Higher-Order Numerical Methods for Transient Wave Equations

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Springer Science & Business Media, Nov 6, 2001 - Science - 349 pages
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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.
 

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Contents

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Page iv - INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France...
Page 347 - A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow, CR Acad. Sci.
Page 345 - REFERENCES Aki, K., Richards. PG (1980). Quantitative Seismology, Theory and Methods. Freeman, San Francisco. Alford, R., Kelly, K., Boore, D. (1974). Accuracy of finite difference modeling of the acoustic wave equation. Geophysics 39, 834-842. Alterman, Z., Karal, FC (1968). Propagation of elastic waves in layered media by finite difference methods. Bull. Seismol. Soc. Am. 58, 367-398. Ampuero. J.-P. (2002). Etude physique et numeYique de la nucl6ation des se.ismes (A physical and numerical study...
Page 345 - On a finite-element method for solving the three-dimensional Maxwell equations, J. Comput. Phys. 109, 222 (1993).
Page 345 - Numerical solution to the timedependent Maxwell equations in two-dimensional singular domains: the singular complement method., J.
Page 346 - G. COHEN, A class of schemes, fourth order in space and time, for the 2D wave equation, Proc.
Page 348 - R. LEIS, Initial boundary value problems in mathematical physics, Wiley, New York, 1988.
Page 348 - HO KREISS, Initial boundary value problems for hyperbolic systems, Comm. Pure Appi. Math. 23, pp.

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