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Matrix-based multigrid : th...
Multigrid methods are often used for solving partial differential equations. This book introduces and analyzes the multigrid approach. The approach used here applies to both test problems on rectangular grids and to more realistic applications with complicated grids and domains. Key Features of this Second Edition: - Discusses multigrid methods from the domain decomposition viewpoint, thus making the material accessible to beginning undergraduate/graduate students - Uses the semialgebraic multigrid approach to handle complex topics (such as the solution of systems of PDEs) - Provides relevant and insightful exercises at the end of each chapter which help reinforce the material - Uses numerous illustrations and examples to motivate the subject matter - Covers important applications in physics, engineering and computer science Matrix-Based Multigrid can serve as a textbook for courses in numerical linear algebra, numerical methods for PDEs, and computational physics at the advanced undergraduate and graduate levels. Since most of the background material is covered, the only prerequisites are elementary linear algebra and calculus. Excerpts from the reviews of the first edition: "This book contains a wealth of information about using multilevel methods to solve partial differential equations (PDEs). . . A common matrix-based framework for developing these methods is used throughout the book. This approach allows methods to be developed for problems under three very different conditions. . . This book will be insightful for practitioners in the field. . . students will enjoy studying this book to see how the many puzzle pieces of the multigrid landscape fit together." (Loyce Adams, SIAM review, Vol. 47(3), 2005) "The discussion very often includes important applications in physics, engineering, and computer science. The style is clear, the details can be understood without any serious prerequisite. The usage of multigrid method for unstructured grids is exhibited by a well commented C++ program. This way the book is suitable for anyone ... who needs numerical solution of partial differential equations." (Peter Hajnal, Acta Scientiarum Mathematicarum, Vol. 70, 2004)
Monografía
monografia Rebiun35820062 https://catalogo.rebiun.org/rebiun/record/Rebiun35820062 m o d cr cn||||||||| 081117s2008 nyua ob 001 0 eng d 2007934905 495285324 646761424 698465319 767198119 985058401 987702558 990389266 1005788762 1011838476 1022042444 1035651851 1044213867 1056374497 1058095233 1060789793 1066640950 1075570503 1078061594 1086916380 1097332365 1102296012 1110758539 1112581995 1162629768 1204023094 1264895406 1391836190 9780387497655 038749765X 0387497641 cloth) 9780387497648 cloth) 9786611861063 6611861068 10.1007/978-0-387-49765-5 doi 9786611861063 AU@ 000048719494 NLGGC 384183530 NZ1 13072220 NZ1 13709405 978-0-387-49764-8 Springer http://www.springerlink.com GW5XE eng pn GW5XE NLGGC NUI E7B OCLCQ OCLCO OCLCQ A7U OCLCQ OCLCF COO YDXCP IDEBK OCLCQ VT2 UAB Z5A LIP OCLCQ ESU OCLCQ STF OCLCQ CEF U3W AU@ OCLCQ WYU ICG YOU CNTRU AUD OCLCQ DCT ERF UKAHL EBLCP OCLCQ OCLCO OCLCQ INARC DKU OCLCO S9M OCLCL PBKS bicssc MAT021000 bisacsh MAT006000 bisacsh Shapira, Yair 1960-) https://id.oclc.org/worldcat/entity/E39PCjrHCWw9Wc9M4cvb4494Md Matrix-based multigrid theory and applications Yair Shapira 2nd ed New York, NY Springer 2008 New York, NY New York, NY Springer 1 online resource (xxiii, 318 pages) illustrations 1 online resource (xxiii, 318 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF Numerical methods and algorithms v. 2 Includes bibliographical references (pages 305-311) and index Concepts and Preliminaries -- The Multilevel-Multiscale Approach -- Preliminaries -- Partial Differential Equations and Their Discretization -- Finite Differences and Volumes -- Finite Elements -- The Numerical Solution of Large Sparse Linear Systems of Algebraic Equations -- Iterative Linear System Solvers -- The Multigrid Iteration -- Matrix-Based Multigrid for Structured Grids -- The Automatic Multigrid Method -- Applications in Image Processing -- The Black-Box Multigrid Method -- The Indefinite Helmholtz Equation -- Matrix-Based Semicoarsening Method -- Matrix-Based Multigrid for Semistructured Grids -- Matrix-Based Multigrid for Locally Refined Meshes -- Application to Semistructured Grids -- Matrix-Based Multigrid for Unstructured Grids -- The Domain-Decomposition Multigrid Method -- The Algebraic Multilevel Method -- Applications -- Semialgebraic Multilevel Method for Systems of Partial Differential Equations -- Appendices -- Time-Dependent Parabolic PDEs -- Nonlinear Equations University staff and students only. Requires University Computer Account login off-campus Multigrid methods are often used for solving partial differential equations. This book introduces and analyzes the multigrid approach. The approach used here applies to both test problems on rectangular grids and to more realistic applications with complicated grids and domains. Key Features of this Second Edition: - Discusses multigrid methods from the domain decomposition viewpoint, thus making the material accessible to beginning undergraduate/graduate students - Uses the semialgebraic multigrid approach to handle complex topics (such as the solution of systems of PDEs) - Provides relevant and insightful exercises at the end of each chapter which help reinforce the material - Uses numerous illustrations and examples to motivate the subject matter - Covers important applications in physics, engineering and computer science Matrix-Based Multigrid can serve as a textbook for courses in numerical linear algebra, numerical methods for PDEs, and computational physics at the advanced undergraduate and graduate levels. Since most of the background material is covered, the only prerequisites are elementary linear algebra and calculus. Excerpts from the reviews of the first edition: "This book contains a wealth of information about using multilevel methods to solve partial differential equations (PDEs). . . A common matrix-based framework for developing these methods is used throughout the book. This approach allows methods to be developed for problems under three very different conditions. . . This book will be insightful for practitioners in the field. . . students will enjoy studying this book to see how the many puzzle pieces of the multigrid landscape fit together." (Loyce Adams, SIAM review, Vol. 47(3), 2005) "The discussion very often includes important applications in physics, engineering, and computer science. The style is clear, the details can be understood without any serious prerequisite. The usage of multigrid method for unstructured grids is exhibited by a well commented C++ program. This way the book is suitable for anyone ... who needs numerical solution of partial differential equations." (Peter Hajnal, Acta Scientiarum Mathematicarum, Vol. 70, 2004) Differential equations, Partial- Numerical solutions Multigrid methods (Numerical analysis) Matrices Engineering Engineering Équations aux dérivées partielles- Solutions numériques Méthodes multigrilles (Analyse numérique) Matrices Ingénierie engineering Bioingeniería Matrices (Matemáticas) Ecuaciones de física matemática Differential equations, Partial- Numerical solutions Matrices Multigrid methods (Numerical analysis) Springer eBooks Springer eBooks Print version Shapira, Yair, 1960-. Matrix-based multigrid. 2nd ed. New York, NY : Springer, 2008 9780387497648 0387497641 (OCoLC)156812946 Numerical methods and algorithms v. 2