Lui, S. H. (Shaun H.) 1961- creator text bibliography nju Hoboken, N.J Wiley �2011 2011 monographic eng

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xiii, 487 pages : illustrations ; 27 cm. "This book provides a comprehensive and self-contained treatment of the numerical methods used to solve partial differential equations (PDEs), as well as both the error and efficiency of the presented methods. Featuring a large selection of theoretical examples and exercises, the book presents the main discretization techniques for PDEs, introduces advanced solution techniques, and discusses important nonlinear problems in many fields of science and engineering. It is designed as an applied mathematics text for advanced undergraduate and/or first-year graduate level courses on numerical PDEs"-- Preface. Acknowledgments -- Finite Difference. -- Second-Order Approximation for [delta] -- Fourth-Order Approximation for [delta] -- Neumann Boundary Condition -- Polar Coordinates -- Curved Boundary -- Difference Approximation for [delta] -- A Convection-Diffusion Equation -- Appendix: Analysis of Discrete Operators -- Summary and Exercises -- Mathematical Theory of Elliptic PDEs -- Function Spaces -- Derivatives -- Sobolev Spaces -- Sobolev Embedding Theory -- Traces -- Negative Sobolev Spaces -- Some Inequalities and Identities -- Weak Solutions -- Linear Elliptic PDEs -- Appendix: Some Definitions and Theorems -- Summary and Exercises -- Finite Elements. 3.1 Approximate Methods of Solution -- Finite Elements in 1D -- Finite Elements in 2D -- Inverse Estimate -- L2 and Negative-Norm Estimates -- A Posteriori Estimate -- Higher-Order Elements -- Quadrilateral Elements -- Numerical Integration -- Stokes Problem -- Linear Elasticity -- Summary and Exercises -- Numerical Linear Algebra -- Condition Numbers -- Classical Iterative Methods -- Krylov Subspace Methods -- Preconditioning -- Direct Methods -- Appendix: Chebyshev Polynomials -- Summary and Exercises -- Spectral Methods -- Trigonometric Polynomials -- Fourier Spectral Method -- Orthogonal Polynomials -- Spectral Gakerkin and Spectral Tau Methods -- Spectral Collocation -- Polar Coordinates -- Neumann Problems -- Fourth-Order PDEs -- Summary and Exercises -- Evolutionary PDEs -- Finite Difference Schemes for Heat Equation -- Other Time Discretization Schemes -- Convection-Dominated equations -- Finite Element Scheme for Heat Equation -- Spectral Collocation for Heat Equation -- Finite Different Scheme for Wave Equation -- Dispersion -- Summary and Exercises -- Multigrid -- Introduction -- Two-Grid Method -- Practical Multigrid Algorithms -- Finite Element Multigrid -- Summary and Exercises -- Domain Decomposition -- Overlapping Schwarz Methods -- Projections -- Non-overlapping Schwarz Method -- Substructuring Methods -- Optimal Substructuring Methods -- Summary and Exercises -- Infinite Domains -- Absorbing Boundary Conditions -- Dirichlet-Neumann Map -- Perfectly Matched Layer -- Boundary Integral Methods -- Fast Multiple Method -- Summary and Exercises -- Nonlinear Problems -- Newton's Method -- Other Methods -- Some Nonlinear Problems -- Software -- Program Verification -- Summary and Exercises. Answers to Selected Exercises. References. Index. S.H. Lui. Machine generated contents note: Preface. Acknowledgments. 1. Finite Difference. 1.1 Second-Order Approximation for [delta].1.2 Fourth-Order Approximation for [delta].1.3 Neumann Boundary Condition. 1.4 Polar Coordinates. 1.5 Curved Boundary. 1.6 Difference Approximation for [delta]2.1.7 A Convection-Diffusion Equation. 1.8 Appendix: Analysis of Discrete Operators. 1.9 Summary and Exercises. 2. Mathematical Theory of Elliptic PDEs. 2.1 Function Spaces. 2.2 Derivatives. 2.3 Sobolev Spaces. 2.4 Sobolev Embedding Theory. 2.5 Traces. 2.6 Negative Sobolev Spaces. 2.7 Some Inequalities and Identities. 2.8 Weak Solutions. 2.9 Linear Elliptic PDEs. 2.10 Appendix: Some Definitions and Theorems. 2.11 Summary and Exercises. 3. Finite Elements. 3.1 Approximate Methods of Solution. 3.2 Finite Elements in 1D.3.3 Finite Elements in 2D.3.4 Inverse Estimate. 3.5 L2 and Negative-Norm Estimates. 3.6 A Posteriori Estimate. 3.7 Higher-Order Elements. 3.8 Quadrilateral Elements. 3.9 Numerical Integration. 3.10 Stokes Problem. 3.11 Linear Elasticity. 3.12 Summary and Exercises. 4. Numerical Linear Algebra. 4.1 Condition Numbers. 4.2 Classical Iterative Methods. 4.3 Krylov Subspace Methods. 4.4 Preconditioning. 4.5 Direct Methods. 4.6 Appendix: Chebyshev Polynomials. 4.7 Summary and Exercises. 5. Spectral Methods. 5.1 Trigonometric Polynomials. 5.2 Fourier Spectral Method. 5.3 Orthogonal Polynomials. 5.4 Spectral Gakerkin and Spectral Tau Methods. 5.5 Spectral Collocation. 5.6 Polar Coordinates. 5.7 Neumann Problems5.8 Fourth-Order PDEs. 5.9 Summary and Exercises. 6. Evolutionary PDEs. 6.1 Finite Difference Schemes for Heat Equation. 6.2 Other Time Discretization Schemes. 6.3 Convection-Dominated equations. 6.4 Finite Element Scheme for Heat Equation. 6.5 Spectral Collocation for Heat Equation. 6.6 Finite Different Scheme for Wave Equation. 6.7 Dispersion. 6.8 Summary and Exercises. 7. Multigrid. 7.1 Introduction. 7.2 Two-Grid Method. 7.3 Practical Multigrid Algorithms. 7.4 Finite Element Multigrid. 7.5 Summary and Exercises. 8. Domain Decomposition. 8.1 Overlapping Schwarz Methods. 8.2 Projections. 8.3 Non-overlapping Schwarz Method. 8.4 Substructuring Methods. 8.5 Optimal Substructuring Methods. 8.6 Summary and Exercises. 9. Infinite Domains. 9.1 Absorbing Boundary Conditions. 9.2 Dirichlet-Neumann Map. 9.3 Perfectly Matched Layer. 9.4 Boundary Integral Methods. 9.5 Fast Multiple Method. 9.6 Summary and Exercises. 10. Nonlinear Problems. 10.1 Newton's Method. 10.2 Other Methods. 10.3 Some Nonlinear Problems. 10.4 Software. 10.5 Program Verification. 10.6 Summary and Exercises. Answers to Selected Exercises. References. Index. Includes bibliographical references and index. Differential equations, Partial Numerical solutions MATHEMATICS Mathematical Analysis Differential equations, Partial Numerical solutions Numerisches Verfahren Partielle Differentialgleichung Numerisches Verfahren Partielle Differentialgleichung QA377 .L84 2011 518/.64 MAT034000 SK 540 SK 520 9780470647288 0470647280 9781118111109 1118111109 9781118111116 1118111117 9781118111130 1118111133 2011013570 http://onlinelibrary.wiley.com/book/10.1002/9781118111130 http://onlinelibrary.wiley.com/book/10.1002/9781118111130 DLC 110516 20171023133843.0 ocn712125079 eng