# Robert Saye

## Bio

Robert Saye studied at the Australian National University and received a Bachelor of Philosophy with First Class Honours (2007), specializing in applied mathematics. He graduated from UC Berkeley with a Ph.D. in applied mathematics in 2013 and held a Luis W. Alvarez Postdoctoral Fellow at Berkeley Lab from 2013 to 2017. He is now a staff member of the Mathematics Group at Berkeley Lab. His research interests include development of advanced and open source numerical algorithms for implicit interface methods, high-order accurate implicit mesh discontinuous Galerkin methods for fluid-interface dynamics, multi-scale multi-physics, fluid flow and fluid-structure interaction, and high performance computing. Current research projects include a HPC4Mfg project in collaboration with PPG Industries, Inc., involving state of the art computer modeling of rotary bell atomization for industrial spray painting, as well as multiphase Stokes solvers, multigrid methods, implicit mesh DG methods, and high-order accurate level set methods.

For more information on Robert's research activities, visit his research page

## Journal Articles

### ML Minion, RI Saye, "Higher-order temporal integration for the incompressible Navier–Stokes equations in bounded domains", Journal of Computational Physics, 2018, 375:797--822, doi: 10.1016/j.jcp.2018.08.054

### Daniel Fortunato, Chris H. Rycroft, Robert Saye, "Efficient operator-coarsening multigrid schemes for local discontinuous Galerkin methods", arXiv:1808.05320, August 16, 2018,

### Robert Saye, "Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid-structure interaction, and free surface flow: Part I", Journal of Computational Physics, September 1, 2017,

### Robert Saye, "Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid-structure interaction, and free surface flow: Part II", Journal of Computational Physics, September 1, 2017,

### Robert Saye, James Sethian, "Multiscale modelling of evolving foams", Journal of Computational Physics, June 15, 2016, doi: 10.1016/j.jcp.2016.02.077

### Robert Saye, "Interfacial gauge methods for incompressible fluid dynamics", Science Advances, June 10, 2016,

### Robert Saye, "High-Order Quadrature Methods for Implicitly Defined Surfaces and Volumes in Hyperrectangles", SIAM Journal on Scientific Computing, April 23, 2015, doi: 10.1137/140966290

### Robert Saye, "High-order methods for computing distances to implicitly defined surfaces", Communications in Applied Mathematics and Computational Science, May 17, 2014, doi: 10.2140/camcos.2014.9.107

### Robert Saye, "An algorithm to mesh interconnected surfaces via the Voronoi interface", Engineering with Computers, October 6, 2013, doi: 10.1007/s00366-013-0335-9

### Robert Saye, James Sethian, "Multiscale Modeling of Membrane Rearrangement, Drainage, and Rupture in Evolving Foams", Science, May 10, 2013, doi: 10.1126/science.1230623

### 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.