A meshless interface integral BEM for solving heat conduction in multi-non-homogeneous media with multiple heat sources

Abstract This paper presented a new transformation technique from multi-domain integrals into equivalent boundary integrals, by utilizing this technique, an efficient meshless interface integral boundary element method (meshless IIBEM) is proposed for solving heat conduction in multi-non-homogeneous media with multiple heat sources. Firstly, the interface integral equation for multi-medium heat conduction is derived, considering the varying properties of thermal conductivities. Compared with conventional multi-domain boundary element method (MDBEM), the presented interface integral equation method is more efficient in data preparing, program coding and computational efficiency. However, a big issue is encountered to develop a meshless IIBEM without internal cells for solving heat conduction in multi-non-homogeneous media, since the commonly used transformation technique from single domain integrals into equivalent boundary ones cannot be directly employed to transform the multi-domain integral appeared in the interface integral equation presented in this paper. A new multi-domain transformation technique is presented in this paper by improving the conventional robust radial integration method (RIM) through using a combination approach with a powerful domain decomposition technique. Using this combination approach, the multi-domain integrals are transformed into a series outer boundary and interface integrals, which can be evaluated precisely through the discretization and integration over the outer boundary and interface elements. A high-precision single integral equation method characterized as meshless IIBEM is developed to solve heat conduction in multi-non-homogeneous media with or without multiple heat sources. Numerical examples are given to verify the correctness of the newly proposed method.