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L.L. Thompson¹, P. Kunthong² and S. Subbarayalu³

¹Department of Mechanical Engineering, Clemson University, SC, United States of America
²Department of Mechanical Engineering, Kasetsart University, Bangkok, Thailand
³Dassault Systmes Simulia Corp., Providence, RI, United States of America

Keywords: time-discontinuous Galerkin, acoustics, waves, hyperbolic systems, spacetime, multi-pass iterative.

Abstract

The time-discontinuous Galerkin (TDG) method provides high-order accuracy with desirable C and L stability for second-order hyperbolic systems governing acoustics. C and L stability provide asymptotic annihilation of high frequency response due to any spurious resolution of small scales. In order to retain the high-order accuracy and stability properties of the parent TDG method while gaining efficiency comparable with standard second-order accurate single-step/single-solve (SS/SS) time stepping algorithms, generalised gradients of residuals of the governing equations are added to the standard TDG variational equation. Using this stabilized framework, together with optimal design of temporal approximations and time-scales, efficient multi-pass iterative solution algorithms are developed which maintain C and L stability, provide high-order accuracy in only two or three iterative passes, and can easily be implemented in standard finite element codes. An alternative decoupling strategy which uses a spectral decomposition of the time arrays is also developed and used to efficiently solve the space-time matrix equations resulting from the TDG method. This approach is especially amendable for parallel implementation. Local adaptive space-time finite element strategies based on the TDG method are also presented.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Computational Science, Engineering & Technology Series ISSN 1759-3158 CSETS: 18 COMPUTATIONAL METHODS FOR ACOUSTICS PROBLEMS Edited by: F. Magoulès Chapter 4 Stabilized Time-Discontinuous Galerkin Methods with Applications to Acoustics L.L. Thompson¹, P. Kunthong² and S. Subbarayalu³ ¹Department of Mechanical Engineering, Clemson University, SC, United States of America ²Department of Mechanical Engineering, Kasetsart University, Bangkok, Thailand ³Dassault Systmes Simulia Corp., Providence, RI, United States of America doi:10.4203/csets.18.4 purchase the full-text of this chapter Full Bibliographic Reference for this chapter L.L. Thompson, P. Kunthong, S. Subbarayalu, "Stabilized Time-Discontinuous Galerkin Methods with Applications to Acoustics", in F. Magoulès, (Editor), "Computational Methods for Acoustics Problems", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 4, pp 99-126, 2008. doi:10.4203/csets.18.4 Keywords: time-discontinuous Galerkin, acoustics, waves, hyperbolic systems, spacetime, multi-pass iterative. Abstract The time-discontinuous Galerkin (TDG) method provides high-order accuracy with desirable C and L stability for second-order hyperbolic systems governing acoustics. C and L stability provide asymptotic annihilation of high frequency response due to any spurious resolution of small scales. In order to retain the high-order accuracy and stability properties of the parent TDG method while gaining efficiency comparable with standard second-order accurate single-step/single-solve (SS/SS) time stepping algorithms, generalised gradients of residuals of the governing equations are added to the standard TDG variational equation. Using this stabilized framework, together with optimal design of temporal approximations and time-scales, efficient multi-pass iterative solution algorithms are developed which maintain C and L stability, provide high-order accuracy in only two or three iterative passes, and can easily be implemented in standard finite element codes. An alternative decoupling strategy which uses a spectral decomposition of the time arrays is also developed and used to efficiently solve the space-time matrix equations resulting from the TDG method. This approach is especially amendable for parallel implementation. Local adaptive space-time finite element strategies based on the TDG method are also presented. purchase the full-text of this chapter (price £25) go to the previous chapter go to the next chapter return to the table of contents return to the book description purchase this book (price £95 +P&P)
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