05148nam 22005895i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001700188072002300205072002300228082001200251245010400263250000700367264003800374300003500412336002600447337002600473338003600499347002400535490005400559505100600613520220701619650001703826650002403843650001903867650001303886650002703899650002803926650002603954650003203980650001704012650002404029650001404053650005404067650002304121650005204144650003204196700002804228710003404256773002004290776003604310830005404346856004804400912001404448999001904462952007704481978-0-387-49765-5DE-He21320180115171409.0cr nn 008mamaa100301s2008 xxu| s |||| 0|eng d a97803874976559978-0-387-49765-57 a10.1007/978-0-387-49765-52doi 4aQA297-299.4 7aPBKS2bicssc 7aMAT0210002bisacsh 7aMAT0060002bisacsh04a51822310aMatrix-Based Multigridh[electronic resource] :bTheory and Applications /cedited by Yair Shapira. a2. 1aBoston, MA :bSpringer US,c2008. aXXIV, 318 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aNumerical Methods and Algorithms,x1571-5698 ;v20 aConcepts 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. aMultigrid 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). 0aMathematics. 0aNumerical analysis. 0aMatrix theory. 0aAlgebra. 0aMathematical analysis. 0aAnalysis (Mathematics). 0aComputer mathematics. 0aComputational intelligence.14aMathematics.24aNumerical Analysis.24aAnalysis.24aComputational Mathematics and Numerical Analysis.24aNumeric Computing.24aLinear and Multilinear Algebras, Matrix Theory.24aComputational Intelligence.1 aShapira, Yair.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387497648 0aNumerical Methods and Algorithms,x1571-5698 ;v240uhttp://dx.doi.org/10.1007/978-0-387-49765-5 aZDB-2-SMA c369536d369536 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK