Multiscale computations for elliptic problems and time averaged waves

Olof Runborg
Department of Mathematics, KTH


Abstract:

Elliptic problems with rapidly varying coefficients are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We discuss different numerical multicsale methods for such problems, which can find the solution significantly faster than traditional techniques, including HMM and LOD. In particular we will show how efficient, localized, basis functions for generalized FEM can be obtained by averaging short time solutions of the wave equations.