A phase-field approach for minimizing the area of triply periodic surfaces with volume constraint

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57 Citations (Scopus)


In this paper, 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 (P), Schwarz diamond (D), and Schoen gyroid (G) 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.

Original languageEnglish
Pages (from-to)1037-1046
Number of pages10
JournalComputer Physics Communications
Issue number6
Publication statusPublished - 2010 Jun

Bibliographical note

Funding Information:
S.-D. Yang was supported in part by a research grant from the College of Science at Korea University . J.S. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2009-0086388 ). The authors are grateful to Professor Do Wan Kim for his suggestions, comments, and valuable inputs of the manuscript.


  • Constant mean curvature
  • Phase-field model
  • Unconditionally gradient stable scheme

ASJC Scopus subject areas

  • Hardware and Architecture
  • General Physics and Astronomy


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