Numerical analysis of the Plateau problem by the method of fundamental solutions
type: Item
instance of: scholarly article
title: Numerical analysis of the Plateau problem by the method of fundamental solutions
zbMATH Open document ID: 1548.65389
author: Koya Sakakibara
author: Yuuki Shimizu
published in: Journal of Scientific Computing
publication date: 2024-06-25T00:00:00Z
review text: 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.
reviewed by: Calin Ioan Gheorghiu
Mathematics Subject Classification ID: 65N80
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 7870823
zbMATH Keywords: Plateau problem
zbMATH Keywords: minimal surfaces
zbMATH Keywords: Laplace equation
zbMATH Keywords: Dirichlet boundary condition
MaRDI profile type: Publication
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DOI: 10.1007/S10915-024-02551-Z
description: scientific article; zbMATH DE number 7870823