Unstable Periodic Discrete Minimal Surfaces

Konrad Polthier ()
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Konrad Polthier: Technische Universität Berlin, Institut für Mathematik

A chapter in Geometric Analysis and Nonlinear Partial Differential Equations, 2003, pp 129-145 from Springer

Abstract: Summary In this paper we define the new alignment energy for non-conforming triangle meshes, and describes its use to compute unstable conforming discrete minimal surfaces. Our algorithm makes use of the duality between conforming and non-conforming discrete minimal surfaces which was observed earlier. In first experiments the new algorithm allows us the computation of unstable periodic discrete minimal surfaces of high numerical precision. The extraordinary precision of the discrete mesh enables us to compute the index of several triply periodic minimal surfaces.

Keywords: Minimal Surface; Simplicial Surface; Color Plate; Adjacent Triangle; Dirichlet Energy (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55627-2_9

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DOI: 10.1007/978-3-642-55627-2_9

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