<p>"The author finds in this book the right balance between theoretical and numerical analysis. [...] The book should be very useful to all of the graduate students, scientists, and engineers who want to learn the basics of the numerical analysis of time-dependent wave equations, and to the more advanced researchers who want a thorough and up-to-date presentation on the discretization of first-order hyperbolic systems." (Mathematical Reviews 2002m)</p>
<p>"To my knowledge, <strong>Higher-Order Numerical Methods for Transient Wave Equations</strong>, by Gary C. Cohen, is the first book to address specifically the use of high-order discretizations in the time domain to solve wave equations. [...] Cohen’s book should be useful, especially to new researchers, and could even be a reference in a course. [...] I recommend the book for its clear and cogent coverage of the material selected by its author." (Physics Today, March 2003)</p>
<p>"It is arguably a 'must' for any university physics or engineering library. For those working in the field, the book would deserve a place on their bookshelf [...]." (The Physicist)</p>
<p>"This is a remarkable book about numerical treatment of wave-type equations in the time domain. [...] The book will be of particular interest to mathematicans, physicists and engineers working in academia as well as in industry on the field of numerical analysis of wave-like phenomena." (Zentralblatt der Mathematik)</p>
<p>"In summary, this book is a very valuable reference for the readers of this journal who are interested in the computational methods for transit waves. What make this book unique are the novel mass-lumping techniques for finite element methods, which are still being actively investigated." (Qing Huo Liu (Duke University, Durham, North Carolina), Journal of the Acoustical Society of America, American Institute of Physics July 2003, vol. 114, page 21) </p>

Solving efficiently the wave equations involved in modeling acoustic, elastic or electromagnetic wave propagation remains a challenge both for research and industry. To attack the problems coming from the propagative character of the solution, the author constructs higher-order numerical methods to reduce the size of the meshes, and consequently the time and space stepping, dramatically improving storage and computing times. This book surveys higher-order finite difference methods and develops various mass-lumped finite (also called spectral) element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem. A central role is played by the notion of the dispersion relation for analyzing the methods. The last chapter is devoted to unbounded domains which are modeled using perfectly matched layer (PML) techniques. Numerical examples are given.
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This book surveys higher-order finite difference methods and develops various mass-lumped finite (also called spectral) element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem.
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I. Basic Definitions and Properties.- 1. The Basic Equations.- 2. Functional Issues.- 3. Plane Wave Solutions.- II. Finite Difference Methods.- 4. Construction of the Schemes in Homogeneous Media.- 5. The Dispersion Relation.- 6. Stability of the Schemes.- 7. Numerical Dispersion and Anisotropy.- 8. Construction of the Schemes in Heterogeneous Media.- 9. Stability by Energy Techniques.- 10. Reflection-Transmission Analysis.- III. Finite Element Methods.- 11. Mass-Lumping in 1D.- 12. Spectral Elements.- 13. Mass-Lumped Mixed Formulations and Edge Elements.- 14. Modeling Unbounded Domains.- A.1.1 Notation.- A.2.1 Notation.
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Solving efficiently the wave equations involved in modeling acoustic, elastic or electromagnetic wave propagation remains a challenge both for research and industry. To attack the problems coming from the propagative character of the solution, the author constructs higher-order numerical methods to reduce the size of the meshes, and consequently the time and space stepping, dramatically improving storage and computing times. This book surveys higher-order finite difference methods and develops various mass-lumped finite (also called spectral) element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem. A central role is played by the notion of the dispersion relation for analyzing the methods. The last chapter is devoted to unbounded domains which are modeled using perfectly matched layer (PML) techniques. Numerical examples are given.
Les mer
Springer Book Archives
Springer Book Archives
No comparable text on the numerical treatment of wave equations is presently available The author presents a host of modern numerical techniques of high accuracy and stability so far not accessible in book form Includes supplementary material: sn.pub/extras
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GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
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Produktdetaljer

ISBN
9783642074820
Publisert
2010-12-15
Utgiver
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet

Forfatter