Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

TL;DR

This paper introduces an adaptive multiscale model reduction framework using Generalized Multiscale Finite Element Methods, enabling local reduction in complex high-contrast media without scale separation.

Contribution

It presents a general adaptive framework for multiscale model reduction that handles high contrast and lack of scale separation, expanding the applicability of multiscale finite element methods.

Findings

Effective local model reduction in high contrast media

Framework applicable without scale separation

Discussed multiple practical applications

Abstract

In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.