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

摘要

We calculate the minimal surface bounded by four-sided figures whoseprojection on a plane is a rectangle, starting with the bilinear interpolationand using, for smoothness, the Chebyshev polynomial expansion in ourdiscretized numerical algorithm to get closer to satisfying the zero meancurvature condition. We report values for both the bilinear and improved areas,suggesting a quantitative evaluation of the bilinear interpolation. Ananalytical expression of the Schwarz minimal surface with polygonal boundariesand its 3-dimensional plot is also given.