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Zbl 1216.65021
Yang, Seong-Deog; Lee, Hyun Geun; Kim, Junseok
A phase-field approach for minimizing the area of triply periodic surfaces with volume constraint. (English)
[J] Comput. Phys. Commun. 181, No. 6, 1037-1046 (2010). ISSN 0010-4655

Summary: We present an accurate and efficient algorithm to generate constant mean curvature surfaces with volume constraint using a phase-field model. We implement our proposed algorithm using an unconditionally gradient stable nonlinear splitting scheme. Starting from the periodic nodal surface approximation to minimal surfaces, we can generate various constant mean curvature surfaces with given volume fractions. We generate and study the Schwarz primitive, Schwarz diamond, and Schoen gyroid surfaces with various volume fractions. This technique for generating constant mean curvature surfaces can be used to design biomedical scaffolds with optimal mechanical and biomorphic properties.

MSC 2000:: *65D17 Computer aided design (modeling of curves and surfaces)

Keywords: phase-field model; unconditionally gradient stable scheme; constant mean curvature surfaces; Schwarz primitive surface; Schwarz diamond surface; numerical and graphical examples; algorithm; minimal surface; Schoen gyroid surfaces

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