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Numerical computation of constant mean curvature surfaces using finite elements

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Metzger,  Jan
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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(Preprint), 473KB

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Citation

Metzger, J. (2004). Numerical computation of constant mean curvature surfaces using finite elements. Classical and Quantum Gravity, 21(19), 4625-4646. Retrieved from http://www.iop.org/EJ/abstract/0264-9381/21/19/010.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-51F2-6
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.