Level set methods to compute minimal surfaces in a medium with exclusions (voids)

Abstract

In [59], periodic minimal surfaces in a medium with exclusions (voids) are constructed and in this paper we present two algorithms for computing these minimal surfaces. The two algorithms use evolution of level sets by mean curvature. The first algorithm solves the governing nonlinear PDE directly and enforces numerically an orthogonality condition that the surfaces satisfy when they meet the boundaries of the exclusions. The second algorithm involves $h$-adaptive finite element approximations of a linear convection-diffusion equation, which has been shown to linearize the governing nonlinear PDE for weighted mean curvature flow.