Title: Simulation of the three-dimensional Laplace equation on an interactive three-dimensional spreadsheet

Authors: C.Y. Lam

Addresses: School of Mechanical & Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore

Abstract: This paper describes a spreadsheet program to solve the Laplace equation in three independent variables subject to constant Dirichlet boundary conditions by the Gauss-Seidel method and the successive over-relaxation (SOR) method. The program was developed using the popular Lotus 1-2-3 spreadsheet package. Macros were created to facilitate user-friendliness and interactiveness in the program. Extensive instructive, error and help messages are prompted automatically. As a result, no spreadsheet experience is required in using the program. The advanced three-dimensional spreadsheet feature was used to display the numerical results in a three-dimensional format for easy visualisation. Facilities for graphing and printing of the converged results are also provided. These features, which are not normally achievable by the conventional programming technique, are demonstrated in a numerical example. The program is particularly valuable when fast solutions of physical problems modelled by the Laplace equation are desirable.

Keywords: 3D Laplace equation; numerical simulation; spreadsheet applications; Dirichlet boundary condition; Gauss-Seidel method; successive over-relaxation; SOR method; spreadsheets; modelling.

DOI: 10.1504/IJCAT.1996.062317

International Journal of Computer Applications in Technology, 1996 Vol.9 No.5/6, pp.259 - 271

Published online: 03 Jun 2014 *

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