Computer Minimal Surfaces on a Transputer Network
Volume 4, Issue 2
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.