A meshless singular boundary method for three-dimensional inverse heat conduction problems in general anisotropic media

The singular boundary method (SBM) is a relatively new meshless boundary collocation method for the numerical solution of certain elliptic boundary value problems. The method, based on the notion of the boundary element method (BEM) and method of fundamental solutions (MFS), fully inherits the merits of both and in the meantime possessing its unique advantages. Due to the boundary-only discretizations and its semi-analytical nature, the method can be viewed as an ideal candidate for the solution of inverse problems. In this study, we document the first attempt to apply the SBM, together with several regularization techniques, for the solution of inverse heat conduction problems in three-dimensional (3D) anisotropic media. Four benchmark numerical examples are well-studied which indicate that the proposed scheme is accurate, computationally efficient and numerically stable for the solution of 3D inverse problems with various levels of noisy input data.