Matrix-Based Multigrid: Theory and Applications

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) ... Ausführliche Beschreibung

1. Person: Shapira, Yair
Weitere Körperschaften: SpringerLink (Online service)
Weitere Personen: SpringerLink (Online service)
Format: E-Buch
Sprache: English
Veröffentlicht: New York, NY Springer US 2008, 2008
Beschreibung: XXIV, 318 p online resource
Ausgabe: 2nd ed. 2008
Serien: Numerical Methods and Algorithms
Schlagworte: Computational Mathematics and Numerical Analysis
Engineering
Linear and Multilinear Algebras, Matrix Theory
Computer science / Mathematics
Computational Intelligence
Numerical analysis
Numerical Analysis
Numeric Computing
Electronic data processing
Matrix theory
Global analysis (Mathematics)
Analysis
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100 1 |a Shapira, Yair 
245 0 0 |a Matrix-Based Multigrid  |h Elektronische Ressource  |b Theory and Applications  |c by Yair Shapira 
250 |a 2nd ed. 2008 
260 |a New York, NY  |b Springer US  |c 2008, 2008 
300 |a XXIV, 318 p  |b online resource 
505 0 |a 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 Equati 
653 |a Computational Mathematics and Numerical Analysis 
653 |a Engineering 
653 |a Linear and Multilinear Algebras, Matrix Theory 
653 |a Computer science / Mathematics 
653 |a Computational Intelligence 
653 |a Numerical analysis 
653 |a Numerical Analysis 
653 |a Numeric Computing 
653 |a Electronic data processing 
653 |a Matrix theory 
653 |a Global analysis (Mathematics) 
653 |a Analysis 
710 2 |a SpringerLink (Online service) 
041 0 7 |a eng  |2 ISO 639-2 
989 |b Springer  |a Springer eBooks 2005- 
490 0 |a Numerical Methods and Algorithms 
856 |u https://doi.org/10.1007/978-0-387-49765-5?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 518 
520 |a 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.  
520 |a 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 . . .  
520 |a who needs numerical solution of partial differential equations." (Peter Hajnal, Acta Scientiarum Mathematicarum, Vol. 70, 2004) 
520 |a 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.  

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