Numerical Analysis of the Plateau Problem by the Method of Fundamental Solutions

Toward identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our numerical scheme is based on the method of fundamental solutions. We establish the convergence analysis for Dirichlet en...

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Bibliographic Details
Published in:Journal of scientific computing 2024-07, Vol.100 (1), p.2, Article 2
Main Authors: Sakakibara, Koya, Shimizu, Yuuki
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Boundary value problems
Computational Mathematics and Numerical Analysis
Dirichlet problem
Error analysis
Finite element analysis
Finite volume method
Geometry
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Mesh generation
Minimal surfaces
Numerical analysis
Optimization
Theoretical
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Summary:Toward identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our numerical scheme is based on the method of fundamental solutions. We establish the convergence analysis for Dirichlet energy and L ∞ -error analysis for mean curvature. Each of the approximate solutions in our scheme is a smooth surface, a significant difference from previous studies that required mesh generation.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-024-02551-z