Numerical computation of constant mean curvature surfaces using finite elements

摘要

This paper presents a method for computing two-dimensional constant mean curvature surfaces. The method in question uses the variational aspect of the problem to implement an efficient algorithm. In principle, it is a flow-like method in that it is linked to the gradient flow for the area functional, which gives reliable convergence properties. In the background, a preconditioned conjugate gradient method works, which gives the speed of a direct elliptic multigrid method.