Eecient Analytic Series Solutions for Potential Flow Problems

The solution of Laplace's equation for a wide range of spatial domains and boundary conditions is a valuable asset in the study of potential theory. However, purely numerical schemes are often computationally ineecient, while analytical techniques have traditionally been too cumbersome. Recently, classical (separation of variables) series solutions have been modiied to solve Laplace's equation with both irregular and free boundaries. Using the theory of eigenfunction expansions to provide a theoretical basis for the method, the problem is seen to consist of a sequence of curve tting exercises. In this paper, a new approach based on interpolation is presented for the series coeecients estimation problem. It has the advantages of providing a conceptually simpler view of the series technique, and of estimating the series coeecients significantly faster than alternative approaches. A free boundary problem from steady hillside seepage will be solved to illustrate the new technique.