Surface Area Minimization of Triply-Periodic Surfaces with Volume Fraction Constratin Via the Level Set Method

SIAM Computational Science & Engineering Conference, Costa Mesa, CA, February 21, 2007



We present a variational level set approach for theoretically and computationally studying triply-periodic surfaces that minimize the total surface area when there is a constraint on the volume fraction of the regions that the surface separates. We demonstrate that optimal surfaces are precisely those possessing constant mean curvature. We then study the optimality of several well-known minimal surfaces and explore the properties of optimal surfaces when the volume fractions of the two phaess are not equal. Parallel LSMLIB is used to handle the computational cost of the three-dimensional shape optimization problem.