A seamless algorithm for multiscale simulations

Friday, October 16, 2009 - 2:15pm - 2:55pm
EE/CS 3-180
I will present a seamless algorithm for the study of multiscale problems. The multiscale method aims at
capturing the macroscale behavior of a given system which is modeled by an (incomplete) macroscale model. This is done by
coupling the macro model with a micro model: The macro model provides the necessary constraint for the micro model and the
micro model supplies the missing data (e.g. the constitutive relation or the boundary conditions) needed in the macro model.
In the multiscale method, the macro and micro models evolve simultaneously using different time steps, and they exchange
data at every step. The micro model uses its own appropriate (micro) time step. The macro model uses a macro time step but
runs at a slower pace than required by accuracy and stability considerations in order for the micro dynamics to have sufficient
time to adapt to the environment provided by the macro state. The method has the advantage that it does not require the
reinitialization of the micro model at each macro time step or each macro iteration step. The data computed from the micro model
is implicitly averaged over time.
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