Coarse-Grid Multiscale Model Reduction Techniques for Flows in Heterogeneous Media and Applications

摘要: In this paper, we give an overview of our results [36, 39, 46, 47] from the point view coarse-grid multiscale model reduction by highlighting some common issues in coarse-scale approximations and two-level preconditioners. Reduced models discussed paper rely on spaces computed solving local spectral problems. We define problems with a weight function choice initial basis functions. emphasize importance functions for both approximation particular, discuss various choices use them simulations. show that naive functions, e.g., piecewise linear can lead to large dimensional are needed achieve (1) reasonable accuracy or (2) contrast-independent condition number preconditioned matrix within additive Schwarz methods. While using careful spaces, smaller coarse spaces.