Towards 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 $L^\infty$-error analysis for mean curvature. Each of the approximate solutions in our scheme is a smooth surface, which is a significant difference from previous studies that required mesh division.
翻译:为了确定与边界几何相同边界的最小表面数量,我们提出了一个高速和精确的数字方法。我们的数字方法以基本解决办法的方法为基础。我们建立了对Drichlet能源的趋同分析,和对平均曲线的$Linfty$-error分析。我们方案中的每一种近似解决办法都是平滑的表面,这与以前需要网状分割的研究有很大不同。