메뉴 건너뛰기




Volumn 34, Issue 4, 1997, Pages 1616-1639

The spectral projection decomposition method for elliptic equations in two dimensions

Author keywords

Domain decomposition; Elliptic problems; Spectral methods

Indexed keywords


EID: 0001460384     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994265334     Document Type: Article
Times cited : (12)

References (30)
  • 1
    • 0347990832 scopus 로고
    • Domain Decomposition Methods: Some Results of Theory and Applications
    • R. Glowinski, Y. A. Kuznetsov, G. Meurant, J. Périaux, and O. Widlund, eds., SIAM, Philadelphia, PA
    • V. AGOSHKOV, Domain Decomposition Methods: Some Results of Theory and Applications, in Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, Y. A. Kuznetsov, G. Meurant, J. Périaux, and O. Widlund, eds., SIAM, Philadelphia, PA, 1991, pp. 3-18.
    • (1991) Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations , pp. 3-18
    • Agoshkov, V.1
  • 2
    • 0003036621 scopus 로고
    • The Poincaré-Steklov's operators and the domain decomposition algorithms in variational problems
    • Nauka, Moscow (in Russian)
    • V. AGOSHKOV AND V. LEBEDEV, The Poincaré-Steklov's operators and the domain decomposition algorithms in variational problems, Computational Processes and Systems, 2 (1985), pp. 173-227; Nauka, Moscow (in Russian).
    • (1985) Computational Processes and Systems , vol.2 , pp. 173-227
    • Agoshkov, V.1    Lebedev, V.2
  • 5
    • 84966238014 scopus 로고
    • An iterative method for elliptic problems on regions partitioned into substructures
    • J. BRAMBLE, J. PASCIAK, AND A. SCHATZ, An iterative method for elliptic problems on regions partitioned into substructures, Math. Comp., 46 (1986), pp. 361-369.
    • (1986) Math. Comp. , vol.46 , pp. 361-369
    • Bramble, J.1    Pasciak, J.2    Schatz, A.3
  • 6
    • 0039035534 scopus 로고
    • The Schwarz algorithm for spectral methods
    • C. CANUTO AND D. FUNARO, The Schwarz algorithm for spectral methods, SIAM J. Numer. Anal., 25 (1988), pp. 24-40.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 24-40
    • Canuto, C.1    Funaro, D.2
  • 8
    • 84974325009 scopus 로고
    • Domain decomposition algorithms
    • Cambridge University Press, London
    • T. CHAN AND T. MATHEW, Domain decomposition algorithms, in Acta Numerica, Cambridge University Press, London, 1994, pp. 61-143.
    • (1994) Acta Numerica , pp. 61-143
    • Chan, T.1    Mathew, T.2
  • 10
    • 0006182474 scopus 로고
    • Some domain decomposition algorithms for elliptic problems
    • L. Hayes and D. Kincaid, eds., Academic Press, New York
    • M. DRYJA AND O. WIDLUND, Some domain decomposition algorithms for elliptic problems, in Iterative Methods for Large Linear Systems, L. Hayes and D. Kincaid, eds., Academic Press, New York, 1989, pp. 273-291.
    • (1989) Iterative Methods for Large Linear Systems , pp. 273-291
    • Dryja, M.1    Widlund, O.2
  • 11
    • 0026978939 scopus 로고
    • Additive Schwarz methods for elliptic finite element problems in three dimensions
    • T. F. Chan, D. Keyes, G. Meurant, J. Scroggs, and R. Voigt, eds., SIAM, Philadelphia, PA
    • M. DRYJA AND O. WIDLUND, Additive Schwarz methods for elliptic finite element problems in three dimensions, in Proc. Fifth Conf. on Domain Decomposition Methods for Partial Differential Equations, T. F. Chan, D. Keyes, G. Meurant, J. Scroggs, and R. Voigt, eds., SIAM, Philadelphia, PA, 1992.
    • (1992) Proc. Fifth Conf. on Domain Decomposition Methods for Partial Differential Equations
    • Dryja, M.1    Widlund, O.2
  • 12
    • 0012775712 scopus 로고
    • Some recent results on Schwarz type domain decomposition algorithms
    • A. Quarteroni et al., eds., American Mathematical Society, Providence, RI
    • M. DRYJA AND O. WIDLUND, Some recent results on Schwarz type domain decomposition algorithms, in Proc. Sixth Conf. on Domain Decomposition Methods for Partial Differential Equations, A. Quarteroni et al., eds., American Mathematical Society, Providence, RI, 1994, pp. 53-62.
    • (1994) Proc. Sixth Conf. on Domain Decomposition Methods for Partial Differential Equations , pp. 53-62
    • Dryja, M.1    Widlund, O.2
  • 13
    • 0000429099 scopus 로고
    • An iterative procedure with interface relaxation for domain decomposition methods
    • D. FUNARO, A. QUARTERONI, AND P. ZANOLLI, An iterative procedure with interface relaxation for domain decomposition methods, SIAM J. Numer. Anal., 25 (1988), pp. 1213-1236.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 1213-1236
    • Funaro, D.1    Quarteroni, A.2    Zanolli, P.3
  • 14
    • 0001238431 scopus 로고
    • Caratterizzazione delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili
    • E. GAGLIARDO, Caratterizzazione delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Rend. Sem. Mat. Univ. Padova, 27 (1957), pp. 284-305.
    • (1957) Rend. Sem. Mat. Univ. Padova , vol.27 , pp. 284-305
    • Gagliardo, E.1
  • 18
    • 0024917277 scopus 로고
    • Spectral element methods for the incompressible Navier-Stokes equations
    • A. K. Noor and J. T. Oden, eds., ASME, New York
    • Y. MADAY AND A. PATERA, Spectral element methods for the incompressible Navier-Stokes equations, in State-of-the-Art Surveys on Computational Mechanics, A. K. Noor and J. T. Oden, eds., ASME, New York, 1989.
    • (1989) State-of-the-Art Surveys on Computational Mechanics
    • Maday, Y.1    Patera, A.2
  • 20
    • 85013126603 scopus 로고
    • Spectral methods for problem in complex geometries
    • S. ORSZAG, Spectral methods for problem in complex geometries, J. Comput. Phys., 37 (1980), pp. 70-92.
    • (1980) J. Comput. Phys. , vol.37 , pp. 70-92
    • Orszag, S.1
  • 21
    • 51249165943 scopus 로고
    • The construction of a well-conditioned basis for the projection decomposition method
    • E. OVTCHINNIKOV, The construction of a well-conditioned basis for the projection decomposition method, Calcolo, 30 (1993), pp. 255-271.
    • (1993) Calcolo , vol.30 , pp. 255-271
    • Ovtchinnikov, E.1
  • 22
    • 48549109395 scopus 로고
    • A spectral element method for fluid dynamics: Laminar flow in a channel expansion
    • A. PATERA, A spectral element method for fluid dynamics: Laminar flow in a channel expansion, J. Comput. Phys., 54 (1984), pp. 468-488.
    • (1984) J. Comput. Phys. , vol.54 , pp. 468-488
    • Patera, A.1
  • 25
    • 0002293638 scopus 로고
    • Domain decomposition and parallel processing for the numerical solution of partial differential equations
    • A. QUARTERONI, Domain decomposition and parallel processing for the numerical solution of partial differential equations, Surveys Math. Indust., 1 (1991), pp. 75-118.
    • (1991) Surveys Math. Indust. , vol.1 , pp. 75-118
    • Quarteroni, A.1
  • 26
    • 0010375775 scopus 로고
    • Domain decomposition preconditioned for the spectral collocation methods
    • A. QUARTERONI AND G. S. LANDRIANI, Domain decomposition preconditioned for the spectral collocation methods, J. Sci. Comput., 3 (1988), pp. 45-75.
    • (1988) J. Sci. Comput. , vol.3 , pp. 45-75
    • Quarteroni, A.1    Landriani, G.S.2
  • 27
    • 0009481914 scopus 로고
    • Theory and application of Steklov-Poincaré operators for boundary-value problems
    • R. Spigler, ed., Kluwer Academic Publishers, Dordrecht, the Netherlands
    • A. QUARTERONI AND A. VALLI, Theory and application of Steklov-Poincaré operators for boundary-value problems, in Applied and Industrial Mathematics, R. Spigler, ed., Kluwer Academic Publishers, Dordrecht, the Netherlands, 1990, pp. 179-203.
    • (1990) Applied and Industrial Mathematics , pp. 179-203
    • Quarteroni, A.1    Valli, A.2
  • 29
    • 0001004798 scopus 로고
    • On traces of functions from Sobolev spaces on piecewise-smooth surfaces
    • in Russian
    • G. YAKOVLEV, On traces of functions from Sobolev spaces on piecewise-smooth surfaces, Math. Coll., 74(4) (1967), pp. 526-542 (in Russian).
    • (1967) Math. Coll. , vol.74 , Issue.4 , pp. 526-542
    • Yakovlev, G.1
  • 30
    • 51249173618 scopus 로고
    • Domain decomposition algorithms for spectral methods
    • P. ZANOLLI, Domain decomposition algorithms for spectral methods, Calcolo, 24 (1987), pp. 201-240.
    • (1987) Calcolo , vol.24 , pp. 201-240
    • Zanolli, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.