Numerical Calculation of a Minimal Surface Using Bilinear Interpolations and Chebyshev Polynomials

2006/08/17 by Sadataka Furui, Furui, Sadataka, Bilal Masud +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Electromagnetic Scattering and Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0608043

21 pages, 13 figures, An analytical expression of the Schwarz minimal surface with polygonal boundaries and its 3-dimensional plot is added

openalex publication_date 2006/08/17 · arxiv created 2007/01/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We calculate the minimal surface bounded by four-sided figures whose projection on a plane is a rectangle, starting with the bilinear interpolation and using, for smoothness, the Chebyshev polynomial expansion in our discretized numerical algorithm to get closer to satisfying the zero mean curvature condition. We report values for both the bilinear and improved areas, suggesting a quantitative evaluation of the bilinear interpolation. An analytical expression of the Schwarz minimal surface with polygonal boundaries and its 3-dimensional plot is also given.

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