Organizer and Course Instructor
James Sethian is Professor of Mathematics at the University of California at Berkeley, and Department Head of the Mathematics Department at the Lawrence Berkeley National Laboratory.
Manufacturing microchips, locating heart walls in MRI scans, sharpening noisy images, tracking flames in turbulent flows, locating geodesics on surfaces, finding optimal paths in robotic navigation and determining multiple arrivals in wave propagation all share a common concern, namely tracking moving interfaces. This is an introductory course in level set techniques and Ordered Upwind Methods. These techniques are currently in use in a wide collection of theoretical engineering, and industrial applications, including the geometry of moving surfaces, medical imaging, the manufacture of semiconductor devices, and fluid mechanics.
This course is an equal blend of theory, algorithms, and applications. It will highlight robust and efficient algorithms for the above applications, as well as many others. Along the way, we will introduce and cover a variety of related topics necessary to build these algorithms, including approximation of viscosity solutions to partial differential equations, the numerical technology from hyperbolic conservation laws, level set methods for propagating interfaces and methods for stationary Hamilton-Jacobi equations. We will especially focus on some new emerging topics which are ripe for current research, including problems in fast methods for general and optimal control, high frequency asymptotics and multiple arrivals in optics and wave propagation, anisotropic front propagation, and applications in CAD/CAM and graphics.
Who Should Attend?
The course is aimed at a general introductory level. The intended audience is mathematicians, applied scientists, practicing engineers, computer graphic artists, and anyone interested in the evolution of boundaries and interfaces.
There are no formal prerequisites; this course is a condensation of a one-semester course at Berkeley on level set methods that is attended by people from across the range of sciences and engineering disciplines. Some emphasis will be placed on real algorithms, hence a basic familiarity with numerical analysis is helpful, but not required.