Stochastic Systems Seminar
Stochastic Systems Seminar
Brown University Joint Materials/Solid Mechanics Seminar Series
Brown University Joint Materials/Solid Mechanics Seminar Series
Applied Mathematics Colloquium
Scientific Computing Seminar
Abstract: Most numerical methods for solving physical problems tend to be extremely costly, for several general reasons that will be explained. Model studies have shown that each of these reasons can in principle be removed by multiscale (e.g., multigrid) algorithms. These algorithms employ separate processing at each scale of the physical space, combined with interscale iterative interactions, in ways which use finer scales very sparingly. Having been developed first and well known as solvers for elliptic PDEs, highly efficient multiscale techniques have more recently been developed for non elliptic and time-dependent problems, and for many other types of computational tasks, including: inverse PDE problems; highly indefinite (e.g., standing wave) equations; Dirac equations in disordered gauge fields; fast computation and updating of large determinants; general fast integral transforms; integral equations; many body interactions; molecular dynamics of macromolecules and fluids; many-atom electronic structures; global and discrete-state optimization; practical network and graph problems; image segmentation and recognition; tomography (medical imaging); fast Monte-Carlo sampling in statistical physics; real-time path-integral; and general, systematic methods of upscaling (accurate numerical derivation of large-scale equations from microscopic laws). The potential for fundamental achievements in physics and chemistry will be outlined.
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