TY - JOUR
T1 - A phase-field approach for minimizing the area of triply periodic surfaces with volume constraint
AU - Yang, Seong Deog
AU - Lee, Hyun Geun
AU - Kim, Junseok
N1 - 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.
PY - 2010/6
Y1 - 2010/6
N2 - 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.
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.
KW - Constant mean curvature
KW - Phase-field model
KW - Unconditionally gradient stable scheme
UR - http://www.scopus.com/inward/record.url?scp=77950518766&partnerID=8YFLogxK
U2 - 10.1016/j.cpc.2010.02.010
DO - 10.1016/j.cpc.2010.02.010
M3 - Article
AN - SCOPUS:77950518766
VL - 181
SP - 1037
EP - 1046
JO - Computer Physics Communications
JF - Computer Physics Communications
SN - 0010-4655
IS - 6
ER -