國立虎尾科技大學 |

Multiscale model reduction = multiscale finite element methods and their generalizations /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Multiscale model reduction/ by Eric Chung, Yalchin Efendiev, Thomas Y. Hou.
其他題名:	multiscale finite element methods and their generalizations /
作者:	Chung, Eric.
其他作者:	Hou, Thomas Y.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xiv, 491 p. :ill. (chiefly color), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Theoretical, Mathematical and Computational Physics. -
電子資源:	https://doi.org/10.1007/978-3-031-20409-8
ISBN:	9783031204098

Multiscale model reduction = multiscale finite element methods and their generalizations /
Chung, Eric.

Multiscale model reductionmultiscale finite element methods and their generalizations /[electronic resource] :by Eric Chung, Yalchin Efendiev, Thomas Y. Hou. - Cham :Springer International Publishing :2023. - xiv, 491 p. :ill. (chiefly color), digital ;24 cm. - Applied mathematical sciences,v. 2122196-968X ;. - Applied mathematical sciences,v. 212..

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.

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.

ISBN: 9783031204098

Standard No.: 10.1007/978-3-031-20409-8doiSubjects--Topical Terms:

768900
Theoretical, Mathematical and Computational Physics.

LC Class. No.: QA76.9.C65

Dewey Class. No.: 511.8

Multiscale model reduction = multiscale finite element methods and their generalizations /
LDR:02960nam a2200337 a 4500 001 1106004
003 DE-He213
005 20230607140544.0
006 m d
007 cr nn 008maaau
008 231013s2023 sz s 0 eng d
020 $a 9783031204098 $q (electronic bk.)
020 $a 9783031204081 $q (paper)
024 7 $a 10.1007/978-3-031-20409-8 $2 doi
035 $a 978-3-031-20409-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA76.9.C65
072 7 $a PBKS $2 bicssc
072 7 $a MAT021000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 511.8 $2 23
090 $a QA76.9.C65 $b C559 2023
100 1 $a Chung, Eric. $3 1415371
245 1 0 $a Multiscale model reduction $h [electronic resource] : $b multiscale finite element methods and their generalizations / $c by Eric Chung, Yalchin Efendiev, Thomas Y. Hou.
260 $a Cham : $c 2023. $b Springer International Publishing : $b Imprint: Springer,
300 $a xiv, 491 p. : $b ill. (chiefly color), digital ; $c 24 cm.
490 1 $a Applied mathematical sciences, $x 2196-968X ; $v v. 212
505 0 $a 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.
520 $a 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.
650 2 4 $a Theoretical, Mathematical and Computational Physics. $3 768900
650 2 4 $a Computational Science and Engineering. $3 670319
650 1 4 $a Numerical Analysis. $3 671433
650 0 $a Multiscale modeling. $3 782126
700 1 $a Hou, Thomas Y. $3 897647
700 1 $a Efendiev, Yalchin. $3 897646
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Applied mathematical sciences, $v v. 212. $3 1415372
856 4 0 $u https://doi.org/10.1007/978-3-031-20409-8
950 $a Mathematics and Statistics (SpringerNature-11649)