Sunday, August 13

Qualitative Study of Dynamical Systems with Adaptive Numerical Methods

9:00 AM-9:50 AM
Kaoli (Salon 5)
Chair: Peter Bates, Brigham Young University, USA

Our goal is efficient solution of differential equations while assuring that the numerical solutions preserve important qualitative features. While mesh adaptivity is widely recognized as a necessary computational tool, there is little precise analysis of its effects.

The speaker will present a class of moving mesh methods for adaptively solving time dependent PDEs. Key to their interpretation and analysis is their formulation first in continuous form, with the mesh function representing a continuous change of variables. One can often choose the adaptivite technique to allow underlying solution structure to be automatically preserved. Examples include PDEs having self-similar solutions. These solutions, commonly attractors for important physical systems, can be computed with numerical methods inheriting this attractivity. The speaker will discuss the substantial general computational challenges, especially for higher dimensional problems.

Robert D. Russell
Department of Computer Science
Simon Fraser University, Canada
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