Publications
https://orcid.org/0000-0001-7256-6941
Preprints
- R. Saye, A comparative study of efficient multigrid solvers for high-order local discontinuous Galerkin methods: Poisson, elliptic interface, and multiphase Stokes problems, 2024, arXiv:abs/2412.12506
Journal Articles (Published)
- 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 pdf
- 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. Saye, On two conjectures concerning the ternary digits of powers of two, Journal of Integer Sequences, 25(3), 1–9 (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
Conference Proceedings
- J. A. Sethian and R. I. Saye, Modeling of Paint Atomization in Rotary Bell Spray Painting, in C. Elliott, H. Garcke, B. Niethammer, G. Simonett (orgs.) Interfaces, Free Boundaries and Geometric Partial Differential Equations. Oberwolfach Reports 8, 49–52 (2024) Link
- 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
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