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. Discrete geometry offers one avenue to develop this
connection.
A physics problem is also a geometry problem. Exploration of this
connection traces back over decades and indeed centuries, at least in
a classical sense; but how this connection shapes computation is a
question we are just beginning to understand. Our research group
investigates physical simulation techniques by following a research
process structured around the exploration of this connection.
Our process begins with the smooth setting, seeking out geometric
structures, such as symmetries or invariants, that succinctly capture
physical behavior; these constitute axioms of our mathematical model
for the system. Rather than discretizing this model in a classical
numerical sense (e.g., using finite element, spline, or wavelet
bases) — an approach that might discard the identified structures
— we
build up the discrete picture from the ground up, mimicking the axioms
and development of the smooth setting. The result is a discrete (hence
immediately computable) model of the system, and in particular one
preserves the important structures. The corresponding algorithms are
simple and efficient; their simplicity make them easy to adopt,
maintain and debug. Our algorithms are used primarily in the feature
film, geometric modeling, and consumer sectors of industry.
BIO:
Eitan Grinspun is Assistant Professor of Computer Science at Columbia
University in the City of New York. He was 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 is interested in simulation, geometry processing, and
scientific computing. He was an NVIDIA Fellow in 2001, an Everhart
Distinguished Lecturer in 2003, and an NSF CAREER Award recipient in
2007.
Joint work with graduate students Miklós Bergou, Akash Garg, Rony
Goldenthal, David Harmon, Saurabh Mathur, Breannan Smith, Etienne
Vouga, and Profs. Basile Audoly, Mathieu Desbrun, Peter Schröder,
Rasmus Tamstorf, Max Wardetzky and Denis Zorin.
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