Numerical computation of constant mean curvature surfaces using finite elements

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.

arXiv comment23 pagers, 16 figures, 5 tables. To appear in Classical and quantum Gravity. Version with full resolution graphics available at http://www.mathematik.uni-tuebingen.de/~jan/preprints/

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