BEM analysis of 3D heat conduction in 3D thin anisotropic media

In this paper, the boundary integrals for treating 3D field problems are fully regularized for planar elements by the technique of integration by parts (IBP). As has been well documented in open literatures, these integrals appear to be strongly singular and hyper-singular for the associated fundamental solutions. In the past, the IBP approach has only been applied to regularize the integrals for 2D problems. The present work shows that the IBP can also be further extended to treat 3D problems, where two variables of the local coordinates are involved. The presented formulations are fully explicit and also, most importantly, very straightforward for implementation in program codes. To demonstrate their validity and our implementation, a few example cases of 3D anisotropic heat conduction are investigated by the boundary element method and the calculated results are verified using analyses by ANSYS.