Multiscale Model Reduction by Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.;

Multiscale Finite Element Methods and Their Generalizations

Series: Applied Mathematical Sciences; 212;

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Product details:

Edition number 2023
Publisher Springer International Publishing
Date of Publication 8 June 2024
Number of Volumes 1 pieces, Book

ISBN 9783031204111
Binding Paperback
See also 9783031204081
No. of pages491 pages
Size 235x155 mm
Language English
Illustrations XIV, 491 p. 177 illus., 162 illus. in color. Illustrations, black & white

Long description:

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.- GMsFEM Using Sparsity in the Snapshot Spaces.- Space-time GMsFEM.- 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.- References.- Index.

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