Chung E. Multiscale Model Reduction. Multiscale Finite Element Methods...2023 torrent

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This monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods. Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These methods allow reducing the degrees of freedom based on local offline computations. Moreover, these methods allow deriving rigorous macroscopic equations for multiscale problems without scale separation and high contrast. Multiscale methods are also used to design efficient solvers. This book offers a combination of analytical and numerical methods designed for solving multiscale problems. The book mostly focuses on methods that are based on multiscale finite element methods. Both applications and theoretical developments in this field are presented. The book is suitable for graduate students and researchers, who are interested in this topic.
Introduction
Homogenization and numerical homogenization of linear equations
Local model reduction. Introduction to Multiscale Finite Element Methods
Generalized multiscale finite element methods. Main concepts and overview
Adaptive strategies
Selected global formulations for GMsFEM and energy stable oversampling
Constraint energy minimizing concepts
Non-local multicontinua upscaling
Space-time GMsFEM
Multiscale methods for perforated domains
Multiscale stabilization
GMsFEM for selected applications
Homogenization and numerical homogenization of nonlinear equations
GMsFEM for nonlinear problems
Nonlinear non-local multicontinua upscaling
Global-local multiscale model reduction using GMsFEM
Multiscale methods in temporal splitting. Efficient implicit-explicit methods for multiscale problems