Sethian has worked on numerical algorithms for tracking moving interfaces for over three decades, starting with his seminal 1982 work on curve and surface propagation in combustion, and his 1985 work on entropy conditions, curvature, stability of numerical algorithms. This work led to development of the
level-set method in 1988, which was developed jointly with
Stanley Osher. These are numerical algorithms for tracking moving interfaces in complex situations, and have proved instrumental in a wide collection of applications, including semiconductor processing,
fluid mechanics,
medical imaging,
computer graphics, and
materials science. Jointly with D. Adalsteinsson, Sethian then introduced the idea of adaptivity to level set methods, in which computational labor is focused on the evolving front: their Adaptive Narrow Band level set method and its variants are what makes level set methods efficient and practical, and are the most common form of these techniques in practice today. Together with
Andreas Wiegmann, Sethian pioneered the use of the
Level-set method and the
Immersed-interface method in the field of
Topology optimization. Together with
Alexander Vladimirsky, Sethian developed a class of Dijkstra-like ordered upwind methods for solving static
Hamilton–Jacobi equations. In the case of an Eikonal equation, the first method to do so was developed by Jon N. Tsitsiklis using a control-theoretic approach: followed shortly by Sethian's work on high-order finite-difference Dijkstra-like Fast Marching Methods. Ravikanth Malladi and Sethian pioneered the application of these techniques to image segmentation,
Ron Kimmel and Sethian introduced them to robotic navigation and extended them to curved domains, and
Mihai Popovici and Sethian were the first to use them as fast wave solvers in geophysical seismic imaging. Together with Sergey Fomel, Sethian invented Escape Arrival Methods for computing multiple arrivals in wave propagation and geophysical imaging. Algorithms based on the work of Sethian and his colleagues are now commonly used throughout science and engineering. Examples include informing engineers how to design more precise ink jet plotters, allowing physicians to analyze brain and cardiac images, aiding oil companies in locating petroleum reserves, and telling process engineers how to build reliable computer chips. He maintains the "level set methods and fast marching methods" webpage , which is a popular resource for these methods, and provides a variety of applets, movies, and explanations for both the popular and technical audiences. ==Awards==