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Directors:
Randolph E. Bank
Philip E. Gill
Michael Holst

Administrative Contact:
Terry Le

Office: AP&M 7431
Phone: (858)534-9813
Fax: (858)534-5273
E-mail: tele@ucsd.edu
Applications of FEEC to Geometric Problems

Chris Tiee
UCSD

Abstract:

Geometry and physics have been, in recent times, a great inspiration for mathematical problems. It is therefore useful to consider numerical methods that pay special attention to various invariant geometric structures, and minimize dependence on choices of coordinate systems. Attention to this aspect can lead to better stability and qualitative behavior. One important tool we have in capturing geometric structure is differential forms; many common differential equations find their most natural expressions in terms of forms. The Finite Element Exterior Calculus (FEEC) provides a framework for discretizing differential forms as finite elements. We present examples of how FEEC recasts problems into a more geometric form, and describe generalization to hyperbolic problems, by, specifically, application of FEEC to solving Maxwell's equations. We describe a choice of discretization (Whitney Forms) and possible generalizations and their issues.

Tuesday, October 15, 2013
11:00AM AP&M 2402