Seamless Multiscale Methods via Dynamics on Fiber Bundles

CSIC Building (#406), Seminar Room 4122.
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Seamless Multiscale Methods via Dynamics on Fiber Bundles

Professor Weinan E

Princeton University

Abstract:   We will discuss the problem of efficiently capturing macroscopic behavior using microscopic models. This can be done either through a sequential coupling strategy by precomputing the effective macro models using the known micro model, or through a concurrent coupling strategy, by estimating macroscopic model input "on-the-fly" using the microscale model. In the latter category, the coupling between the macro and micro models can be done either by going back and forth between the models, or seamlessly by formulating extended macroscopic models on the associated fiber bundles, thus avoiding the technically difficult step of going back and forth between macro and micro states. We will discuss efficient methods in each category, but we will focus on the formulations for seamless methods.