Location: Gilman Hall Room 50
Title: Adaptive methods for the simulation of diffusion in complex geometries
Abstract: We will review the state of the art in integral equation methods for the solution of the heat equation in moving geometries. With suitable fast algorithms, such methods achieve optimal complexity and, in the homogeneous case, require the discretization of the space-time boundary alone. They achieve high order accuracy with suitable quadratures and are straightforward to implement adaptively in space-time. We will discuss applications to biophysical modeling, reaction-diffusion systems, and computational fluid dynamics.
Bio: Leslie Greengard received his B.A. degree in Mathematics from Wesleyan University in 1979, and his M.D. and Ph.D. degrees from Yale University in 1987. From 1987-1989 he was an NSF Postdoctoral Fellow at Yale University and at the Courant Institute of Mathematical Sciences, NYU, where he is a member of the faculty. He served as the Director of the Courant Institute from 2006-2011. He is presently also Director of the Center for Computational Mathematics at the Flatiron Institute, a division of the Simons Foundation. Greengard, together with V. Rokhlin, developed the Fast Multiple Method (FMM) for problems in gravitation, electrostatics and electromagnetics. Much of Greengard’s research has been aimed at the development of high-order accurate integral equation methods for partial differential equations in complex geometry. He is a member of the National Academy of Sciences, the National Academy of Engineering and the American Academy of Arts and Sciences.
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