The time-discontinuous Galerkin (TDG) method possesses high-order accuracy and desirable C-and L-stability for second-order hyperbolic systems including structural acoustics. C- and L-stability provide asymptotic annihilation of high frequency response due to spurious resolution of small scales. These non-physical responses are due to limitations in spatial discretization level for large-complex systems. In order to retain the high-order accuracy of the parent TDG method for high temporal approximation orders within an efficient multi-pass iterative solution algorithm which maintains stability, generalized gradients of residuals of the equations of motion expressed in state-space form are added to the TDG variational formulation. The resultant algorithm is shown to belong to a family of Pade approximations for the exponential solution to the spatially discrete hyperbolic equation system. The final form of the algorithm uses only a few iteration passes to reach the order of accuracy of the parent solution. Analysis of the multi-pass algorithm shows that the first iteration pass belongs to the family of (p+1)-stage stiff accurate Singly-Diagonal-Implicit-Runge-Kutta (SDIRK) method. The methods developed can be viewed as a generalization to the SDIRK method, retaining the desirable features of efficiency and stability, now extended to high-order accuracy. An example of a transient solution to the scalar wave equation demonstrates the efficiency and accuracy of the multi-pass algorithms over standard second-order accurate single-step/single-solve (SS/SS) methods.
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ASME 2006 International Mechanical Engineering Congress and Exposition
November 5–10, 2006
Chicago, Illinois, USA
Conference Sponsors:
- Noise Control and Acoustics Division
ISBN:
0-7918-4776-4
PROCEEDINGS PAPER
Stabilized Time-Discontinuous Galerkin Methods With Applications to Structural Acoustics
Prapot Kunthong
Prapot Kunthong
Kasetsart University
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Lonny L. Thompson
Clemson University
Prapot Kunthong
Kasetsart University
Paper No:
IMECE2006-15753, pp. 31-40; 10 pages
Published Online:
December 14, 2007
Citation
Thompson, LL, & Kunthong, P. "Stabilized Time-Discontinuous Galerkin Methods With Applications to Structural Acoustics." Proceedings of the ASME 2006 International Mechanical Engineering Congress and Exposition. Noise Control and Acoustics. Chicago, Illinois, USA. November 5–10, 2006. pp. 31-40. ASME. https://doi.org/10.1115/IMECE2006-15753
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