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

Seong Deog Yang; Hyun Geun Lee; Junseok Kim

doi:10.1016/j.cpc.2010.02.010

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

Seong Deog Yang, Hyun Geun Lee, Junseok Kim

Research output: Contribution to journal › Article › peer-review

59 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	1037-1046
Number of pages	10
Journal	Computer Physics Communications
Volume	181
Issue number	6
DOIs	https://doi.org/10.1016/j.cpc.2010.02.010
Publication status	Published - 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.

Keywords

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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10.1016/j.cpc.2010.02.010

Cite this

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

abstract = "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.",

keywords = "Constant mean curvature, Phase-field model, Unconditionally gradient stable scheme",

author = "Yang, {Seong Deog} and Lee, {Hyun Geun} and Junseok Kim",

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. ",

year = "2010",

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AB - 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.

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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