Implementation of isogeometric boundary element method for 2-D steady heat transfer analysis

In this paper, the recently developed hybrid numerical method based on isogeometric analysis (IGA) and boundary element method (BEM), named as IGABEM, is further extended to study steady heat transfer problems in two dimensions (2D). The IGA employs spline basis functions (e.g., NURBS) as shape functions for geometric description and field approximation. The NURBS only describe the boundary of objects, and the BEM also directly deals with the boundaries. Therefore, the combined IGABEM is highly attractive as it takes advantages of the common boundary representation of both the IGA and the BEM. The formulation of IGABEM for steady heat transfer is derived, and its performance and accuracy are verified through numerical test cases by comparing the obtained results with analytical and finite element method solutions. The convergence of the developed approach for steady heat transfer problems is also analyzed. The computer codes of the IGABEM developed for steady heat transfer analysis can be accessed at: http://www.idmes.cn/codes.html.