  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.
