Mini-Workshop: Numerical Upscaling: Theory and Applications

Abstract

Numerical upscaling is often the only way in which various multiscale problems can be handled. Numerics related to solving auxiliary problems appearing in asymptotic homogenization, as well as numerical treatment of multiscale problems with non-separable scales, are discussed here. Among the main topics discussed, are classification of multiscale problems and multiscale numerical algorithms; deriving coarse scale approximations via approximate truncations or based on variational principles; iterations over scales; accuracy and robustness of numerical upscaling algorithms; similarity and differences between different approaches (multigrid, multiscale FEM, heterogeneous multiscale method, etc.); convergence issues; area of applicability of the numerical upscaling, etc.