TY - JOUR

T1 - A variational level set approach for surface area minimization of triply-periodic surfaces

AU - Jung, Y.

AU - Chu, K. T.

AU - Torquato, S.

N1 - Funding Information:
Y.J. and S.T. gratefully acknowledge the support of the Air Force Office for Scientific Research under grant number F49620-03-1-0406. K.T.C. gratefully acknowledges the support of the National Science Foundation through grant DMR-0502946. The authors thank H.T. Davis for his help in our attempts to obtain the original data for the plots from [10] , D.J. Srolovitz for his encouragement and support in the development of the LSMLIB parallel level set method software library, A. Donev for helpful comments on the manuscript, and W. Wischer for his technical support in carrying out the parallel computations.

PY - 2007/5/1

Y1 - 2007/5/1

N2 - In this paper, we study triply-periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a theoretical characterization of and a numerical algorithm for computing these surfaces. We use our theoretical and computational formulation to study the optimality of the Schwartz primitive (P), Schwartz diamond (D), and Schoen gyroid (G) surfaces when the volume fractions of the two phases are equal and explore the properties of optimal structures when the volume fractions of the two phases are not equal. Due to the computational cost of the fully three-dimensional shape optimization problem, we implement our numerical simulations using a parallel level set method software package.

AB - In this paper, we study triply-periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a theoretical characterization of and a numerical algorithm for computing these surfaces. We use our theoretical and computational formulation to study the optimality of the Schwartz primitive (P), Schwartz diamond (D), and Schoen gyroid (G) surfaces when the volume fractions of the two phases are equal and explore the properties of optimal structures when the volume fractions of the two phases are not equal. Due to the computational cost of the fully three-dimensional shape optimization problem, we implement our numerical simulations using a parallel level set method software package.

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U2 - 10.1016/j.jcp.2006.10.007

DO - 10.1016/j.jcp.2006.10.007

M3 - Article

AN - SCOPUS:33947160127

VL - 223

SP - 711

EP - 730

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

ER -