A variational level set approach to multiphase motion
Journal of Computational Physics
Journal of Computational Physics
A topology-preserving level set method for shape optimization
Journal of Computational Physics
A variational level set method for the topology optimization of steady-state Navier-Stokes flow
Journal of Computational Physics
Parametric polynomial minimal surfaces of degree six with isothermal parameter
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Level-set based topology optimization for electromagnetic dipole antenna design
Journal of Computational Physics
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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.