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This article offers a comprehensive overview of the results obtained through numerical methods in solving the minimal surface equation, along with exploring the applications of minimal surfaces in science, technology, and architecture. The content is enriched with practical examples highlighting the diverse applications of minimal surfaces.

The method for calculating the specific conductivity tensor of an anisotropically conductive medium, proposed in this paper, distinguishes itself by the simplicity of physical measurements: it suffices to make an equally thick rectangle-shaped sample with four electrodes fixed on its sides and to take various measurements of current intensity and differences of potentials. The necessary mathematical calculations can be promptly performed, even without using a complex computing technique. The accuracy of the results obtained depends on the dimensions of the sample and on the ratios of the conductivity tensor components.

In this paper we consider the numerical solution of the large system of nonlinear differential equations. We assume that the system simulates the semiconductor circuit. We apply the well known event driven techniques to get some approximation of solution fast. We extend those techniques by considering pairs of nodes, instead of single nodes, as usual. The “pairwise” solution is more efficient in tightly coupled circuits. The improvement of efficiency of solution is important optimizing the parameters of circuits. In many cases we need the global optimization of equation parameters. Then, the modeling speed could be the main factor of successful application.