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Dispersion-corrected explicit integration of the wave equation. (English) Zbl 1009.76054
Summary: We introduce a dispersion correction into a centered difference explicit time integration scheme for wave propagation problems. The extra term introduces a change in the wave speed, depending on local wave characteristics. A rigorous theoretical analysis is provided for the scalar wave equation on a regular mesh, and a notable improvement in the ability to conserve wave fronts is demonstrated by two numerical examples. The correction is reinterpreted by application to a typical finite element formulation in terms of mass and stiffness matrices, resulting in a general dispersion correction of the explicit centered difference time integration algorithm for acoustic and elastic wave propagation problems.

76M10 Finite element methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
74J10 Bulk waves in solid mechanics
Full Text: DOI
[1] Vichnevetsky, R.; Bowles, J.B., Fourier analysis of numerical approximations of hyperbolic equation, SIAM studies in applied mathematics, (1982), SIAM Philadelphia, PA · Zbl 0495.65041
[2] Schreyer, H.L., Dispersion of semidiscretized and fully discretized systems, () · Zbl 0537.73056
[3] Krenk, S., Optimal formulation of simple finite elements, () · Zbl 0624.73078
[4] Richtmyer, R.D.; Morton, K.W., Difference methods for initial-value problems, (1967), Interscience New York · Zbl 0155.47502
[5] O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method. Vol. 2. Solid and Fluid Mechanics, Dynamics and Non-linearity, McGraw-Hill, Maidenhead, UK, 1991 · Zbl 0974.76004
[6] Geradin, M.; Rixen, D., Mechanical vibrations, (1997), Wiley Chichester, UK
[7] Whitham, G.B., Linear and nonlinear waves, (1974), Wiley New York · Zbl 0373.76001
[8] Hughes, T.J.R., The finite element method, (1987), Prentice-Hall Englewood Cliffs, NJ
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