Singular boundary method for inverse heat conduction problems in general anisotropic media

Abstract

This study documents the first attempt to apply the singular boundary method, a recently developed meshless boundary collocation method, to the solution of inverse anisotropic heat conduction problems. The method cures the perplexing fictitious boundary issue associated with the method of fundamental solutions while inheriting the merits of the latter of being truly meshless, integration-free and easy to programme. Thanks to its boundary-only discretization and semi-analytical nature, the method can be viewed as an ideal candidate for the solution of inverse problems. Four benchmark examples indicate that the proposed method, in connection with proper regularization techniques, is accurate, computationally efficient and numerically stable for the solution of inverse problems with various levels of noisy Cauchy data.