Abstract

Many moving interface problems evolve complex material
interfaces through topological changes, under velocities
determined by elliptic systems of partial differential
equations. A combination of semi-Lagrangian contouring,
fast distance finding and Ewald summation yields robust
efficient methods for such problems. High-resolution
computations with geometric, Stokes and viscoelastic
flows exhibit merging, anisotropy, faceting, curvature,
dynamic topology and nonlocal interactions.

The interface motion is converted to a contouring
problem with an explicit second-order semi-Lagrangian
advection formula. Grid-free adaptive refinement
resolves complex interface geometry. A fast new
Voronoi-based algorithm computes distances to high-order
interface patches. Elliptic systems are solved by a
fast new locally-corrected boundary integral formulation
derived by Ewald summation and accelerated by new
geometric nonequidistant fast Fourier transforms.