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 discuss both analytical and numerical multiscale methods, which have been developed to overcome this difficulty. We will illustrate these technologies by a few applications. The mathematical background from homogenization, averaging and information theory will be described. We will also touch on some recent developments, for example, so called frequency or scale marching in optimization.

Bio: Prof. Bjorn Engquist is the leading computational mathematician all over the world. He has made numerous fundamental contributions in different fields of computational mathematics, including the absorbing boundary conditions for PDEs, numerical conservation laws, numerical multiscale modedling, fast methods for high frequency wave equations, etc. He is a member of the American Academy of Arts & Sciences, a member of the Royal Swedish Academy of Sciences and the Royal Swedish Academy of Engineering Sciences, and an invited speaker at the ICM (1983 and 1998), European Congress of Mathematics (1992), and European Congress of Fluid Mechanics (1991). He received the first SIAM James H. Wilkinson Prize in Numerical Analysis and Scientific Computing (1982), Peter Henrici Prize (2011), and George David Birkhoff Prize (2012). He was selected to the Norwegian Academy of Science and Letters in 2011.