SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Structure-preserving discretization of continuum theories

D. Pavlov, M. Desbrun, E. Gawlik, P. Mullen and J. Marsden

Abstract
In this talk I will describe several discrete models of infinite dimensional systems which preserve underlying geometric structures. This work started with development of the first variational integrator for Euler fluids. Since then, our methods have been developed further and are now applicable to a great variety of infinite-dimensional systems, such as magnetohydrodynamics or complex fluids. I will discuss our new approach to discretization based on ideas of noncommutative geometry. One of the goals of this work is creating a new model of discrete differential geometry that leads to a structure preserving discretization of general relativity.

Bibliography
[1] D. Pavlov, P. Mullen, Y. Tong, E. Kanso, J.E. Marsden and M. Desbrun, Structure-preserving discretization of incompressible fluids, Phys. D 240, 443 (2011).
[2] E.S. Gawlik, P. Mullen, D. Pavlov, J.E. Marsden and M. Desbrun, Geometric, variational discretization of continuum theories, Phys. D 240, 1724 (2011).

Organized by         Universidad de Valladolid     IMUVA