Multipole methods for boundary-value problems involving a sphere in a tube

摘要

It is shown how the same mathematical technique can be used to solve a number of different problems all concerned with the same geometry. The multipole method, which can be thought of as an extension of separation of variables to problems where the boundaries lie on the coordinate surfaces of two different coordinate systems, is used to solve the problems of potential flow, Stokes flow, and acoustic scattering for the case of a sphere situated on the axis of a circular cylindrical tube.