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

[+] Author and Article Information
M. D. Bird, C. R. Steele

Division of Applied Mechanics, Stanford University, Stanford, CA 94305

J. Appl. Mech 59(2), 398-404 (Jun 01, 1992) (7 pages) doi:10.1115/1.2899533 History: Received March 07, 1991; Revised August 05, 1991; Online March 31, 2008


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 Möbius transformation method due to Honein et al. (1991).

Copyright © 1992 by The American Society of Mechanical Engineers
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