Doghonay Arjmand
Division of Scientific Computing
Department of Information Technology
Uppsala University
Uppsala
In a multi scale problem several scales interact with each other to form a system which has variations over a wide range of scales. A direct numerical approximation is prohibitively expensive due to the need to resolve the smallest scales over a computational domain which is typically much larger than the size of the small scales. In practice, it is often adequate to have a local average description of the overall multiscale system. In such a case, it is possible to exploit multiscale coupling strategies to maintain a low computational cost. In this talk, I will overview a set of multiscale methods based on the heterogeneous multi scale methods (HMM) framework and show numerical and theoretical results in the context of elliptic, parabolic, and second order hyperbolic problems.