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出版社:世界圖書出版公司
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ISBN:9787510086274
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作者:(德)特洛特貝格
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頁數:631
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出版日期:2015-01-01
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印刷日期:2015-01-01
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包裝:平裝
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開本:16開
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版次:1
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印次:1
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特洛特貝格編寫的《多重網格(英文版)》是一部旨在為數學、物理、化學、氣像學、流體和連續力學等眾多領域的專家和學者介紹多重網格方法的教程。多重網格法在金融和經濟學中也占據著越來越重要的地位,有讀者認為這是多重網格法*好的書,沒有之一,相信這樣的評價是客觀的。書中介紹了解決偏微分方程的多重網格法,和多重網格法的*高層次的*新研究以及在實踐中的應用。
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Preface 1 IⅡtrOduction 1.1 Types ofPDEs 1.2 Grids and Discretization Approaches 1.2.1 Grids 1.2.2 Discretization Approaches 1.3 Some Notation 1.3.1 Continuous Boundary Value Problems l.3.2 Discrete Boundary Value Problems 1.3.3 Inner Products and NOrlTIS 1.3.4 Stencil Notation 1.4 Poisson’s Equation and Model Problem 1 1.4.1 Matrix Terminology 1.4.2 Poisson Solvers 1.5 A First Glance at Multigrid 1.5.1 The Two Ingredients ofMultigrid 1.5.2 High and Low Frequencies,and Coarse Meshes 1.5.3 From Two Grids to Multigrid 1.5.4 Multigrid Features 1.5.5 Multigrid History 1.6 Intermezzo:Some Basic Facts and Methods 1.6.1 Iterative Solvers.Splittings and Preconditioners 2 Basic Multigrid I 2.1 Error Smoothing Procedures 2.1.1 Jacobi.type Iteration(Relaxation) 2.1.2 Smoothing Properties of山一Jacobi Relaxation 2.1.3 Gauss.Seidel.type Iteration(Relaxation) 2.1.4 Parallel Properties of Smoothers 2.2 Introducing the Two.grid Cycle 2.2.1 Iteration by Approximate Solution ofthe Defect Equation 2.2.2 Coarse Grid Correction 2.2.3 Structure ofthe Two—grid Operator 2.3 Multigrid Components 2.3.1 Choices of Coarse Grids 2.3.2 Choice of the Coarse Grid Operator 2.3.3 Transfer Operators:Restriction 2.3.4 Transfer Operators:Interpolation 2.4 The Multigrid Cycle 2.4.1 Sequences of Grids and Operators 2.4.2 Recursive Definition 2.4.3 Computational W.0rk 2.5 Multigrid Convergence and E幣ciency 2.5.1 An Efficient 2D Multigrid Poisson Solver 2.5.2 How to Measure the Multigrid Convergence Factor in Practice 2.5.3 Numerical E伍ciency 2.6 Full Multigrid 2.6.1 Structure of Full Multigrid 2.6.2 Computational W10rk 2.6.3 FMG for Poisson’S Equation 2.7 Further Remarks on Transfer Operators 2.8 First Generalizations 2.8.1 2D Poisson—like Difrerential Equations 2.8.2 Time.dependent Problems 2.8.3 Cartesian Grids in Nonrectangular Domains 2.8.4 Multigrid Components for Cell.centered Discretizations 2.9 Multigridin 3D 2.9.1 TIle 3D Poisson Problem 2.9.2 3D Multigrid Components 2.9.3 Computational WOrk in 3D 3 Elementary Multigrid Theory 3.1 Survey 3.2 Why it iS Su伍cient tO Derive Two.grid Convergence Factors 3.2.1 Independent Convergence of Multigrid 3.2.2 A 111eoretical Estimate for Full Multigrid 3.3 How to Derive Two—grid Convergence Factors by Rigorous Fourier Analysis 3.3.1 Asymptotic Two.grid Convergence. 3.3.2 Norms ofthe Two—grid Operator 3.3.3 Results for Multigrid 3.3.4 Essential Steps and Details of the Two.grid Analysis 3.4 Range of Applicability of the Rigorous Fourier Analysis,Other Approaches 3.4.1 The 3D Case …… 4 Local Fourier Analysis 5 Basic Multigrid II 6 ParalleI Multigrid in Practice 7 More Advanced Multigrid 8 Multigrid for Systems of Equations 9 Adaptive Muitigrid 10 Some More Multigrid Applications ADDendixes
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