Numerical computation of constant mean curvature surfaces using finite elements

TL;DR

This paper introduces an efficient finite element-based numerical method for computing two-dimensional constant mean curvature surfaces, leveraging variational principles and advanced iterative solvers for reliable and fast convergence.

Contribution

It presents a novel finite element approach combined with a preconditioned conjugate gradient method for accurate and efficient computation of constant mean curvature surfaces.

Findings

Reliable convergence demonstrated through gradient flow approach

High computational efficiency achieved with multigrid preconditioning

Applicable to complex surface geometries

Abstract

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, that gives the speed of a direct elliptic multigrid method.