Thin bridges in isotropic electrostatics

Fast hierarchical methods for potential eld evaluations have in recent years found interesting applications in computational physics and engineering. For example, these methods have been used in combination with integral equation methods for solving the electrostatic and elastostatic equations for materials with inclusions. A lingering obstacle on the way to constructing a general purpose algorithm for inclusion problems is the treatment of inclusion interfaces that lie very close to each other. The diiculty is to assess the need for resolution and to evaluate layer potentials close to their sources in a fast and accurate fashion. This paper presents an automated algorithm for such an assessment and evaluation. The robustness and speed of the algorithm is demonstrated through a series of examples involving thin bridges, coatings, narrow necks, corners, cusps, and random mixtures.