Multi-region heat conduction problems by boundary element method

This paper is concerned with boundary element solution of two dimensional steady-state heat conduction problems in multi-regions. In the proposed method, each region with different heat transfer properties is considered as a piecewise homogeneous in a heterogeneous system. The solution scheme akin to a finite difference method or finite element method sweeping treatment is adopted. The generated integral equation for a typical region is swept to obtain the system matrix for all regions in a single step without considering compatibility conditions explicitly at interfaces. In the case of linear or higher order elements, the non-square global system matrix is solved by the singular value decomposition method. Multi-region test problems for square and circular domains are considered and numerical results are presented.