Isogeometric boundary element method for solving 2D multi-media heat conduction problems

Abstract

In this work, we employ the isogeometric boundary element approach to investigate heat transfer mechanisms in various media. We derive and construct integral equations for the interface of different media to address heat transfer issues. Our proposed modeling technique for two-dimensional problems can be dynamically constructed by incorporating control points and weight factors. In comparison to other numerical software, this approach offers high customizability, improves model accuracy, mitigates mesh errors, and seamlessly integrates the advantages of Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) through the isogeometric method. The boundary element approach boasts several advantages, with numerical stability and excellent precision being paramount. The amalgamation of the isogeometric approach with the boundary element method holds promise for future applications in practical engineering. Simultaneously, we address the domain integral using the radial integration approach. The algorithmic results reveal that the isogeometric boundary element method, in contrast to the traditional boundary element method, expands the applicability of the latter while maintaining good stability and robustness. This provides substantial support for further software integration.