Events

545 Mudd, 2:45 PM Bjorn Engquist University of Texas at Austin "Computational Multiscale Modeling" Abstract: In multiscale processes different phenomena interact on different scales in time and space. Computer simulations of such processes are challenging since the smallest scales should be accurately represented over domains that cover the largest scales. This results in a very large number of unknowns and prohibitingly long computing times. We will briefly discuss analytical techniques and then focus on numerical multiscale methods, which have been developed to overcome this difficulty, in particular, the Heterogeneous Multiscale Method (HMM). It is a computational framework focusing on the larger scales that only uses fine scale simulations locally. We will illustrate these technologies by applications to continuum and atomistic mechanics. The mathematical background from homogenization, averaging and information theory will be described. We will also see how parallel in time algorithms can be used for handling multiscale dynamical systems. The, so-called, parareal method can overcome the natural obstacle of causality for parallelization.