TECHNICAL PAPERS
Sep 13, 2002

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.

Get full access to this article

View all available purchase options and get full access to this article.

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.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 128Issue 10October 2002
Pages: 1050 - 1061

History

Received: Jan 17, 2002
Accepted: Jan 30, 2002
Published online: Sep 13, 2002
Published in print: Oct 2002

Permissions

Request permissions for this article.

Authors

Affiliations

Andrzej J. Safjan
Visiting Professor, Dept. of Aerospace Engineering, 741D H.R. Bright Building, College Station, TX 77843-3141.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share