xu1,4,*, Wei Zhang1
1 School of Architectural Engineering, Huanghuai University, Zhumadian, 463003, China
2 College of Intelligent Construction, Wuchang University of Technology, Wuhan, 430223, China
3 College of Civil Engineering and Architecture, China Three Gorges University, Yichang, 443000, China
4 CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230026, China
* Corresponding Author: Yanming Xu. Email:
(This article belongs to this Special Issue: Recent Advance of the Isogeometric Boundary Element Method and its Applications)

Computer Modeling in Engineering & Sciences 2021, 129(1), 323-339. https://doi.org/10.32604/cmes.2021.016794

Received 26 March 2021; Accepted 08 May 2021; Issue published 24 August 2021

### Abstract

The present work couples isogeometric analysis (IGA) and boundary element methods (BEM) for three dimensional steady heat conduction problems with variable coefficients. The Computer-Aided Design (CAD) geometries are built by subdivision surfaces, and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction analysis. Moreover, the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary integrals. Several numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.

### Keywords

Subdivision surface; isogeometric boundary element method; heat conduction; radial integration

Chen, X., Yin, X., Li, K., Cheng, R., Xu, Y. et al. (2021). Subdivision Surface-Based Isogeometric Boundary Element Method for Steady Heat Conduction Problems with Variable Coefficient. CMES-Computer Modeling in Engineering & Sciences, 129(1), 323–339.

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