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Computer Minimal Surfaces on a Transputer Network

Volume 4, Issue 2
Spring 1994
W. Businger, P.-A. Chevalier, N. Droux, and W. Hett
Engineering College of Biel-Bienne, Switzerland

We consider the numerical solution of a simple version of the Plateau problem: given a closed curve in space, find the minimal surface whose boundary equals the given curve. We treat the case of a surface represented as the graph of a function defined on the unit square. We use the symbolic capabilities of Mathematica to formulate a discretized form of the problem and we solve it numerically. Since the numerical calculations are very time-consuming processes, we speed up the computation by using a parallel computer: a transputer network is linked to the workstation running Mathematica. This parallel machine can be called directly from Mathematica by means of a set of special functions we have developed. Moreover, some special tasks, such as the solution of linear systems, can be carried out with optimized parallel programs.

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