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Mathematics Group

James Sethian

James A. Sethian
Mathematics Dept. Head; CAMERA Director; Mathematics Group Lead
Senior Faculty Scientist
Phone: +1 510 486 6006
Fax: +1 510 486 6199

James Sethian is a professor of mathematics at UC Berkeley, as well as a Berkeley Lab Senior Faculty Scientist, Mathematics Department Head, Group Lead of the Mathematics Group, and Director of the CAMERA Center. He received his Ph.D. in applied mathematics from UC Berkeley in 1982. Sethian continued his research with an NSF postdoc fellowship at the Courant Institute of Mathematics, and then returned to Berkeley as an assistant professor in 1985. He now holds the James H. Simons Chair in Mathematics at UC Berkeley.

Sethian is the author of many scientific articles and books and serves as an associate editor on several journals. He is a member of the National Academy of Engineering and the recipient of numerous prizes and awards. His awards include the Norbert Wiener Prize in Applied Mathematics, which is awarded jointly by the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM), for his representations of the motion of curves, surfaces, interfaces, and wave fronts, and for his applications of mathematical and computational ideas to scientific problems. He was also awarded the 2011 Pioneer Prize, which is awarded by the International Council for Industrial and Applied Mathematics (ICIAM) for his contributions to applications in imaging and shape recovery in medicine, geophysics, tomography, and drop dynamics in inkjets. Sethian works on the theory, algorithms, and applications of moving interfaces as they are applied to problems in fluid mechanics, materials science, and industrial processes, such as inkjet printing, semiconductor fabrication, biological and medical imaging, and geophysics.

Journal Articles

Benedikt J Daurer, Hari Krishnan, Talita Perciano, Filipe RNC Maia, David A Shapiro, James A Sethian, Stefano Marchesini, "Nanosurveyor: a framework for real-time data processing", Advanced structural and chemical imaging, 2017, 3:7,

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

J Donatelli, M Haranczyk, A Hexemer, H Krishnan, X Li, L Lin, F Maia, S Marchesini, D Parkinson, T Perciano, D Shapiro, D Ushizima, C Yang, JA Sethian, "CAMERA: The Center for Advanced Mathematics for Energy Research Applications", Synchrotron Radiation News, 2015, 28:4--9, doi: 10.1080/08940886.2015.1013413

Richard L. Martin, Prabhat, David D. Donofrio, James A. Sethian & Maciej Haranczyk, "Accelerating Analysis of void spaces in porous materials on multicore and GPU platforms", International Journal of High Performance Computing Applications, February 5, 2012, 26:347-357,

Developing computational tools that enable discovery of new materials for energy-related applications is a challenge. Crystalline porous materials are a promising class of materials that can be used for oil refinement, hydrogen or methane storage as well as carbon dioxide capture. Selecting optimal materials for these important applications requires analysis and screening of millions of potential candidates. Recently, we proposed an automatic approach based on the Fast Marching Method (FMM) for performing analysis of void space inside materials, a critical step preceding expensive molecular dynamics simulations. This breakthrough enables unsupervised, high-throughput characterization of large material databases. The algorithm has three steps: (1) calculation of the cost-grid which represents the structure and encodes the occupiable positions within the void space; (2) using FMM to segment out patches of the void space in the grid of (1), and find how they are connected to form either periodic channels or inaccessible pockets; and (3) generating blocking spheres that encapsulate the discovered inaccessible pockets and are used in proceeding molecular simulations. In this work, we expand upon our original approach through (A) replacement of the FMM-based approach with a more computationally efficient flood fill algorithm; and (B) parallelization of all steps in the algorithm, including a GPU implementation of the most computationally expensive step, the cost-grid generation. We report the acceleration achievable in each step and in the complete application, and discuss the implications for high-throughput material screening.

M. Garzon, L. J. Gray, J. A. Sethian, "Axisymmetric boundary integral formulation for a two-fluid system", International Journal for Numerical Methods in Fluids, 2012, 69:1124--1134, doi: 10.1002/fld.2633

Maria Garzon, L. J. Gray, James A. Sethian, "Droplet and bubble pinch-off computations using level sets", Journal of Computational and Applied Mathematics, 2012, 236:3034--3041, doi: 10.1016/

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/

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

Maciej Haranczyk, Richard L. Martin, Prabhat, James A. Sethian & E. Wes Bethel, "Computational Approaches for the High-Throughput Analysis of Porous materials for Energy related applications", Scientific Discovery through Advanced Computing 2011, 2011,

M. Garzon, L. J. Gray, J. A. Sethian, "Simulation of the droplet-to-bubble transition in a two-fluid system", Phys. Rev. E, 2011, 83:046318, doi: 10.1103/PhysRevE.83.046318

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.

C. Rycroft, D. M. Ushizima, R. Saye, C. M. Ghajar, J. A. Sethian, "Building a physical cell simulation and comparing with confocal microscopy", Bay Area Physical Sciences - Oncology Center (NCI) Meeting 2010, UCSF Medical Sciences, September 2010,

Maciej Haranczyk, James A. Sethian, "Automatic Structure Analysis in High-Throughput Characterization of Porous Materials", Journal of Chemical Theory and Computation, 2010, 6:3472-3480, doi: 10.1021/ct100433z

M. Garzon, L. J. Gray, J. A. Sethian, "Numerical simulation of non-viscous liquid pinch-off using a coupled level set-boundary integral method", Journal of Computational Physics, 2009, 228:6079--6106, doi: 10.1016/

M. Haranczyk, J. A. Sethian, "Navigating molecular worms inside chemical labyrinths", Proceedings of the National Academy of Sciences, 2009, 106:21472-2147, doi: 10.1073/pnas.0910016106

Predicting whether a molecule can traverse chemical labyrinths of channels, tunnels, and buried cavities usually requires performing computationally intensive molecular dynamics simulations. Often one wants to screen molecules to identify ones that can pass through a given chemical labyrinth or screen chemical labyrinths to identify those that allow a given molecule to pass. Because it is impractical to test each molecule/labyrinth pair using computationally expensive methods, faster, approximate methods are used to prune possibilities, “triaging” the ability of a proposed molecule to pass through the given chemical labyrinth. Most pruning methods estimate chemical accessibility solely on geometry, treating atoms or groups of atoms as hard spheres with appropriate radii. Here, we explore geometric configurations for a moving “molecular worm,” which replaces spherical probes and is assembled from solid blocks connected by flexible links. The key is to extend the fast marching method, which is an ordered upwind one-pass Dijkstra-like method to compute optimal paths by efficiently solving an associated Eikonal equation for the cost function. First, we build a suitable cost function associated with each possible configuration, and second, we construct an algorithm that works in ensuing high-dimensional configuration space: at least seven dimensions are required to account for translational, rotational, and internal degrees of freedom. We demonstrate the algorithm to study shortest paths, compute accessible volume, and derive information on topology of the accessible part of a chemical labyrinth. As a model example, we consider an alkane molecule in a porous material, which is relevant to designing catalysts for oil processing.

Conference Papers

T Perciano, DM Ushizima, EW Bethel, YD Mizrahi, D Parkinson, JA Sethian, "Reduced-complexity image segmentation under parallel Markov Random Field formulation using graph partitioning", Proceedings - International Conference on Image Processing, ICIP, 2016, 2016-Aug:1259--1263, doi: 10.1109/ICIP.2016.7532560

Ushizima, D.M., Parkinson, D., Nico, P., Ajo-Franklin, J., Macdowell, A., Kocar, B., Bethel E.W, Sethian J.A., "Statistical segmentation and porosity quantification of 3D x-ray microtomography", XXXIV Applications of Digital Image Processing: Proceeding of SPIE 2011, San Diego, CA, USA, August 2011,

M. Garzon, L. Gray, J. A. Sethian, "Potential fluid flow computations involving free boundaries with topological changes", Proc. International Conference on Computational and Mathematical Methods on Science and Engineering, Gijón, Spain, CMMSE, 2009, 2:521--531,


Ushizima, D.M., Weber, G., Morozov, D., Bethel, W., Sethian, J.A., "Algorithms for Microstructure Description applied to Microtomography", Carbon Cycle 2.0 Symposium, February 10, 2012,

Richard L. Martin, Maciej Haranczyk, Prabhat and James A. Sethian, "PDE-based analysis of void space of porous materials on multicore CPUs", Manycore and Accelerator-based High-performance Scientific Computing 2011 (Berkeley, CA), January 24, 2011,


Maciej Haranczyk, Chris H. Rycroft & James A. Sethian, Empty Space and New Materials: Computational Tools for Porous Materials, SIAM News, October 18, 2011,

Crystalline porous materials are some of the most important synthetic products ever made...