A general strategy for the design of seamless multiscale<br/><br/>methods

Wednesday, November 5, 2008 - 10:30am - 11:15am
EE/CS 3-180
Eric Vanden-Eijnden (New York University)
I will present a new general framework for designing multiscale methods. Compared with previous work such as Brandt’s systematic up-scaling, the heterogeneous multiscale method and the “equation-free” approach, this new framework has the distinct feature that it does not require reinitializing the microscale model at each macro time step or each macro iteration step. In the new strategy, the macro- and micro-models evolve simultaneously using different time steps (and therefore different clocks), and they exchange data at every step. The micro-model uses its own
appropriate time step. The macro-model runs at a slower pace than required by accuracy and stability considerations for the macroscale dynamics, in order for the micro-model to relax. I will discuss applications of the new seamless approach to a toy system used in climatic studies, to the modeling of complex fluids, and to free energy calculations in molecular dynamics.

This is joint work with Weinan E and Weiqing Ren with applications performed in collaboration with Ibrahim Fatkullin and Luca Maragliano.
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