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Geometric Computation of Physical Systems

Monday, October 31, 11AM – 12PM
POB 6.304

Eitan Grinspun, Associate Professor, Computer Science, Columbia University

Physical laws govern the behavior of complex mechanical systems. If we can compute the behavior of these systems, then we can study, understand, and make predictions even when direct experimentation is costly, dangerous, or impossible. Yet in practice, an understanding of the physical laws is but one ingredient: efficient simulations must make use of the connection between physical and computational principles. Geometry is the key to developing this connection.

The geometric view of mechanics traces back over centuries. But how this connection shapes computation is a question we are just beginning to understand. We begin by identifying the geometric structures––symmetries and invariants––that succinctly summarize the physics. We develop algorithms by building a corresponding discrete picture from the ground up, mimicking these core structures. The result is a discrete (hence immediately computable) model of the system, and one that "gets the physics right" in a structural sense. The attendant algorithms are simple and efficient, making for rapid adoption, maintenance and debugging, as demonstrated by broad industrial adoption.

We apply this approach to simulating collisions between moving objects, developing an algorithm with three provable guarantees: [geometry:] trajectories have no interpenetrations, [physics:] they obey causality, momentum- and energy-conservation laws, and [computation:] the algorithm completes in finite time. All previous approaches dropped one guarantee in favor of two others; to achieve all three simultaneously we draw on a novel synthesis of asynchronous variational integrators and kinetic data structures.

Short Bio: He was Professeur d'Université Invité at l'Université Pierre et Marie Curie in 2009, a Research Scientist at the Courant Institute of Mathematical Sciences from 2003-2004, and a graduate student at the California Institute of Technology from 1997-2003. He was an NVIDIA Fellow in 2001, an Everhart Distinguished Lecturer in 2003, an NSF CAREER Award recipient in 2007, and is currently an Alfred P. Sloan Research Fellow honored by Popular Science magazine as one of the 2011 "Brilliant Ten."

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