Fast hierarchical methods for potential field evaluations have in rece
nt years found interesting applications in computational physics and e
ngineering. For example, these methods have been used in combination w
ith integral equation methods for solving the electrostatic and elasto
static equations for materials with inclusions. A lingering obstacle o
n the way to constructing a general purpose algorithm for inclusion pr
oblems is the treatment of inclusion interfaces that lie very close to
each other. The difficulty is to assess the need for resolution and t
o evaluate layer potentials close to their sources in a fast and accur
ate fashion. This paper presents an automated algorithm for such an as
sessment and evaluation. The robustness and speed of the algorithm is
demonstrated through a series of examples involving thin bridges, coat
ings, narrow necks, corners, cusps, and random mixtures. (C) 1996 Acad
emic Press, Inc.