Multiscale Finite Element Methods

Release on 2009-01-10 | by Yalchin Efendiev

The book addresses mathematical and numerical issues in multiscale finite element methods and connects them to real-world applications. Narrative introduction provides a key to the book's organization and its scope.

Author: Yalchin Efendiev
Publisher: Springer Science & Business Media
ISBN: 9780387094960
Category: Technology & Engineering
Page: 234
View: 215

Multiscale Finite Element Methods

The aim of this monograph is to describe the main concepts and recent - vances in multiscale ?nite element methods. This monograph is intended for thebroaderaudienceincludingengineers,appliedscientists,andforthosewho are interested in multiscale simulations. The book is intended for graduate students in applied mathematics and those interested in multiscale compu- tions. It combines a practical introduction, numerical results, and analysis of multiscale ?nite element methods. Due to the page limitation, the material has been condensed. Each chapter of the book starts with an introduction and description of the proposed methods and motivating examples. Some new techniques are introduced using formal arguments that are justi?ed later in the last chapter. Numerical examples demonstrating the signi?cance of the proposed methods are presented in each chapter following the description of the methods. In the last chapter, we analyze a few representative cases with the objective of demonstrating the main error sources and the convergence of the proposed methods. A brief outline of the book is as follows. The ?rst chapter gives a general introductiontomultiscalemethodsandanoutlineofeachchapter.Thesecond chapter discusses the main idea of the multiscale ?nite element method and its extensions. This chapter also gives an overview of multiscale ?nite element methods and other related methods. The third chapter discusses the ext- sion of multiscale ?nite element methods to nonlinear problems. The fourth chapter focuses on multiscale methods that use limited global information.

Language: en
Pages: 372

The Multiscale Finite Element Method (MsFEM) and Its Applications

Authors: Yalchin Rafik Efendiev, California Institute of Technology. Division of Engineering and Applied Science

Categories: Electronic dissertations

Type: BOOK - Published: 1999 - Publisher:

Books about The Multiscale Finite Element Method (MsFEM) and Its Applications

Language: en
Pages: 28

Generalized Multiscale Finite-element Method (GMsFEM) for Elastic Wave Propagation in Heterogeneous, Anisotropic Media

Authors: Yalchin Rafik Efendiev, California Institute of Technology. Division of Engineering and Applied Science

Categories: Electronic dissertations

Type: BOOK - Published: 2015 - Publisher:

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We

Language: en
Pages: 35