Publications
https://orcid.org/0000-0001-7256-6941
Journal Articles
- 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 pdf
- 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 pdf
- 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 pdf
- R. I. Saye, High-order quadrature on multi-component domains implicitly defined by multivariate polynomials, Journal of Computational Physics, 448, 110720 (2022). Link pdf
- 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 pdf
- 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 pdf
- 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 pdf
- 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 pdf
- 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
- R. I. Saye, Interfacial gauge methods for incompressible fluid dynamics, Science Advances, 2(6), 1–14 (2016). Link pdf
- R. I. Saye and J. A. Sethian, Multiscale modelling of evolving foams, Journal of Computational Physics, 315, 273–301 (2016). Link pdf
- 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 pdf
- 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 pdf
- 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 pdf
- R. I. Saye, An algorithm to mesh interconnected surfaces via the Voronoi interface, Engineering with Computers, 31(1), 123–139 (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 pdf
- R. I. Saye and J. A. Sethian, The Voronoi Implicit Interface Method and Computational Challenges in Multiphase Physics, Milan Journal of Mathematics, 80(2), 369–379 (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 pdf
Book Chapters
- M. Garzon, R. I. Saye, and J. A. Sethian, Efficient Algorithms for Tracking Moving Interfaces in Industrial Applications: Inkjet Plotters, Electrojetting, Industrial Foams, and Rotary Bell Painting, in Chacón Rebollo, T., Donat, R., Higueras, I. (eds), Recent Advances in Industrial and Applied Mathematics, 1, 173–194 (2022). Link pdf
- R. I. Saye and J. A. Sethian, A review of level set methods to model interfaces moving under complex physics: Recent challenges and advances, in A. Bonito and R. H. Nochetto (eds.), Geometric Partial Differential Equations - Part I, Handbook of Numerical Analysis, 21, 509–554 (2020), Link
In Proceedings
- R. I. Saye and J. A. Sethian, New Interface Methods for Tracking Multiphase Physics, in F. Ancona, A. Bressan, P. Marcati, A. Marson (eds.) Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the 14th International Conference on Hyperbolic Problems (Padova, 2012). AIMS Series on Applied Mathematics 8, 81–87 (2014)
- R. I. Saye and J. A. Sethian, Voronoi Implicit Interfaces: Method and Applications, in C. M. Elliot, Y. Giga, M. Hinze, V. Styles (eds.) Interfaces and Free Boundaries: Analysis, Control and Simulation. Oberwolfach Reports 10(1), 867–950 (2013) Link
- R. I. Saye and J. A. Sethian, Applications of the Voronoi Implicit Interface Method, in M. Hintermüller, G. Leugering, J. Sokolowski (eds.) Mini-Workshop: Geometries, Shapes and Topologies in PDE-based Applications. Oberwolfach Reports 9(4), 3375–3415 (2012) Link
Journal Articles (Misc.)
- R. Saye, On two conjectures concerning the ternary digits of powers of two, Journal of Integer Sequences, 25(3), 1–9 (2022). Link pdf
PhD Thesis
- R. I. Saye, The Voronoi Implicit Interface Method with Applications to Multiphase Fluid Flow and Multiscale Modelling of Foam Dynamics, May 2013, University of California, Berkeley. Link pdf (52MB)
News Articles
- New Math Captures Fluids in Unprecedented Detail, Advanced Scientific Computing Research (ASCR), U.S. Department of Energy Office of Science, 26 Aug 2016
- New Mathematics Accurately Captures Liquids and Surfaces Moving in Synergy, Berkeley Lab Newscenter, 10 Jun 2016
- wyborcza Nauka dla każdego ("Science for everyone"), a Polish newspaper, 16 Jun 2015
- 2013 Visualization Challenge, Honorable Mention, Science 343(6171) (2014), 7 Feb 2014
- Computing Sciences Supported Research Named Among 2013's Best, Berkeley Lab CS News, 20 Dec 2013
- Our favourite pictures of 2013, IOP Physics World, 18 Dec 2013
- Multiscale Modeling of Foams, SIAM News, 1 Nov 2013
- Press related to my Science paper on multi-scale modelling of foam dynamics, May 2013:
- Heady mathematics: Describing popping bubbles in a foam, Berkeley Newscenter
- Mathematics of Popping Bubbles in a Foam, LBL Newscenter
- ScienceShot: The Life Cycle of a Bubble, Science AAAS
- Can't Pop This: Bubble Scientists Reveal the Physics of Soap, KQED Science
- Revealed! The Mysteries of Bubbles – and Clouds Too, Time.com – Science & Space
- When one bubble pops, why do others form around it? Unlocking a bubble mystery, The Washington Post
- Pinning down the physics of bubbles, Los Angeles Times
- Physics Get Frothy as Mathematicians Dissect Mister Bubble [Video], Scientific American
- Unlocking secret lives of bubbles yields perfect foam, NewScientist – Physics & Math
- Working Up a Lather, AMS Mathematical Moments
- Geplatzte Schäume, Wissen & Forschen, page 24, Der Tagesspiegel
- Berkeley Lab Mathematicians Win Cozzarelli Prize, LBL Newscenter, Feb 2012