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Volumn 59, Issue 3-4, 2009, Pages 424-435

Parallel solution in time of ODEs: some achievements and perspectives

Author keywords

"Parareal" algorithm; Block one step methods; Boundary Value Methods (BVMs); Initial Value Problems; Ordinary Differential Equations; Parallel Computing; Parallel factorizations; Parallel methods "in time" for ODEs; Stiff Problems

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; FACTORIZATION; INITIAL VALUE PROBLEMS; OPTIMAL CONTROL SYSTEMS; PARALLEL ALGORITHMS; PARALLEL PROCESSING SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 58249094038     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2008.03.024     Document Type: Article
Times cited : (19)

References (25)
  • 1
    • 0009193978 scopus 로고
    • Parallel factorizations and parallel solvers for tridiagonal linear systems
    • Amodio P., and Brugnano L. Parallel factorizations and parallel solvers for tridiagonal linear systems. Linear Algebra Appl. 172 (1992) 347-364
    • (1992) Linear Algebra Appl. , vol.172 , pp. 347-364
    • Amodio, P.1    Brugnano, L.2
  • 2
    • 0029341268 scopus 로고
    • The parallel QR factorization algorithm for tridiagonal linear systems
    • Amodio P., and Brugnano L. The parallel QR factorization algorithm for tridiagonal linear systems. Parallel Computing 21 (1995) 1097-1110
    • (1995) Parallel Computing , vol.21 , pp. 1097-1110
    • Amodio, P.1    Brugnano, L.2
  • 3
    • 0031078576 scopus 로고    scopus 로고
    • Parallel implementation of block boundary value methods for ODEs
    • Amodio P., and Brugnano L. Parallel implementation of block boundary value methods for ODEs. J. Comput. Appl. Math. 78 (1997) 197-211
    • (1997) J. Comput. Appl. Math. , vol.78 , pp. 197-211
    • Amodio, P.1    Brugnano, L.2
  • 4
    • 0031502534 scopus 로고    scopus 로고
    • Parallel ODE solvers based on block BVMs
    • Amodio P., and Brugnano L. Parallel ODE solvers based on block BVMs. Adv. Comput. Math. 7 (1997) 5-26
    • (1997) Adv. Comput. Math. , vol.7 , pp. 5-26
    • Amodio, P.1    Brugnano, L.2
  • 5
    • 0032182568 scopus 로고    scopus 로고
    • ParalleloGAM: a parallel code for ODEs
    • Amodio P., and Brugnano L. ParalleloGAM: a parallel code for ODEs. Appl. Numer. Math. 28 (1998) 95-106
    • (1998) Appl. Numer. Math. , vol.28 , pp. 95-106
    • Amodio, P.1    Brugnano, L.2
  • 6
    • 48349124600 scopus 로고    scopus 로고
    • Numerical solution of general Bordered ABD linear systems by cyclic reduction
    • Amodio P., Gladwell I., and Romanazzi G. Numerical solution of general Bordered ABD linear systems by cyclic reduction. J. Numer. Anal. Ind. Appl. Math. 1 (2006) 5-12
    • (2006) J. Numer. Anal. Ind. Appl. Math. , vol.1 , pp. 5-12
    • Amodio, P.1    Gladwell, I.2    Romanazzi, G.3
  • 7
    • 33845533427 scopus 로고    scopus 로고
    • BABDCR: a Fortran 90 package for the solution of Bordered ABD linear systems
    • Amodio P., and Romanazzi G. BABDCR: a Fortran 90 package for the solution of Bordered ABD linear systems. ACM Trans. Math. Software 32 (2006) 597-608
    • (2006) ACM Trans. Math. Software , vol.32 , pp. 597-608
    • Amodio, P.1    Romanazzi, G.2
  • 8
    • 0027607183 scopus 로고
    • Parallel factorizations for tridiagonal matrices
    • Amodio P., Brugnano L., and Politi T. Parallel factorizations for tridiagonal matrices. SIAM J. Numer. Anal. 30 (1993) 813-823
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 813-823
    • Amodio, P.1    Brugnano, L.2    Politi, T.3
  • 9
    • 19844366465 scopus 로고    scopus 로고
    • Computational chemistry from the perspective of numerical analysis
    • Le Bris C. Computational chemistry from the perspective of numerical analysis. Acta Numerica 14 (2005) 363-444
    • (2005) Acta Numerica , vol.14 , pp. 363-444
    • Le Bris, C.1
  • 10
    • 0031274968 scopus 로고    scopus 로고
    • On the potentiality of sequential and parallel codes based on extended trapezoidal rules (ETRs)
    • Brugnano L., and Trigiante D. On the potentiality of sequential and parallel codes based on extended trapezoidal rules (ETRs). Appl. Numer. Math. 25 (1997) 169-184
    • (1997) Appl. Numer. Math. , vol.25 , pp. 169-184
    • Brugnano, L.1    Trigiante, D.2
  • 11
    • 0031078576 scopus 로고    scopus 로고
    • Parallel implementation of block boundary value methods on nonlinear problems: theoretical results
    • Brugnano L., and Trigiante D. Parallel implementation of block boundary value methods on nonlinear problems: theoretical results. Appl. Numer. Math. 78 (1997) 197-211
    • (1997) Appl. Numer. Math. , vol.78 , pp. 197-211
    • Brugnano, L.1    Trigiante, D.2
  • 14
    • 58249087415 scopus 로고    scopus 로고
    • Burrage K. (Ed)
    • In: Burrage K. (Ed). Parallel Methods for ODEs. Adv. Comput. Math. 7 1-2 (1997)
    • (1997) Adv. Comput. Math. , vol.7 , Issue.1-2
  • 15
    • 58249093657 scopus 로고    scopus 로고
    • Nonlinear convergence analysis for the Parareal algorithm
    • Domain Decomposition Methods in Science and Engineering XVII. Langer U., Discacciati M., Keyes D.E., Widlund O.B., and Zulehner W. (Eds), Springer, Berlin
    • Gander M.J., and Hairer E. Nonlinear convergence analysis for the Parareal algorithm. In: Langer U., Discacciati M., Keyes D.E., Widlund O.B., and Zulehner W. (Eds). Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering vol. 60 (2008), Springer, Berlin 45-56
    • (2008) Lecture Notes in Computational Science and Engineering , vol.60 , pp. 45-56
    • Gander, M.J.1    Hairer, E.2
  • 16
    • 84880377633 scopus 로고    scopus 로고
    • On the superlinear and linear convergence of the Parareal algorithm
    • Domain Decomposition Methods in Science and Engineering XVI. Widlund O.B., and Keyes D.E. (Eds), Springer, Berlin
    • Gander M.J., and Vandewalle S. On the superlinear and linear convergence of the Parareal algorithm. In: Widlund O.B., and Keyes D.E. (Eds). Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering vol. 55 (2007), Springer, Berlin 291-298
    • (2007) Lecture Notes in Computational Science and Engineering , vol.55 , pp. 291-298
    • Gander, M.J.1    Vandewalle, S.2
  • 17
    • 41449117770 scopus 로고    scopus 로고
    • Analysis of the Parareal time-parallel time-integration method
    • Gander M.J., and Vandewalle S. Analysis of the Parareal time-parallel time-integration method. SIAM J. Sci. Comput. 29 (2007) 556-578
    • (2007) SIAM J. Sci. Comput. , vol.29 , pp. 556-578
    • Gander, M.J.1    Vandewalle, S.2
  • 18
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential operator
    • Hochbruck M., and Lubich C. On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34 (1997) 1911-1925
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 20
    • 0038662511 scopus 로고    scopus 로고
    • A parareal in time procedure for the control of partial differential equations
    • Maday Y., and Turinici G. A parareal in time procedure for the control of partial differential equations. C. R. Acad. Sci. Paris, Ser. I 335 (2002) 387-392
    • (2002) C. R. Acad. Sci. Paris, Ser. I , vol.335 , pp. 387-392
    • Maday, Y.1    Turinici, G.2
  • 21
    • 58249089699 scopus 로고    scopus 로고
    • The Parareal in time iterative solver: a further direction to parallel implementation
    • Domain Decomposition Methods in Science and Engineering. Barth T.J., Griebel M., Keyes D.E., Nieminen R.M., Roose D., Schlick T., Kornhuber R., Hoppe R., Périaux J., Pironneau O., Widlund O., and Xu J. (Eds), Springer, Berlin
    • Maday Y., and Turinici G. The Parareal in time iterative solver: a further direction to parallel implementation. In: Barth T.J., Griebel M., Keyes D.E., Nieminen R.M., Roose D., Schlick T., Kornhuber R., Hoppe R., Périaux J., Pironneau O., Widlund O., and Xu J. (Eds). Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering vol. 40 (2005), Springer, Berlin 441-448
    • (2005) Lecture Notes in Computational Science and Engineering , vol.40 , pp. 441-448
    • Maday, Y.1    Turinici, G.2
  • 22
    • 8144228833 scopus 로고    scopus 로고
    • RD-rational approximations of the matrix exponential
    • Moret I., and Novati P. RD-rational approximations of the matrix exponential. BIT 44 (2004) 595-615
    • (2004) BIT , vol.44 , pp. 595-615
    • Moret, I.1    Novati, P.2
  • 23
    • 0026818185 scopus 로고
    • Analysis of some Krylov subspace approximations to the matrix exponential operator
    • Saad Y. Analysis of some Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 29 (1992) 209-228
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 209-228
    • Saad, Y.1
  • 24
    • 58249083831 scopus 로고    scopus 로고
    • G.A. Staff, The Parareal algorithm. A survey of present work, Report of the Norwegian University of Science and Technology, Dept. of Math. Sciences, 2003
    • G.A. Staff, The Parareal algorithm. A survey of present work, Report of the Norwegian University of Science and Technology, Dept. of Math. Sciences, 2003
  • 25
    • 58249088543 scopus 로고    scopus 로고
    • S. Ulbrich, Generalized SQP-methods with "Parareal" time decomposition for time-dependent PDE-constrained optimization, Technical Report, Fachbereich Mathematik, TU Darmstadt, 2005
    • S. Ulbrich, Generalized SQP-methods with "Parareal" time decomposition for time-dependent PDE-constrained optimization, Technical Report, Fachbereich Mathematik, TU Darmstadt, 2005


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.