A Solution Procedure for Laplace’s Equation on Multiply Connected Circular Domains

1 June 1992

journal article
Published by ASME International in Journal of Applied Mechanics

Vol. 59 (2) , 398-404
https://doi.org/10.1115/1.2899533

Abstract

A solution procedure is presented for the two-dimensional Laplace’s equation on circular domains with circular holes and arbitrary boundary conditions. The shape functions use the traditional trigonometric Fourier series on the boundaries with a power series decay into the domain thereby satisfying the governing equation exactly. The interaction of the boundaries is expressed simply and exactly resulting in quick processing time. The only simplification made is the use of a finite number of terms in the boundary conditions. The results are compared with a Green’s function method due to Naghdi (1991) and a Mo¨bius transformation method due to Honein et al. (1991).

Keywords

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