Robert Saye studied at the Australian National University and received a Bachelor of Philosophy with First Class Honours (2007), specializing in applied mathematics. He expects to graduate from UC Berkeley with a Ph.D. in applied mathematics in 2013. His research interests include problems involving multiple moving interfaces, development of advanced numerical methods, multi-scale physics, fluid flow and fluid-structure interaction, high performance computing methods and scientific visualization.
R. I. Saye, J. A. Sethian, "Analysis and applications of the Voronoi Implicit Interface Method", Journal of Computational Physics, 2012, 231:6051 - 608, doi: 10.1016/j.jcp.2012.04.004
Robert I. Saye, James A. Sethian, "The Voronoi Implicit Interface Method and Computational Challenges in Multiphase Physics", Milan Journal of Mathematics, 2012, 80:369--379, doi: 10.1007/s00032-012-0187-6
Robert I. Saye, James A. Sethian, "The Voronoi Implicit Interface Method for computing multiphase physics", Proceedings of the National Academy of Sciences, 2011, 108:19498--195, doi: 10.1073/pnas.1111557108
We introduce a numerical framework, the Voronoi Implicit Interface Method for tracking multiple interacting and evolving regions (phases) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.), intricate jump conditions, internal constraints, and boundary conditions. The method works in two and three dimensions, handles tens of thousands of interfaces and separate phases, and easily and automatically handles multiple junctions, triple points, and quadruple points in two dimensions, as well as triple lines, etc., in higher dimensions. Topological changes occur naturally, with no surgery required. The method is first-order accurate at junction points/lines, and of arbitrarily high-order accuracy away from such degeneracies. The method uses a single function to describe all phases simultaneously, represented on a fixed Eulerian mesh. We test the method’s accuracy through convergence tests, and demonstrate its applications to geometric flows, accurate prediction of von Neumann’s law for multiphase curvature flow, and robustness under complex fluid flow with surface tension and large shearing forces.