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Volumn 36, Issue 1, 1996, Pages 54-76

Preconditioning waveform relaxation iterations for differential systems

Author keywords

Error analysis; Overlapping; Parallel computing; Preconditioning; Splittings; Waveform relaxation

Indexed keywords


EID: 0042439581     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01740544     Document Type: Article
Times cited : (22)

References (27)
  • 1
    • 0027153796 scopus 로고
    • The use of Runge-Kutta formulae in waveform relaxation methods
    • A. Bellen and M. Zennaro, The use of Runge-Kutta formulae in waveform relaxation methods, Appl. Numer. Math., 11 (1993), pp. 95-114.
    • (1993) Appl. Numer. Math. , vol.11 , pp. 95-114
    • Bellen, A.1    Zennaro, M.2
  • 2
    • 0028413789 scopus 로고
    • Contractivity of waveform relaxation Runge-Kutta iterations and related limit methods for dissipative systems in the maximum norm
    • A. Bellen, Z. Jackiewicz and M. Zennaro, Contractivity of waveform relaxation Runge-Kutta iterations and related limit methods for dissipative systems in the maximum norm, SIAM J. Numer. Anal., 31 (1994), pp. 499-523.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 499-523
    • Bellen, A.1    Jackiewicz, Z.2    Zennaro, M.3
  • 5
    • 51249166420 scopus 로고
    • Numerical integration of ordinary differential equations on manifolds
    • P. E. Crouch and R. Grossman, Numerical integration of ordinary differential equations on manifolds, J. Nonlinear Science, 3 (1993), pp. 1-33.
    • (1993) J. Nonlinear Science , vol.3 , pp. 1-33
    • Crouch, P.E.1    Grossman, R.2
  • 6
    • 2542526489 scopus 로고
    • A comparison result for multisplittings based on overlapping blocks and its application to waveform relaxation methods
    • ETH, Zürich, Switzerland
    • A. Frommer and B. Pohl, A comparison result for multisplittings based on overlapping blocks and its application to waveform relaxation methods, Research Report No. 93-05, Seminar für Angewandte Mathematik, ETH, Zürich, Switzerland, 1993.
    • (1993) Research Report No. 93-05, Seminar für Angewandte Mathematik
    • Frommer, A.1    Pohl, B.2
  • 7
    • 85006447862 scopus 로고
    • On the parallel solution of parabolic equations
    • E. Gallopoulos and Y. Saad, On the parallel solution of parabolic equations. In Proc. ACM SIGARCH-89, 1989, pp. 17-28.
    • (1989) Proc. ACM SIGARCH-89 , pp. 17-28
    • Gallopoulos, E.1    Saad, Y.2
  • 10
    • 0013453233 scopus 로고
    • Estimating waveform relaxation convergence
    • B. Leimkuhler, Estimating waveform relaxation convergence, SIAM J. Sci. Comput., 14 (1993), pp. 872-889.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 872-889
    • Leimkuhler, B.1
  • 11
    • 0013364299 scopus 로고
    • Rapid convergence of waveform relaxation
    • B. Leimkuhler and A. Ruehli, Rapid convergence of waveform relaxation, Appl. Numer. Math., 11 (1993), pp. 211-224.
    • (1993) Appl. Numer. Math. , vol.11 , pp. 211-224
    • Leimkuhler, B.1    Ruehli, A.2
  • 13
  • 15
    • 0040519093 scopus 로고
    • Chebyshev acceleration of Picard-Lindelöf iteration
    • Ch. Lubich, Chebyshev acceleration of Picard-Lindelöf iteration, BIT, 32 (1991), pp. 535-538.
    • (1991) BIT , vol.32 , pp. 535-538
    • Lubich, Ch.1
  • 16
    • 0001363909 scopus 로고
    • Convergence of dynamic iteration methods for initial value problems
    • U. Miekkala and O. Nevanlinna, Convergence of dynamic iteration methods for initial value problems, SIAM J. Sci. Stat. Comput., 8 (1987), pp. 459-482.
    • (1987) SIAM J. Sci. Stat. Comput. , vol.8 , pp. 459-482
    • Miekkala, U.1    Nevanlinna, O.2
  • 17
    • 0023577978 scopus 로고
    • Sets of convergence and stability regions
    • U. Miekkala and O. Nevanlinna, Sets of convergence and stability regions, BIT, 27 (1987), pp. 557-584.
    • (1987) BIT , vol.27 , pp. 557-584
    • Miekkala, U.1    Nevanlinna, O.2
  • 18
    • 0001065602 scopus 로고
    • Remarks on Picard-Lindelöf iteration
    • O. Nevanlinna, Remarks on Picard-Lindelöf iteration, Part I, BIT, 29 (1989), pp. 328-346.
    • (1989) BIT , vol.29 , Issue.1 PART , pp. 328-346
    • Nevanlinna, O.1
  • 19
    • 0010890116 scopus 로고
    • Remarks on Picard-Lindelöf iteration
    • O. Nevanlinna, Remarks on Picard-Lindelöf iteration, Part II, BIT, 29 (1989), pp. 535-562.
    • (1989) BIT , vol.29 , Issue.2 PART , pp. 535-562
    • Nevanlinna, O.1
  • 20
    • 0010945263 scopus 로고
    • Linear acceleration of Picard-Lindelöf iteration
    • O. Nevanlinna, Linear acceleration of Picard-Lindelöf iteration, Numer. Math., 57 (1990), pp. 147-156.
    • (1990) Numer. Math. , vol.57 , pp. 147-156
    • Nevanlinna, O.1
  • 22
    • 0000812823 scopus 로고
    • Waveform iteration and the shifted Picard splitting
    • R. D. Skeel, Waveform iteration and the shifted Picard splitting, SIAM J. Sci. Stat. Comput., 10 (1989), pp. 756-776.
    • (1989) SIAM J. Sci. Stat. Comput. , vol.10 , pp. 756-776
    • Skeel, R.D.1
  • 23
    • 0007148549 scopus 로고
    • Student Report, Division of Mathematical Sciences, Norwegian Institute of Technology, Trondheim, Norway
    • R. E. Spilling, Dynamic iteration and the pseudospectral method, Student Report, Division of Mathematical Sciences, Norwegian Institute of Technology, Trondheim, Norway, 1993.
    • (1993) Dynamic Iteration and the Pseudospectral Method
    • Spilling, R.E.1
  • 24
    • 38249007178 scopus 로고
    • On the convergence of the discretized multisplitting waveform relaxation algorithm
    • B. Pohl, On the convergence of the discretized multisplitting waveform relaxation algorithm, Appl. Numer. Math., 11 (1993), pp. 251-258.
    • (1993) Appl. Numer. Math. , vol.11 , pp. 251-258
    • Pohl, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.