Numerical analysis of the Plateau problem by the method of fundamental solutions
The authors are concerned with a fast and accurate algorithm for finding the number of minimal surfaces sharing the same boundary data. They use the method of fundamental solutions (MFS) which, unlike the previous methods, does not imply the use of a mesh generation. They build a practical algorithm based on Nesterov's accelerated gradient descent [\textit{Yu. E. Nesterov}, Sov. Math., Dokl. 27, 372--376 (1983; Zbl 0535.90071); translation from Dokl. Akad. Nauk SSSR 269, 543--547 (1983)] and show its capabilities by carrying out some numerical experiments. The paper ends with an algorithm for computing multiple minimal surfaces based on the numerical scheme introduced in this paper.
scientific article; zbMATH DE number 7870823
scientific article