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Volumn 16, Issue 1, 1996, Pages 75-91

A parallel iterative nonoverlapping domain decomposition procedure for elliptic problems

Author keywords

[No Author keywords available]

Indexed keywords

DOMAIN DECOMPOSITION METHODS;

EID: 0030508286     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/16.1.75     Document Type: Article
Times cited : (22)

References (32)
  • 1
    • 0022918065 scopus 로고
    • Iterative methods for the solution of elliptic problems on regions partitioned into substructures
    • BJORSTAD, P., & WIDLUND, O. 1986 Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal. 23, 1097-1120.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 1097-1120
    • Bjorstad, P.1    Widlund, O.2
  • 2
    • 0039002581 scopus 로고
    • Alternating direction multistep methods for parabolic problems - Iterative stabilization
    • BRAMBLE, J. H., EWING, R. E., & LI, G. 1989a Alternating direction multistep methods for parabolic problems - iterative stabilization. SIAM J. Numer. Anal. 26, 904-919.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 904-919
    • Bramble, J.H.1    Ewing, R.E.2    Li, G.3
  • 3
    • 84966202987 scopus 로고
    • Incomplete iterations in multstep backward difference methods for parabolic problems with smooth and nonsmooth data
    • BRAMBLE, J. H., PASCIAK, J. E., SAMMON, P. H., & THOMEE, V. 1989b Incomplete iterations in multstep backward difference methods for parabolic problems with smooth and nonsmooth data. Math. Comput. 52, 339-367.
    • (1989) Math. Comput. , vol.52 , pp. 339-367
    • Bramble, J.H.1    Pasciak, J.E.2    Sammon, P.H.3    Thomee, V.4
  • 4
    • 84966238014 scopus 로고
    • An iterative method for elliptic problems on regions partitioned into substructures
    • BRAMBLE, J. H., PASCIAK, J. E., & SCHATZ, A. H. 1986 An iterative method for elliptic problems on regions partitioned into substructures. Math. Comput. 46, 361-369.
    • (1986) Math. Comput. , vol.46 , pp. 361-369
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 5
    • 0007414358 scopus 로고
    • Analysis and tests of a local domain decomposition preconditioner
    • (R. Glowinski, Y. Kuznetsov, G. Meurant, J. Périaux and O. B. Widlund, eds). Philadelphia, PA: SIAM
    • DE ROECK, Y. H., & LE TALLEC, P. 1991 Analysis and tests of a local domain decomposition preconditioner. Proc. Fourth Int. Symp. on Domain Decomposition Methods for Partial Differential Equations (R. Glowinski, Y. Kuznetsov, G. Meurant, J. Périaux and O. B. Widlund, eds). Philadelphia, PA: SIAM, pp 112-128.
    • (1991) Proc. Fourth Int. Symp. on Domain Decomposition Methods for Partial Differential Equations , pp. 112-128
    • De Roeck, Y.H.1    Le Tallec, P.2
  • 6
    • 0001836507 scopus 로고
    • Domain decomposition method and the Helmholtz problem
    • (G. Cohen, L. Halpern and P. Joly, eds). Philadelphia, PA: SIAM
    • DESPRÉS, B. 1991 Domain decomposition method and the Helmholtz problem. Mathematical and Numerical Aspects of Wave Propagation Phenomena (G. Cohen, L. Halpern and P. Joly, eds). Philadelphia, PA: SIAM, pp 44-52.
    • (1991) Mathematical and Numerical Aspects of Wave Propagation Phenomena , pp. 44-52
    • Després, B.1
  • 7
    • 0039595292 scopus 로고
    • Incomplete iteration for time-stepping a nonlinear parabolic Galerkin method
    • DOUGLAS, J. JR., DUPONT, T., & EWING, R. E. 1979 Incomplete iteration for time-stepping a nonlinear parabolic Galerkin method. SIAM J. Numer. Anal. 16, 503-522.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 503-522
    • Douglas J., Jr.1    Dupont, T.2    Ewing, R.E.3
  • 8
    • 0040186500 scopus 로고
    • A time-stepping method for Galerkin approximations for nonlinear parabolic equations
    • (Springer Lecture Notes in Mathematics 630) (G. A. Watson, ed). Berlin: Springer
    • DOUGLAS, J. JR., DUPONT, T., & PERCELL, P. 1978 A time-stepping method for Galerkin approximations for nonlinear parabolic equations. Numerical Analysis, Dundee 1977 (Springer Lecture Notes in Mathematics 630) (G. A. Watson, ed). Berlin: Springer, pp 64-75.
    • (1978) Numerical Analysis, Dundee 1977 , pp. 64-75
    • Douglas J., Jr.1    Dupont, T.2    Percell, P.3
  • 9
    • 21144463078 scopus 로고
    • A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods
    • DOUGLAS, J. JR., PAES LEME, P. J., ROBERTS, J. E., & WANG, J. 1993 A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods. Numer. Math. 65, 95-108.
    • (1993) Numer. Math. , vol.65 , pp. 95-108
    • Douglas J., Jr.1    Paes Leme, P.J.2    Roberts, J.E.3    Wang, J.4
  • 10
    • 0001235787 scopus 로고
    • Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures
    • DOUGLAS, J. JR., & RUSSELL, T. F. 1982 Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal. 19, 871-885.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 871-885
    • Douglas J., Jr.1    Russell, T.F.2
  • 12
    • 0000429099 scopus 로고
    • An iterative procedure with interface relaxation for domain decomposition methods
    • FUNARO, D., QUARTERONI, A., & ZANOLLI, P. 1988 An iterative procedure with interface relaxation for domain decomposition methods. SIAM J. Numer. Anal. 25, 1213-1236.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 1213-1236
    • Funaro, D.1    Quarteroni, A.2    Zanolli, P.3
  • 13
    • 0026108674 scopus 로고
    • Domain decomposition methods for large linearly elliptic three-dimensional problems
    • LE TALLEC, P., DE ROECK, Y. H., & VIDRASCU, M. 1991 Domain decomposition methods for large linearly elliptic three-dimensional problems. J. Comput. Appl. Math. 34, 93-117.
    • (1991) J. Comput. Appl. Math. , vol.34 , pp. 93-117
    • Le Tallec, P.1    De Roeck, Y.H.2    Vidrascu, M.3
  • 14
    • 0002043434 scopus 로고
    • On the Schwarz alternating method I
    • (R. Glowinski, G. H. Golub, G. A. Meurant and J. Periaux, eds). Philadelphia, PA: SIAM
    • LIONS, P. L. 1988 On the Schwarz alternating method I. First Int. Symp. on Domain Decomposition Methods for Partial Differential Equations (R. Glowinski, G. H. Golub, G. A. Meurant and J. Periaux, eds). Philadelphia, PA: SIAM, pp 1-42.
    • (1988) First Int. Symp. on Domain Decomposition Methods for Partial Differential Equations , pp. 1-42
    • Lions, P.L.1
  • 15
    • 0003121787 scopus 로고
    • On the Schwarz alternating method III: A variant for nonoverlapping subdomains
    • (T. F. Chan, R. Glowinski, J. Periaux and O. B. Widlund, eds). Philadelphia, PA: SIAM
    • LIONS, P. L. 1990 On the Schwarz alternating method III: a variant for nonoverlapping subdomains. Third Int. Symp. on Domain Decomposition Methods for Partial Differential Equations (T. F. Chan, R. Glowinski, J. Periaux and O. B. Widlund, eds). Philadelphia, PA: SIAM, pp 202-223.
    • (1990) Third Int. Symp. on Domain Decomposition Methods for Partial Differential Equations , pp. 202-223
    • Lions, P.L.1
  • 17
    • 0027558407 scopus 로고
    • Balancing domain decomposition
    • MANDEL, J. 1993 Balancing domain decomposition. Commun. Numer. Methods Eng. 9, 233-241.
    • (1993) Commun. Numer. Methods Eng. , vol.9 , pp. 233-241
    • Mandel, J.1
  • 18
    • 0002220131 scopus 로고
    • An iterative procedure for domain decomposition methods: A finite element approach
    • (R. Glowinski, G. H. Golub, G. A. Meurant and J. Periaux, eds). Philadelphia, PA: SIAM
    • MARINI, L. D., & QUARTERONI, A. 1988 An iterative procedure for domain decomposition methods: a finite element approach. First Int. Symp. on Domain Decomposition Methods for Partial Differential Equations (R. Glowinski, G. H. Golub, G. A. Meurant and J. Periaux, eds). Philadelphia, PA: SIAM, pp 129-143.
    • (1988) First Int. Symp. on Domain Decomposition Methods for Partial Differential Equations , pp. 129-143
    • Marini, L.D.1    Quarteroni, A.2
  • 19
    • 0000364321 scopus 로고
    • A relaxation procedure for domain decomposition methods using finite elements
    • MARINI, L. D., & QUARTERONI, A. 1989 A relaxation procedure for domain decomposition methods using finite elements. Numer. Math. 55, 575-598.
    • (1989) Numer. Math. , vol.55 , pp. 575-598
    • Marini, L.D.1    Quarteroni, A.2
  • 21
    • 0022145330 scopus 로고
    • Time stepping along characteristics with incomplete iteration for a Galerkin approximation of miscible displacement in porous media
    • RUSSELL, T. F. 1985 Time stepping along characteristics with incomplete iteration for a Galerkin approximation of miscible displacement in porous media. SIAM J. Numer. Anal. 22, 970-1013.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 970-1013
    • Russell, T.F.1
  • 22
    • 0003559010 scopus 로고
    • A parallel implementation of an iterative substructuring algorithm for problems in three dimensions
    • SMITH, B. F. 1993 A parallel implementation of an iterative substructuring algorithm for problems in three dimensions. SIAM J. Sci. Stat. Comput. 14, 406-423.
    • (1993) SIAM J. Sci. Stat. Comput. , vol.14 , pp. 406-423
    • Smith, B.F.1
  • 23
    • 0026995615 scopus 로고
    • Some Schwarz methods for symmetric and nonsymmetric elliptic problems
    • (D. E. Keyes, T. F. Chan, G. Meurant, J. S. Scroggs and R. G. Voigt, eds). Philadelphia, PA: SIAM
    • WIDLUND, O. B. 1992 Some Schwarz methods for symmetric and nonsymmetric elliptic problems. Fifth Int. Symp. on Domain Decomposition Methods for Partial Differential Equations, Proc. Appl. Math. 55 (D. E. Keyes, T. F. Chan, G. Meurant, J. S. Scroggs and R. G. Voigt, eds). Philadelphia, PA: SIAM, pp 19-36.
    • (1992) Fifth Int. Symp. on Domain Decomposition Methods for Partial Differential Equations, Proc. Appl. Math. , vol.55 , pp. 19-36
    • Widlund, O.B.1
  • 24
    • 0039595282 scopus 로고
    • Multistep schems for mixed finite element methods for second order parabolic problems
    • YANG, D. Q. 1989 Multistep schems for mixed finite element methods for second order parabolic problems. J. Qingdao Univ. 2, 56-62.
    • (1989) J. Qingdao Univ. , vol.2 , pp. 56-62
    • Yang, D.Q.1
  • 25
    • 38249010068 scopus 로고
    • A characteristic mixed method with dynamic finite element space for convection-dominated diffusion problems
    • YANG, D. Q. 1992 A characteristic mixed method with dynamic finite element space for convection-dominated diffusion problems. J. Comput. Appl. Math. 43, 343-353.
    • (1992) J. Comput. Appl. Math. , vol.43 , pp. 343-353
    • Yang, D.Q.1
  • 26
    • 21344486795 scopus 로고
    • Grid modification for the wave equation with attenuation
    • YANG, D. Q. 1994a Grid modification for the wave equation with attenuation. Numer. Math. 67, 391-401.
    • (1994) Numer. Math. , vol.67 , pp. 391-401
    • Yang, D.Q.1
  • 27
    • 0040781037 scopus 로고
    • Parallel iterative nonoverlapping domain decomposition methods for elliptic and time-dependent problems
    • San Diego, California July
    • YANG, D. Q. 1994b Parallel iterative nonoverlapping domain decomposition methods for elliptic and time-dependent problems. Presented at the SIAM Annual Meeting, San Diego, California July 25-29.
    • (1994) SIAM Annual Meeting , pp. 25-29
    • Yang, D.Q.1
  • 28
    • 0029140081 scopus 로고
    • Different domain decompositions at different times for capturing moving local phenomena
    • To appear
    • YANG, D. Q. 1995a Different domain decompositions at different times for capturing moving local phenomena. J. Comput. Appl. Math. 58. (To appear)
    • (1995) J. Comput. Appl. Math. , vol.58
    • Yang, D.Q.1
  • 29
    • 21844486503 scopus 로고
    • Grid modification for second order hyperbolic problems
    • To appear
    • YANG, D. Q. 1995b Grid modification for second order hyperbolic problems. Math. Comput. 64. (To appear)
    • (1995) Math. Comput. , vol.64
    • Yang, D.Q.1


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