MARC details
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05108nam a2200337 a 4500 |
| 001 - CONTROL NUMBER |
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00006370 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
WSP |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20230530094025.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS |
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m d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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091123s2015 si a sb 001 0 eng d |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2014040541 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9789814578462 |
| Qualifying information |
electronic bk. |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
WSPC |
| Language of cataloging |
eng |
| Transcribing agency |
WSPC |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515.3533 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Korneev, Vadim Glebovich and Langer, Ulrich |
| 245 10 - TITLE STATEMENT |
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| Title |
Dirichlet–Dirichlet Domain Decomposition Methods for Elliptic Problems : |
| Remainder of title |
h and hp Finite Element Discretizations |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc. |
Singapore : |
| Name of publisher, distributor, etc. |
World Scientific Pub. Co., |
| Date of publication, distribution, etc. |
©2015. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
484 p. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references (p. 443-458) and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1. Introduction. 1.1. Dirichlet-Dirichlet domain decomposition methods in retrospect. 1.2. Two origins of domain decomposition methods -- 2. Fundamentals of the Schwarz methods. 2.1. Elliptic model problems and their discretizations. 2.2. Domain decomposition methods as preconditioning. 2.3. Main factors influencing convergence -- 3. Overlapping domain decomposition methods. 3.1. Construction principles. 3.2. Discretizations and generalized quasiuniformity conditions. 3.3. Algorithms with generous overlap. 3.4. Loss in convergence due to small overlap. 3.5. Multilevel versions -- 4. Nonoverlapping DD methods for h FE discretizations in 2d. 4.1. Schur complement algorithms for h discretizations. 4.2. Dirichlet-Dirichlet DD algorithms -- 5. BPS-type DD preconditioners for 3d elliptic problems. 5.1. DD algorithms and their main components. 5.2. Condition number and complexity estimates -- 6. DD Algorithms for discretizations with chaotically Piecewise variable orthotropism. 6.1. Single slim domain. 6.2. Schur complement preconditioning by DD. 6.3. Orthotropic discretizations with arbitrary aspect ratios on thin rectangles. 6.4. Discretizations with Piecewise variable orthotropism on domains composed of shape irregular rectangles -- 7. Nonoverlapping DD methods for hp discretizations of 2d elliptic equations. 7.1. Structure of DD preconditioners and its reflection in the relative condition number. 7.2. Prolongations and bounded extension splitting. 7.3. Square reference p-elements, their stiffness and mass matrices. 7.4. Preconditioning of stiffness and mass matrices by finite-difference matrices. 7.5. Schur complement preconditioners for reference elements -- 8. Fast Dirichlet solvers for 2d reference elements. 8.1. Fast Dirichlet solvers for hierarchical reference elements. 8.2. Numerical testing of DD solver for Dirichlet problem in a L-shaped domain. 8.3. Fast Dirichlet solvers for 2d spectral reference elements. 8.4. The numerical complexity of DD methods in two dimensions -- 9. Nonoverlapping Dirichlet-Dirichlet DD methods for hp discretizations of 3d elliptic equations. 9.1. General structure of DD and Schur complement preconditioners. 9.2. Reference elements and finite-difference preconditioners. 9.3. Fast preconditioner-solvers for internal and face problems. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
Domain decomposition (DD) methods provide powerful tools for constructing parallel numerical solution algorithms for large scale systems of algebraic equations arising from the discretization of partial differential equations. These methods are well-established and belong to a fast developing area. In this volume, the reader will find a brief historical overview, the basic results of the general theory of domain and space decomposition methods as well as the description and analysis of practical DD algorithms for parallel computing. It is typical to find in this volume that most of the presented DD solvers belong to the family of fast algorithms, where each component is efficient with respect to the arithmetical work. Readers will discover new analysis results for both the well-known basic DD solvers and some DD methods recently devised by the authors, e.g., for elliptic problems with varying chaotically piecewise constant orthotropism without restrictions on the finite aspect ratios. The hp finite element discretizations, in particular, by spectral elements of elliptic equations are given significant attention in current research and applications. This volume is the first to feature all components of Dirichlet–Dirichlet-type DD solvers for hp discretizations devised as numerical procedures which result in DD solvers that are almost optimal with respect to the computational work. The most important DD solvers are presented in the matrix/vector form algorithms that are convenient for practical use. |
| 533 ## - REPRODUCTION NOTE |
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| Type of reproduction |
Electronic reproduction. |
| Place of reproduction |
Singapore : |
| Agency responsible for reproduction |
World Scientific Publishing Co., |
| Date of reproduction |
2015. |
| Note about reproduction |
System requirements: Adobe Acrobat Reader. |
| -- |
Mode of access: World Wide Web. |
| -- |
Available to subscribing institutions. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Decomposition (Mathematics) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Differential equations, Partial. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Finite element method. |
| 655 #0 - INDEX TERM--GENRE/FORM |
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| Genre/form data or focus term |
Electronic books. |
| 776 1# - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| International Standard Book Number |
9789814578455 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://www.worldscientific.com/worldscibooks/10.1142/9035#t=toc">http://www.worldscientific.com/worldscibooks/10.1142/9035#t=toc</a> |
| Link text |
ebook |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
E-Books |
