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1999 | 26 | 2 | 229-242
Tytuł artykułu

Frequency analysis of preconditioned waveform relaxation iterations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting from semi-discretization of the heat equation in one and two dimensions. This theory and some heuristic arguments predict that preconditioning is most effective for the first few iterations.
Rocznik
Tom
26
Numer
2
Strony
229-242
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-01-12
Twórcy
  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
  • Department of Mathematics, Arizona State University, Tempe, Arizona 85287 , U.S.A.
Bibliografia
  • [1] K. Burrage, Parallel and Sequential Methods for Ordinary Differential Equations, Oxford Univ. Press, Oxford, 1995.
  • [2] K. Burrage, Z. Jackiewicz, S. P. Nørsett and R. Renaut, Preconditioning waveform relaxation iterations for differential systems, BIT 36 (1996), 54-76.
  • [3] Z. Jackiewicz, B. Owren and B. D. Welfert, Pseudospectra of waveform relaxation operators, Computers Math. Appl. 36 (1998), 67-85.
  • [4] B. Leimkuhler, Estimating waveform relaxation convergence, SIAM J. Sci. Comput. 14 (1993), 872-889.
  • [5] E. Lelerasmee, A. Ruehli and A. Sangiovanni-Vincentelli, The waveform relaxation method for time domain analysis of large scale integrated circuits, IEEE Trans. on CAD of IC and Systems 1 (1982), 131-145.
  • [6] U. Miekkala and O. Nevanlinna, Convergence of dynamic iteration methods for initial value problems, SIAM J. Sci. Statist. Comput. 8 (1987), 459-482.
  • [7] O. Nevanlinna, Remarks on Picard-Lindelöf iteration, Part I, BIT 29 (1989), 328-346.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv26i2p229bwm
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