UID:
almahu_9949199431902882
Format:
XVIII, 349 p. 92 illus., 2 illus. in color.
,
online resource.
Edition:
1st ed. 2002.
ISBN:
9783662048238
Series Statement:
Scientific Computation,
Content:
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.
Note:
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.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783642074820
Additional Edition:
Printed edition: ISBN 9783540415985
Additional Edition:
Printed edition: ISBN 9783662048245
Language:
English
DOI:
10.1007/978-3-662-04823-8
URL:
https://doi.org/10.1007/978-3-662-04823-8
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