Press Release:

Numerical Analysis of Multiscale Computations

The Banff International Research Station will host the "Numerical Analysis of Multiscale Computations" workshop next week, December 6 - December 11, 2009. The ever increasing power of modern computers and the accompanying development of numerical algorithms is pushing the use of large scale computing in science and engineering into new territories. Where one used to simulate single physics models, like fluid flow, and electromagnetic waves, one is now focusing on more difficult, and computationally expensive, problems where many physics models are coupled together. These are problems where the single physics models are not accurate enough. For instance, in simulation of complex fluids, such as polymers in a solvent, the flow can reasonably be described by the classical equations of Navier-Stokes with certain well-tuned parameters obtained through empirical arguments based on physical insights. The accuracy hinges critically on the quality of the heuristics, which is often not satisfactory. In the emerging methods, one tries instead to go back to first principles, and the values of the parameters would instead be obtained by direct numerical simulation of the detailed interaction of the polymers and the background fluid. The resulting method typically requires solving problems involving vast differences in spatial and temporal scales; the polymers are for instance typically many magnitudes smaller than the domain over which we want to compute the flow, while at the same time they are magnitudes bigger than the size of the fluid particles. We call such problems where a coarse, macroscale, physical model (Navier-Stokes) is coupled to a fine, microscale, model (polymer simulation) multiscale problems. It is the difference in scales which makes such problems very computationally demanding. Solving the fine scale equations accurately over the length and time scales of the macroscopic quantities, is usually an impossible task. In this workshop we will consider the mathematics of multiscale problems and in particular a new class of numerical methods which aim to make the coupling between the coarse and fine scale models more efficient. This new kind of multiscale approach makes it feasible to treat problems that were previously out of reach, and to obtain higher accuracy when simulating important physical phenomena in the applied sciences including, materials science, chemistry, fluid dynamics, and biology.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).

BIRS Scientific Director, Nassif Ghoussoub
E-mail: birs-director[@]