The hybrid boundary element method applied to problems of potential theory in nonhomogeneous materials

Since the introduction of the hybrid boundary element method in 1987, it has been applied to various problems of elasticity and potential theory, including time-dependent problems. This paper focuses on establishing the conceptual framework for applying both the variational formulation and a simplified version of the hybrid boundary element method to nonhomogeneous materials. Several classes of fundamental solutions for problems of potential are derived. Thus, the boundary-only feature of the method is preserved even with a spatially varying material property. Several numerical examples are given in terms of an efficient patch test including irregularly bounded, unbounded, and multiply connected regions submitted to high gradients.