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Matrix-Based Multigrid [The...
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 Rebiun16868264 https://catalogo.rebiun.org/rebiun/record/Rebiun16868264 cr nn 008mamaa 100301s2008 xxu| s |||| 0|eng d 9780387497655 10.1007/978-0-387-49765-5 doi UPVA 996876796103706 UAM 991007839478204211 CBUC 991004879447306711 CBUC 991010406321006709 CBUC 991003832324406714 CBUC 991013456575606708 CBUC 991001069145906712 CBUC 991010406321006709 CUNEF 991000429452808131 PBKS bicssc MAT006000 bisacsh Shapira, Yair Matrix-Based Multigrid Recurso electrnico] Theory and Applications edited by Yair Shapira 2 Boston, MA Springer US 2008 Boston, MA Boston, MA Springer US digital Numerical Methods and Algorithms 1571-5698 2 List of Figures -- List of Tables -- Preface -- Part I. Concepts and Preliminaries -- 1. The Multilevel--Multiscale Approach -- 2. Preliminaries -- Part II. Partial Differential Equations and Their Discretization -- 3. Finite Differences and Volumes -- 4. Finite Elements -- Part III. Numerical Solution of Linear Systems -- 5. Iterative Linear System Solvers -- 6. The Multigrid Iteration -- Part IV. Multigrid for Structured Grids -- 7. Automatic Multigrid -- 8. Applications in Image Processing -- 9. Black-Box Multigrid -- 10. The Indefinite Helmholtz Equation -- 11. Matrix-Based Semicoarsening -- Part V. Multigrid for Semistructured Grids -- 12. Multigrid for Locally Refined Meshes -- 13. Application to Semistructured Grids -- Part VI. Multigrid for Unstructured Grids -- 14. Domain Decomposition -- 15. The Algebraic Multilevel Method -- 16. Applications -- 17. Semialgebraic Multilevel for Systems of PDEs -- Part VII. Appendices -- 18. Time-Dependent Parabolic PDEs -- 19. Nonlinear Equations -- References -- Index. Acceso restringido a miembros de la UGR 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) Mathematics Computer science Electronic data processing Matrix theory Computer science Mathematics Engineering Mathematics Computational Mathematics and Numerical Analysis Numeric Computing Linear and Multilinear Algebras, Matrix Theory Computational Intelligence Mathematics of Computing Numerical and Computational Physics SpringerLink (Online service) SpringerLink ebooks (Servicio en lnea) Springer eBooks Springer eBooks Printed edition 9780387497648 Numerical Methods and Algorithms 1571-5698 2