Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

• Published in: Journal of computational physics Vol. 320; no. C; pp. 69 - 95
• Main Authors: Chung, Eric, Efendiev, Yalchin, Hou, Thomas Y.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.09.2016; Elsevier
• Subjects: Computation; Finite element method; Heterogeneous media; Ingredients; Mathematical analysis; Model reduction; Multiscale; Multiscale finite element method; Multiscale methods; Numerical homogenization; Porous media; Scale (ratio); Separation; Porous media; Numerical homogenization; Heterogeneous media; Multiscale; Multiscale finite element method
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2016.04.054

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.