Speaker: Peter Schröder , CalTech
Date: Friday, October 14 2005
Relevant URL: http://www.cs.caltech.edu/~ps/
Modeling the shape and physical behavior of the world around us has a long and illustrious history. In fact much of classical differential geometry came about through the study of mathematical models for physical objects and their properties. With the advent of computers it became possible to use this machinery for numerical computation. Unfortunately one must turn continuous mathematical models into discretized equations for this purpose. This conversion often loses much of the essential structures of the underlying equations. For example, the simulation of a rigid body in free motion may inexplicably gain or loose momentum.
In my talk I will give an overview of recent work at Caltech which aims to remove this distinction between mathematical models and computation by formulating the entire machinery of differential geometry and calculus in a discrete setting from the very start. This often leads to much simpler, cleaner, and more stable algorithms which can be designed to have the same symmetries and conserved quantities as the continuous systems one wishes to model.
I will illustrate these ideas with a number of applications ranging from geometric modeling to fluid simulation.
Joint work with Mathieu Desbrun, Jerry Marsden, Alexander Bobenko, Boris Springboarn, Yiying Tong, Eva Kanso, Sharif Elcott, and Liliya Kharevych.
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