A transform method for Laplace's equation in multiply connected circular domains

Abstract

A new general transform method for the solution of mixed boundary value problems (BVPs) for Laplace's equation in multiply connected circular domains is formulated. Circular domains are those with boundaries that are a union of circular arcs and/or straight line segments. Constructive schemes based on the method are showcased by application to some concrete problems in fluid mechanics. In particular, a BVP of topical interest in the study of superhydrophobic surfaces is solved and compared with an existing numerical solution.