An efficient solver for the high-order accurate time-discontinuous Galerkin (TDG) method for second-order hyperbolic systems

Finite Elements in Analysis and Design

Volumn 41, Issue 7-8, 2005, Pages 729-762

  Kunthong, Prapot ^a   Thompson, Lonny L ^a  

^a AMRL   (United States)

Author keywords

High order accurate time stepping schemes; Predictor multi corrector algorithms; Second order hyperbolic equation; Time discontinuous Galerkin method; Time integration methods

Indexed keywords

ADAPTIVE ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; FINITE ELEMENT METHOD; ITERATIVE METHODS; MATRIX ALGEBRA;

HIGH-ORDER ACCURATE TIME STEPPING SCHEMES; PREDICTOR/MULTI-CORRECTOR ALGORITHMS; SECOND-ORDER HYPERBOLIC EQUATIONS; TIME-DISCONTINUOUS GALERKIN METHODS; TIME-INTEGRATION METHODS;

GALERKIN METHODS;

EID: 14844304729     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.finel.2004.09.003     Document Type: Conference Paper

References (35)

1. T.J. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Publication, Inc., 2000.
2. M.A. Dokainish, and K. Subbaraj A survey of direct time-integration methods in computational structural dynamics - I Explicit methods Comput. Struct. 32 6 1989 1371 1386
3. K. Subbaraj, and M.A. Dokainish A survey of direct time-integration methods in computational structural dynamics - II Implicit methods Comput. Struct. 32 6 1989 1387 1401
4. X. Zhou, and K.K. Tamma Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics Internat. J. Numer. Methods Eng. 59 2004 597 668
5. G.G. Dahlquist A special stability problem for linear multistep methods BIT 3 1963 27 43
6. N.M. Newmark A method of computation for structural dynamics J. Eng. Mech. Div. ASCE 85 EM3 1959 67 94
7. J. Chung, and G.M. Hulbert A time integration algorithm for structural dynamics with improved numerical dissipation The Generalized- α method J. Appl. Mech. TRANS. ASME 60 1993 371 375
8. H.M. Hilber, T.J.R. Hughes, and R.L. Taylor Improved numerical dissipation for time integration algorithms in structural dynamics Earthquake Eng. Struct. Dynam. 5 1977 283 292
9. W.L. Wood, M. Bossak, and O.C. Zienkiewicz An alpha modification of Newmark's method Internat. J. Numer. Methods Eng. 15 1981 1562 1566
10. W. Seward, G. Fairweather, and R. Johnston A survey of high-order methods for the numerical integration of semidiscrete parabolic problems IMA J. Numer. Anal. 4 1984 375 425
11. M. Austin High-order integration of smooth dynamical systems Theory and numerical experiments Internat. J. Numer. Methods Eng. 36 1993 2107 2122
12. C.E. Kees, and C.T. Miller Higher order time integration methods for two-phase flow Adv. Water Resources 25 2002 159 177
13. J. Donea, B. Roig, and A. Huerta High-order accurate time-stepping schemes for convection-diffusion problems Comput. Methods Appl. Mech. Eng. 182 2000 249 275
14. R. Alexander Diagonally implicit Runge-Kutta methods for stiff O.D.E.'s SIAM J. Numer. Anal. 14 6 1977 1006 1021
15. B. Owren, and H. Simonsen Alternative integration methods for problems in structural dynamics Comput. Methods Appl. Mech. Eng. 122 1995 1 10
16. T.J. Hughes, and G.M. Hulbert Space-time finite element methods for elastodynamics Formulations and error estimates Comput. Methods Appl. Mech. Eng. 66 1988 339 363
17. G.M. Hulbert Time finite element methods for structural dynamics Internat. J. Numer. Methods Eng. 33 1992 307 331
18. T.C. Fung Weighting parameters for unconditionally stable higher-order accurate time step integration algorithms. Part 1 - First-order equations Internat. J. Numer. Methods Eng. 45 1999 941 970
19. T.C. Fung Weighting parameters for unconditionally stable higher-order accurate time step integration algorithms. Part 2 - Second-order equations Internat. J. Numer. Methods Eng. 45 1999 971 1006
20. L.L. Thompson, D. He, Adaptive space-time finite element methods for the wave equation on unbounded domains, Comput. Methods Appl. Mech. Eng., 2004, in press.
21. S. Subbarayalu, L.L. Thompson, hp -adaptive time-discontinuous Galerkin finite element methods for time-dependent waves, Proceedings of 2004 ASME International Mechanical Engineering Congress & Exposition, November 2004, Anaheim, CA., Paper IMECE 2004-60403.
22. X.D. Li, and N.-E. Wiberg Structural dynamic analysis by a time-discontinuous Galerkin finite element method Internat. J. Numer. Methods Eng. 39 1996 2131 2152
23. N.-E. Wiberg, and X.D. Li Adaptive finite element procedures for linear and nonlinear dynamics Internat. J. Num. Methods Eng. 46 1999 1781 1802
24. C.-C. Chien, and T.-Y. Wu An improved predictor/multi-corrector algorithm for a time-discontinuous Galerkin finite element method in structural dynamics Comput. Mech. 25 2000 430 437
25. M. Mancuso, and F. Ubertini An efficient integration procedure for linear dynamics based on a time discontinuous Galerkin formulation Comput. Mech. 32 2003 154 168
26. M. Mancuso, and F. Ubertini The Nørsett time integration methodology for finite element transient analysis Comput. Methods Appl. Mech. Eng. 191 2002 3297 3327
27. C.-C. Chien, and T.-Y. Wu An advanced time-discontinuous Galerkin finite element method for structural dynamics Comput. Model. Eng. Sci. 2 2 2001 213 226
28. A. Graham Kronecker Products and Matrix Calculus with Applications 1981 Wiley New York, USA
29. R.S. Burington Handbook of Mathematical Table and Formulas fifth ed. 1972 McGraw-Hill Book Company New York
30. E.D. Rainville Special Functions 1960 The Macmillan Company New York, USA
31. G.H. Golub, and C.F. van Loan Matrix Computations third ed. 1996 The Johns Hopkins University Press Baltimore, MD, USA
32. S. Pissanetzky Sparse Matrix Technology 1984 Academic Press Inc. Orlando, FL
33. E. Hairer, S. Nørsett, and G. Wanner Solving Ordinary Differential Equations I Nonstiff Problems 1993 Springer Berlin
34. E. Hairer, and G. Wanner Solving Ordinary Differential Equations II Stiff and Differential-Algebraic Problems 1991 Springer Berlin
35. G.M. Hulbert, and T.J. Hughes Space-time finite element methods for second-order hyperbolic equations Comput. Methods Appl. Mech. Eng. 84 1990 327 348