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Volumn 42, Issue 3, 2008, Pages 443-469

Multiplicative Schwarz methods for discontinuous Galerkin approximations of elliptic problems

Author keywords

Discontinuous Galerkin methods; Domain decomposition methods; Schwarz preconditioners

Indexed keywords


EID: 42549128309     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an:2008012     Document Type: Article
Times cited : (39)

References (41)
  • 1
    • 34547483058 scopus 로고    scopus 로고
    • Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: Non-overlapping case
    • P.F. Antonietti and B. Ayuso, Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: Non-overlapping case. ESAIM: M2AN 41 (2007) 21-54.
    • (2007) ESAIM: M2AN , vol.41 , pp. 21-54
    • Antonietti, P.F.1    Ayuso, B.2
  • 2
  • 3
    • 0001163226 scopus 로고
    • An interior penalty finite element method with discontinuous elements
    • D.N. Arnold, An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 (1982) 742-760.
    • (1982) SIAM J. Numer. Anal , vol.19 , pp. 742-760
    • Arnold, D.N.1
  • 4
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • electronic
    • D.N. Arnold, F. Brezzi, B. Cockburn and L.D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2001) 1749-1779 (electronic).
    • (2001) SIAM J. Numer. Anal , vol.39 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 5
    • 0001416032 scopus 로고    scopus 로고
    • A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
    • F. Bassi and S. Rebay, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131 (1997) 267-279.
    • (1997) J. Comput. Phys , vol.131 , pp. 267-279
    • Bassi, F.1    Rebay, S.2
  • 6
    • 0031291518 scopus 로고    scopus 로고
    • F. Bassi, S. Rebay, G. Mariotti, S. Pedinotti and M. Savini, A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows, in Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, R. Decuypere and G. Dibelius Eds., Technologisch Instituut, Antwerpen, Belgium (1997) 99-108.
    • F. Bassi, S. Rebay, G. Mariotti, S. Pedinotti and M. Savini, A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows, in Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, R. Decuypere and G. Dibelius Eds., Technologisch Instituut, Antwerpen, Belgium (1997) 99-108.
  • 7
    • 0345062335 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for convection-diffusion problems
    • C.E. Baumann and J.T. Oden, A discontinuous hp finite element method for convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 175 (1999) 311-341.
    • (1999) Comput. Methods Appl. Mech. Engrg , vol.175 , pp. 311-341
    • Baumann, C.E.1    Oden, J.T.2
  • 8
    • 84966225192 scopus 로고
    • Convergence estimates for product iterative methods with applications to domain decomposition
    • J.H. Bramble, J.E. Pasciak, J.P. Wang and J. Xu, Convergence estimates for product iterative methods with applications to domain decomposition. Math. Comp. 57 (1991) 1-21.
    • (1991) Math. Comp , vol.57 , pp. 1-21
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.P.3    Xu, J.4
  • 9
    • 34447095908 scopus 로고    scopus 로고
    • A W-cycle algorithm for a weakly over-penalized interior penalty method
    • S.C. Brenner and O. Luke, A W-cycle algorithm for a weakly over-penalized interior penalty method. JNAIAM J. Numer. Anal. Indust. Appl. Math 196 (2007) 3823-3832.
    • (2007) JNAIAM J. Numer. Anal. Indust. Appl. Math , vol.196 , pp. 3823-3832
    • Brenner, S.C.1    Luke, O.2
  • 10
    • 42549155274 scopus 로고    scopus 로고
    • A weakly over-penalized non-symmetric Interior Penalty method
    • S.C. Brenner and O. Luke, A weakly over-penalized non-symmetric Interior Penalty method. Comput. Methods Appl. Mech. Engrg. 2 (2007) 35-48.
    • (2007) Comput. Methods Appl. Mech. Engrg , vol.2 , pp. 35-48
    • Brenner, S.C.1    Luke, O.2
  • 12
    • 29144463388 scopus 로고    scopus 로고
    • 0 interior penalty methods
    • 0 interior penalty methods. Numer. Math. 102 (2005) 231-255.
    • (2005) Numer. Math , vol.102 , pp. 231-255
    • Brenner, S.C.1    Wang, K.2
  • 13
    • 33750724895 scopus 로고    scopus 로고
    • Convergence of multigrid algorithms for interior penalty methods
    • S.C. Brenner and J. Zhao, Convergence of multigrid algorithms for interior penalty methods. Appl. Numer. Anal. Comput. Math. 2 (2005) 3-18.
    • (2005) Appl. Numer. Anal. Comput. Math , vol.2 , pp. 3-18
    • Brenner, S.C.1    Zhao, J.2
  • 15
    • 0027640852 scopus 로고
    • Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems
    • X.-C. Cai and O.B. Widlund, Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems. SIAM J. Numer. Anal. 30 (1993) 936-952.
    • (1993) SIAM J. Numer. Anal , vol.30 , pp. 936-952
    • Cai, X.-C.1    Widlund, O.B.2
  • 17
    • 0344393366 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for time-dependent convection-diffusion systems
    • electronic
    • B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440-2463 (electronic).
    • (1998) SIAM J. Numer. Anal , vol.35 , pp. 2440-2463
    • Cockburn, B.1    Shu, C.-W.2
  • 19
    • 33750694584 scopus 로고    scopus 로고
    • Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations
    • V.A. Dobrev, R.D. Lazarov, P.S. Vassilevski and L.T. Zikatanov, Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations. Numer. Linear Algebra Appl. 13 (2006) 753-770.
    • (2006) Numer. Linear Algebra Appl , vol.13 , pp. 753-770
    • Dobrev, V.A.1    Lazarov, R.D.2    Vassilevski, P.S.3    Zikatanov, L.T.4
  • 20
    • 0001456343 scopus 로고
    • Interior penalty procedures for elliptic and parabolic Galerkin methods
    • Computing Methods in Applied Sciences Second Internat. Sympos, Versailles, Springer, Berlin
    • J. Douglas, Jr. and T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin methods, in Computing Methods in Applied Sciences (Second Internat. Sympos., Versailles, 1975), Lecture Notes in Physics 58, Springer, Berlin (1976) 207-216.
    • (1975) Lecture Notes in Physics , vol.58 , pp. 207-216
    • Douglas Jr., J.1    Dupont, T.2
  • 21
    • 0000011239 scopus 로고
    • Variational iterative methods for nonsymmetric systems of linear equations
    • S.C. Eisenstat, H.C. Elman and M.H. Schultz, Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20 (1983) 345-357.
    • (1983) SIAM J. Numer. Anal , vol.20 , pp. 345-357
    • Eisenstat, S.C.1    Elman, H.C.2    Schultz, M.H.3
  • 22
    • 0041419444 scopus 로고    scopus 로고
    • Two-level additive Schwarz methods for a discontinuous Galerkin approximation of second order elliptic problems
    • electronic
    • X. Feng and O.A. Karakashian, Two-level additive Schwarz methods for a discontinuous Galerkin approximation of second order elliptic problems. SIAM J. Numer. Anal. 39 (2001) 1343-1365 (electronic).
    • (2001) SIAM J. Numer. Anal , vol.39 , pp. 1343-1365
    • Feng, X.1    Karakashian, O.A.2
  • 23
    • 0004236492 scopus 로고    scopus 로고
    • 3rd Edn, Johns Hopkins University Press, Baltimore, USA
    • G.H. Golub and C.F. Van Loan, Matrix Computations. 3rd Edn., Johns Hopkins University Press, Baltimore, USA (1996).
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 24
    • 0345060037 scopus 로고    scopus 로고
    • A multilevel discontinuous Galerkin method
    • J. Gopalakrishnan and G. Kanschat, A multilevel discontinuous Galerkin method. Numer. Math. 95 (2003) 527-550.
    • (2003) Numer. Math , vol.95 , pp. 527-550
    • Gopalakrishnan, J.1    Kanschat, G.2
  • 25
    • 2942574812 scopus 로고    scopus 로고
    • Preconditioning methods for local discontinuous Galerkin discretizations
    • electronic
    • G. Kanschat, Preconditioning methods for local discontinuous Galerkin discretizations. SIAM J. Sci. Comput. 25 (2003) 815-831 (electronic).
    • (2003) SIAM J. Sci. Comput , vol.25 , pp. 815-831
    • Kanschat, G.1
  • 26
    • 17444402857 scopus 로고    scopus 로고
    • Block preconditioners for LDG discretizations of linear incompressible flow problems
    • G. Kanschat, Block preconditioners for LDG discretizations of linear incompressible flow problems. J. Sci. Comput. 22/23 (2005) 371-384.
    • (2005) J. Sci. Comput , vol.22-23 , pp. 371-384
    • Kanschat, G.1
  • 27
    • 0038129714 scopus 로고    scopus 로고
    • An overlapping domain decomposition preconditioner for a class of discontinuous Galerkin approximations of advection-diffusion problems
    • electronic
    • C. Lasser and A. Toselli, An overlapping domain decomposition preconditioner for a class of discontinuous Galerkin approximations of advection-diffusion problems. Math. Comp. 72 (2003) 1215-1238 (electronic).
    • (2003) Math. Comp , vol.72 , pp. 1215-1238
    • Lasser, C.1    Toselli, A.2
  • 29
    • 10044241890 scopus 로고    scopus 로고
    • A fully implicit parallel algorithm for simulating the non-linear electrical activity of the heart
    • M. Murillo and X.-C. Cai, A fully implicit parallel algorithm for simulating the non-linear electrical activity of the heart. Numer. Linear Algebra Appl. 11 (2004) 261-277.
    • (2004) Numer. Linear Algebra Appl , vol.11 , pp. 261-277
    • Murillo, M.1    Cai, X.-C.2
  • 30
    • 78651592194 scopus 로고    scopus 로고
    • Multilevel Schwarz and multigrid preconditioners for the bidomain system
    • Domain Decomposition Methods in Science and Engineering, U. Langer, M. Discacciati, D. Keyes, O. Widlund and W. Zulehner Eds, 60, Springer, Heidelberg
    • L.F. Pavarino and S. Scacchi, Multilevel Schwarz and multigrid preconditioners for the bidomain system, in Domain Decomposition Methods in Science and Engineering XVII, U. Langer, M. Discacciati, D. Keyes, O. Widlund and W. Zulehner Eds., Lecture Notes in Computational Science and Engineering 60, Springer, Heidelberg (2008) 631-638.
    • (2008) Lecture Notes in Computational Science and Engineering , vol.17 , pp. 631-638
    • Pavarino, L.F.1    Scacchi, S.2
  • 31
    • 42549136464 scopus 로고    scopus 로고
    • L.F. Pavarino and A. Toselli, Recent Developments in Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering 23. Springer-Verlag, Berlin (2002). [Selected papers from the Workshop on Domain Decomposition held at ETH Zürich, Zürich, June 7-8 (2001)].
    • L.F. Pavarino and A. Toselli, Recent Developments in Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering 23. Springer-Verlag, Berlin (2002). [Selected papers from the Workshop on Domain Decomposition held at ETH Zürich, Zürich, June 7-8 (2001)].
  • 33
    • 0033511173 scopus 로고    scopus 로고
    • Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
    • B. Rivière, M.F. Wheeler and V. Girault, Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I. Comput. Geosci. 3 (1999) 337-360.
    • (1999) Comput. Geosci , vol.3 , pp. 337-360
    • Rivière, B.1    Wheeler, M.F.2    Girault, V.3
  • 34
    • 42549123661 scopus 로고    scopus 로고
    • V. Simoncini and D.B. Szyld, New conditions for non-stagnation of minimal residual methods. Technical Report 07-04-17, Department of Mathematics, Temple University, USA (2007), to appear in Numerische Mathematik.
    • V. Simoncini and D.B. Szyld, New conditions for non-stagnation of minimal residual methods. Technical Report 07-04-17, Department of Mathematics, Temple University, USA (2007), to appear in Numerische Mathematik.
  • 36
    • 42549129223 scopus 로고    scopus 로고
    • R. Stenberg, Mortaring by a method of J.A. Nitsche, in Computational mechanics (Buenos Aires, 1998), Centro Internac. Métodos Numér. Ing., Barcelona, Spain (1998).
    • R. Stenberg, Mortaring by a method of J.A. Nitsche, in Computational mechanics (Buenos Aires, 1998), Centro Internac. Métodos Numér. Ing., Barcelona, Spain (1998).
  • 38
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • J. Xu, Iterative methods by space decomposition and subspace correction. SIAM Rev. 34 (1992) 581-613.
    • (1992) SIAM Rev , vol.34 , pp. 581-613
    • Xu, J.1
  • 40
    • 0026846317 scopus 로고
    • A new class of iterative methods for nonselfadjoint or indefinite problems
    • J. Xu, A new class of iterative methods for nonselfadjoint or indefinite problems. SIAM J. Numer. Anal. 29 (1992) 303-319.
    • (1992) SIAM J. Numer. Anal , vol.29 , pp. 303-319
    • Xu, J.1
  • 41
    • 0036016141 scopus 로고    scopus 로고
    • The method of alternating projections and the method of subspace corrections in Hilbert space
    • electronic
    • J. Xu and L. Zikatanov, The method of alternating projections and the method of subspace corrections in Hilbert space. J. Amer. Math. Soc. 15 (2002) 573-597 (electronic).
    • (2002) J. Amer. Math. Soc , vol.15 , pp. 573-597
    • Xu, J.1    Zikatanov, L.2


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