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Mathematics Group

Robert Saye

Robert Saye 250x250
Robert Saye
Research Scientist
Phone: 510-486-5296


Robert Saye is a research scientist in the Mathematics Group at LBNL. He held a Luis W. Alvarez Postdoctoral Fellow at Berkeley Lab from 2013 to 2017, received his Ph.D. in Applied Mathematics from UC Berkeley in 2013, and Bachelor of Philosophy with First Class Honours (2007) from the Australian National University in 2008. He is an awardee of the prestigious U.S. Department of Energy Early Career Research Program, 2021-2026. Other awards include the 2011 Cozarelli Prize (joint with co-author James Sethian) from the Proceedings of the National Academy of Science, the 2013 Bernard Friedman Memorial Prize in Applied Mathematics from UC Berkeley, and 2007 University Medal in Mathematics from the Australian National University.

Robert's research interests include numerical methods for multi-phase multi-physics in dynamic and extremely complex geometry; numerical methods for interface dynamics; high-order algorithms; and high performance computing. Examples include high-order discontinuous Galerkin (DG) methods; high-order algorithms for level set methods and implicitly-defined geometry; scalable and fast multigrid algorithms for elliptic interface problems and multi-phase Stokes problems; and high-order quadrature algorithms in complex geometry.

He develops and maintains the open-source code Algoim, a collection of high-order accurate numerical methods and C++ algorithms for working with implicitly-defined geometry and level set methods.

Selected publications are listed below. For a comprehensive list, and more information on Robert's research activities, visit his research page

Selected Publications

  • L. P. Corcos, R. I. Saye, and J. A. Sethian, A hybrid finite difference level set–implicit mesh discontinuous Galerkin method for multi-layer coating flows, Journal of Computational Physics, 507, 112960 (2024). Link
  • Robert I. Saye, A connected component labeling algorithm for implicitly defined domains, Communications in Applied Mathematics and Computational Science, 18(1), 29–54 (2023). Link
  • Robert I. Saye, James A. Sethian, Brandon Petrouskie, Aaron Zatorsky, Xinyu Lu, and Reza Rock, Insights from high-fidelity modeling of industrial rotary bell atomization, Proceedings of the National Academy of Sciences, 120(4), e2216709120 (2023). Link
  • V. Gulizzi and R. Saye, Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods, Computer Methods in Applied Mechanics and Engineering, 395, 114971 (2022). Link
  • R. I. Saye, High-order quadrature on multi-component domains implicitly defined by multivariate polynomials, Journal of Computational Physics, 448, 110720 (2022). Link
  • R. I. Saye, Fast multigrid solution of high-order accurate multiphase Stokes problems, Communications in Applied Mathematics and Computational Science, 15(2), 147–196 (2020). Link
  • R. Saye, Efficient Multigrid Solution of Elliptic Interface Problems using Viscosity-Upwinded Local Discontinuous Galerkin Methods, Communications in Applied Mathematics and Computational Science, 14(2), 247–283 (2019). Link
  • D. Fortunato, C. H. Rycroft, and R. Saye, Efficient Operator-Coarsening Multigrid Schemes for Local Discontinuous Galerkin Methods, SIAM Journal on Scientific Computing, 41(6), A3913–A3937 (2019). Link
  • M. L. Minion and R. I. Saye, Higher-order temporal integration for the incompressible Navier-Stokes equations in bounded domains, Journal of Computational Physics, 375, 797–822 (2018). Link
  • R. I. 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, Journal of Computational Physics
    • Part I, 344, 647–682 (2017). Link
    • Part II, 344, 683–723 (2017). Link
  • R. I. Saye, Interfacial gauge methods for incompressible fluid dynamics, Science Advances, 2(6), 1–14 (2016). Link
  • R. I. Saye and J. A. Sethian, Multiscale modelling of evolving foams, Journal of Computational Physics, 315, 273–301 (2016). Link
  • R. I. Saye, High-Order Quadrature Methods for Implicitly Defined Surfaces and Volumes in Hyperrectangles, SIAM Journal on Scientific Computing, 37(2), A993–A1019 (2015). Link
  • R. I. Saye and J. A. Sethian, The Life Cycle of a Bubble Cluster: Insight from Mathematics, Algorithms, and Supercomputers – 2013 NSF and Science journal International Science and Engineering Visualization Challenge, Science, 343(6171), 700–614 (2014). Link
  • R. I. Saye, High-order methods for computing distances to implicitly defined surfaces, Communications in Applied Mathematics and Computational Science, 9(1), 107–141 (2014). Link
  • R. I. Saye and J. A. Sethian, Multiscale Modeling of Membrane Rearrangement, Drainage, and Rupture in Evolving Foams, Science, 340(6133), 720–724 (2013). Link
  • R. I. Saye and J. A. Sethian, Analysis and applications of the Voronoi Implicit Interface Method, Journal of Computational Physics, 231(18), 6051–6085 (2012). Link
  • R. I. Saye and J. A. Sethian, The Voronoi Implicit Interface Method for computing multiphase physics, Proceedings of the National Academy of Sciences, 108(49), 19498–19503 (2011). Link