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001 978-0-387-49765-5
003 DE-He213
005 20161121231206.0
007 cr nn 008mamaa
008 100301s2008 xxu| s |||| 0|eng d
020 _a9780387497655
_9978-0-387-49765-5
024 7 _a10.1007/978-0-387-49765-5
_2doi
050 4 _aQA297-299.4
072 7 _aPBKS
_2bicssc
072 7 _aMAT021000
_2bisacsh
072 7 _aMAT006000
_2bisacsh
082 0 4 _a518
_223
245 1 0 _aMatrix-Based Multigrid
_h[electronic resource] :
_bTheory and Applications /
_cedited by Yair Shapira.
250 _a2.
264 1 _aBoston, MA :
_bSpringer US,
_c2008.
300 _aXXIV, 318 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aNumerical Methods and Algorithms,
_x1571-5698 ;
_v2
505 0 _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.
520 _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).
650 0 _aMathematics.
650 0 _aNumerical analysis.
650 0 _aMatrix theory.
650 0 _aAlgebra.
650 0 _aMathematical analysis.
650 0 _aAnalysis (Mathematics).
650 0 _aComputer mathematics.
650 0 _aComputational intelligence.
650 1 4 _aMathematics.
650 2 4 _aNumerical Analysis.
650 2 4 _aAnalysis.
650 2 4 _aComputational Mathematics and Numerical Analysis.
650 2 4 _aNumeric Computing.
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
650 2 4 _aComputational Intelligence.
700 1 _aShapira, Yair.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387497648
830 0 _aNumerical Methods and Algorithms,
_x1571-5698 ;
_v2
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-49765-5
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c509909
_d509909