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Volumn 18, Issue 1, 1997, Pages 56-68

A cyclic reduction approach to the numerical solution of boundary value ODEs

Author keywords

ABD systems; Boundary value problems; Parallel solvers

Indexed keywords

BLOCK DIAGONAL STRUCTURE; CYCLIC REDUCTION ALGORITHM; DISTRIBUTED MEMORY PARALLEL COMPUTER;

EID: 0030621835     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827595287225     Document Type: Article
Times cited : (17)

References (22)
  • 1
    • 0027607183 scopus 로고
    • Parallel factorizations for tridiagonal matrices
    • P. AMODIO, L. BRUGNANO, AND T. POLITI, Parallel factorizations for tridiagonal matrices, SIAM J. Numer. Anal., 30 (1993), pp. 813-823.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 813-823
    • Amodio, P.1    Brugnano, L.2    Politi, T.3
  • 2
    • 0027702693 scopus 로고
    • A parallel version of the cyclic reduction algorithm on a hypercube
    • P. AMODIO AND N. MASTRONARDI, A parallel version of the cyclic reduction algorithm on a hypercube, Parallel Comput., 19 (1993), pp. 1273-1281.
    • (1993) Parallel Comput. , vol.19 , pp. 1273-1281
    • Amodio, P.1    Mastronardi, N.2
  • 3
    • 3042985310 scopus 로고    scopus 로고
    • Parallel solution of almost block diagonal systems on a hypercube
    • P. AMODIO AND M. PAPRZYCKI, Parallel solution of almost block diagonal systems on a hypercube, Linear Algebra Appl., 241-243 (1996), pp. 85-103.
    • (1996) Linear Algebra Appl. , vol.241-243 , pp. 85-103
    • Amodio, P.1    Paprzycki, M.2
  • 6
    • 0038387017 scopus 로고
    • On parallel methods for boundary value ODE's
    • U. M. ASCHER AND S. Y. P. CHAN, On parallel methods for boundary value ODE's, Computing, 46 (1991), pp. 1-17.
    • (1991) Computing , vol.46 , pp. 1-17
    • Ascher, U.M.1    Chan, S.Y.P.2
  • 7
    • 0000161555 scopus 로고
    • On direct methods for solving Poisson's equations
    • B. L. BUZBEE, G. H. GOLUB, AND C. W. NIELSON, On direct methods for solving Poisson's equations, SIAM J. Numer. Anal., 7 (1970), pp. 627-656.
    • (1970) SIAM J. Numer. Anal. , vol.7 , pp. 627-656
    • Buzbee, B.L.1    Golub, G.H.2    Nielson, C.W.3
  • 8
    • 0030123372 scopus 로고    scopus 로고
    • High Performance Solution of Partial Differential Equations Discretized Using a Chebyshev Spectral Collocation Method
    • C. CYPHERS, M. PAPRZYCKI, AND A. KARAGEORGHIS, High Performance Solution of Partial Differential Equations Discretized Using a Chebyshev Spectral Collocation Method, J. Comput. Appl. Math., 69 (1996), pp. 71-80.
    • (1996) J. Comput. Appl. Math. , vol.69 , pp. 71-80
    • Cyphers, C.1    Paprzycki, M.2    Karageorghis, A.3
  • 9
    • 84976770923 scopus 로고
    • SOLVEBLOCK: A package for solving almost block diagonal linear systems
    • C. DE BOOR AND R. WEISS, SOLVEBLOCK: A package for solving almost block diagonal linear systems, ACM Trans. Math. Software, 6 (1980), pp. 80-87.
    • (1980) ACM Trans. Math. Software , vol.6 , pp. 80-87
    • De Boor, C.1    Weiss, R.2
  • 10
    • 0020822005 scopus 로고
    • FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination
    • J. C. DIAZ, G. FAIRWEATHER, AND P. KEAST, FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination, ACM Trans. Math. Software, 9 (1983), pp. 358-375.
    • (1983) ACM Trans. Math. Software , vol.9 , pp. 358-375
    • Diaz, J.C.1    Fairweather, G.2    Keast, P.3
  • 11
    • 0027911840 scopus 로고
    • Parallel solution of almost block diagonal systems on the CRAY Y-MP using level 3 BLAS
    • I. GLADWELL AND M. PAPRZYCKI, Parallel solution of almost block diagonal systems on the CRAY Y-MP using level 3 BLAS, J. Comput. Appl. Math., 45 (1993), pp. 181-189.
    • (1993) J. Comput. Appl. Math. , vol.45 , pp. 181-189
    • Gladwell, I.1    Paprzycki, M.2
  • 12
    • 0016994637 scopus 로고
    • Some aspects of the cyclic reduction algorithm for block tridiagonal linear systems
    • D. HELLER, Some aspects of the cyclic reduction algorithm for block tridiagonal linear systems, SIAM J. Numer. Anal., 13 (1976), pp. 484-496.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 484-496
    • Heller, D.1
  • 13
    • 0022696923 scopus 로고
    • Numerical methods for stiff two-point boundary value problems
    • H. O. KREISS, K. NICHOLS, AND D. BROWN, Numerical methods for stiff two-point boundary value problems, SIAM J. Numer. Anal., 23 (1986), pp. 325-368.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 325-368
    • Kreiss, H.O.1    Nichols, K.2    Brown, D.3
  • 14
    • 0022031291 scopus 로고
    • Decoupling and stability of algorithms for boundary value problems
    • R. M. M. MATTHEIJ, Decoupling and stability of algorithms for boundary value problems, SIAM Rev., 27 (1985), pp. 1-44.
    • (1985) SIAM Rev. , vol.27 , pp. 1-44
    • Mattheij, R.M.M.1
  • 15
    • 0026173680 scopus 로고
    • Solving almost block diagonal systems on parallel computers
    • M. PAPRZYCKI AND I. GLADWELL, Solving almost block diagonal systems on parallel computers, Parallel Comput., 17 (1991), pp. 133-153.
    • (1991) Parallel Comput. , vol.17 , pp. 133-153
    • Paprzycki, M.1    Gladwell, I.2
  • 16
    • 0038387010 scopus 로고
    • Using Level 3 BLAS to Solve Almost Block Diagonal Systems
    • J. Dongarra, K. Kennedy, P. Messina, D. C. Sorensen, and R. V. Voigt, eds., SIAM, Philadelphia, PA
    • M. PAPRZYCKI AND I. GLADWELL, Using Level 3 BLAS to Solve Almost Block Diagonal Systems, in Proc. Fifth SIAM Conference on Parallel Processing for Scientific Computing, J. Dongarra, K. Kennedy, P. Messina, D. C. Sorensen, and R. V. Voigt, eds., SIAM, Philadelphia, PA, 1992, pp. 52-62.
    • (1992) Proc. Fifth SIAM Conference on Parallel Processing for Scientific Computing , pp. 52-62
    • Paprzycki, M.1    Gladwell, I.2
  • 17
    • 0016929260 scopus 로고
    • Alternate row and column elimination for solving certain linear systems
    • J. M. VARAH, Alternate row and column elimination for solving certain linear systems, SIAM J. Numer. Anal., 13 (1976), pp. 71-75.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 71-75
    • Varah, J.M.1
  • 18
    • 0027911857 scopus 로고
    • Parallel treatment of block-bidiagonal matrices in the solution of ordinary differential boundary value problems
    • K. WRIGHT, Parallel treatment of block-bidiagonal matrices in the solution of ordinary differential boundary value problems, J. Comput. Appl. Math., 45 (1993), pp. 191-200.
    • (1993) J. Comput. Appl. Math. , vol.45 , pp. 191-200
    • Wright, K.1
  • 19
    • 0001529832 scopus 로고
    • Stable parallel algorithms for two-point boundary value problems
    • S. WRIGHT, Stable parallel algorithms for two-point boundary value problems, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 742-764.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 742-764
    • Wright, S.1
  • 20
    • 21344482160 scopus 로고
    • Stable parallel elimination for boundary value ODE's
    • S. WRIGHT, Stable parallel elimination for boundary value ODE's, Numer. Math., 67 (1994), pp. 521-536.
    • (1994) Numer. Math. , vol.67 , pp. 521-536
    • Wright, S.1
  • 21
    • 0042192743 scopus 로고
    • 3L Ltd., Livingston, Scotland
    • Parallel FORTRAN User Guide, 3L Ltd., Livingston, Scotland, 1988.
    • (1988) Parallel FORTRAN User Guide
  • 22


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.