Time-Domain Methods for Solving Problems of Linear Acoustics
Publication: Journal of Engineering Mechanics
Volume 128, Issue 10
Abstract
This paper describes a class of high-order Taylor-Galerkin methods for solving problems of linear acoustics characterized by the classical (scalar) wave equation. The methods provide high-order temporal accuracy and unconditional stability on arbitrary nonuniform finite element meshes of varying element sizes and shape functions.
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References
Astley, R. J.(1998). “Transient spheroidal elements for unbounded wave problems.” Comput. Methods Appl. Mech. Eng., 164, 3–15.
Cipolla, J. L., and Butler, M. J.(1998). “Infinite elements in the time domain using a prolate spheroidal multipole expansion.” Int. J. Numer. Methods Eng., 43, 889–908.
Demkowicz, L., Oden, J. T., Rachowicz, W., and Hardy, O.(1989). “Toward a universal h-p adaptive finite element strategy. Part 1: Constrained approximation and data structure.” Comput. Methods Appl. Mech. Eng., 77, 79–112.
Hairer, E., Nørsett, S. P., and Wanner, G. (1987). Solving ordinary differential equations I, Springer, New York.
Hairer, E., and Wanner, G.(1973). “Multistep-multistage-multiderivative methods for ordinary differential equations.” Computing, 11, 287–303.
Hughes, T. J. (1983). “Analysis of transient algorithms with particular reference to stability behavior.” Computational methods for transient analysis, T. Belytschko and T. J. Hughes, eds., Elsevier, Amsterdam.
Junger, M. C., and Feit, D. (1986). Sound, structures and their interaction, MIT Press, Cambridge, Mass.
Kastlunger, K. H., and Wanner, G.(1972a). “Runge-Kutta process with multiple nodes.” Computing, 9, 9–24.
Kastlunger, K. H., and Wanner, G.(1972b). “On Turan-type implicit Runge-Kutta methods.” Computing, 9, 317–325.
Leis, R. (1986). Initial boundary value problems in mathematical physics, Wiley, New York.
Majda, A. (1984). Compressible fluid flow and systems and conservation laws in several space variables, Springer, New York.
Newmark, N. M.(1959). “A method of computation for structural dynamics.” J. Eng. Mech. Div., 85, 67–94.
Oden, J. T., and Carey, G. F. (1983). Finite elements: Mathematical aspects, Vol. IV, Prentice-Hall, Englewood Cliffs, N.J.
Pathria, D.(1997). “The correct formulation of intermediate boundary conditions for Runge-Kutta time integration of initial boundary value problems.” SIAM J. Sci. Comput. (USA), 18, 1255–1266.
Rachowicz, W.(1993). “An anisotropic h-type mesh-refinement strategy.” Comput. Methods Appl. Mech. Eng., 109, 169–18.
Safjan, A., and Oden, J. T.(1995). “High-order Taylor-Galerkin methods for first-order linear hyperbolic systems.” J. Comput. Phys., 120, 206–236.
Scherer, R.(1972). “Fehlerabschätzung für ein Runge-Kutta-Verfahren mit mehrfachen Knoten.” Computing, 10, 391–396.
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Copyright © 2002 American Society of Civil Engineers.
History
Received: Jan 17, 2002
Accepted: Jan 30, 2002
Published online: Sep 13, 2002
Published in print: Oct 2002
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