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Volumn 24, Issue 1, 2005, Pages 613-646

Hybrid Multigrid/Schwarz algorithms for the spectral element method

Author keywords

Domain decomposition; Multigrid; P version finite element; Schwarz methods; Spectral element methods

Indexed keywords

COMPUTATIONAL COMPLEXITY; ERROR CORRECTION; FINITE ELEMENT METHOD; ITERATIVE METHODS; LARGE SCALE SYSTEMS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; NATURAL SCIENCES COMPUTING; PROBLEM SOLVING;

EID: 23244435610     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-004-4787-3     Document Type: Article
Times cited : (129)

References (43)
  • 1
    • 0038042421 scopus 로고    scopus 로고
    • Multigrid solver for the inner problem in domain decomposition methods for p-fem
    • Beuchler, S. (2002). Multigrid solver for the inner problem in domain decomposition methods for p-fem. SIAM J. Numer. Anal. 40, 928-944.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 928-944
    • Beuchler, S.1
  • 2
    • 0031082724 scopus 로고    scopus 로고
    • Diagonal edge preconditioners in p-version and spectral element methods
    • Casarin, M.A. (1997). Diagonal edge preconditioners in p-version and spectral element methods. SIAM J. Sci. Comput. 18, 610-620.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 610-620
    • Casarin, M.A.1
  • 3
    • 0000997330 scopus 로고    scopus 로고
    • Quasi-optimal Schwarz methods for the conforming spectral element discretization
    • Casarin, M.A. (1997). Quasi-optimal Schwarz methods for the conforming spectral element discretization. SIAM J. Numer. Anal. 34, 2482-2502.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2482-2502
    • Casarin, M.A.1
  • 4
    • 23244432383 scopus 로고    scopus 로고
    • Schwarz preconditioners for the spectral element Stokes and Navier-Stokes discretizations
    • Bjørstad, P., Espedal, M., and Keyes, D. (eds.), Wiley, New York
    • Casarin, M.A. (1998). Schwarz preconditioners for the spectral element Stokes and Navier-Stokes discretizations. In Bjørstad, P., Espedal, M., and Keyes, D. (eds.), Domain Decomposition 9 Proc., Wiley, New York, pp. 72-79.
    • (1998) Domain Decomposition 9 Proc. , pp. 72-79
    • Casarin, M.A.1
  • 6
    • 0028458640 scopus 로고
    • Spectral-element preconditioners for the Uzawa pressure operator applied to incompressible flows
    • Couzy, W., and Deville, M.O. (1994). Spectral-element preconditioners for the Uzawa pressure operator applied to incompressible flows. J. Sci. Comput. 9, 107-112.
    • (1994) J. Sci. Comput. , vol.9 , pp. 107-112
    • Couzy, W.1    Deville, M.O.2
  • 7
    • 0000489687 scopus 로고
    • A fast Schur complement method for the spectral element discretization of the incompressible Navier-Stokes equations
    • Couzy, W., and Deville, M.O. (1995). A fast Schur complement method for the spectral element discretization of the incompressible Navier-Stokes equations. J. Comput. Phys. 116, 135-142.
    • (1995) J. Comput. Phys. , vol.116 , pp. 135-142
    • Couzy, W.1    Deville, M.O.2
  • 9
    • 0001194652 scopus 로고
    • Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning
    • Deville, M.O., and Mund, E.H. (1985). Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning. J. Comp. Phys. 60, 517-533.
    • (1985) J. Comp. Phys. , vol.60 , pp. 517-533
    • Deville, M.O.1    Mund, E.H.2
  • 10
    • 0000464822 scopus 로고
    • Finite element preconditioning for pseudospectral solutions of elliptic problems
    • Deville, M.O., and Mund, E.H. (1990). Finite element preconditioning for pseudospectral solutions of elliptic problems. SIAM J. Sci. Stat. Comput. 11, 311-342.
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , pp. 311-342
    • Deville, M.O.1    Mund, E.H.2
  • 11
    • 0003922593 scopus 로고
    • An additive variant of the Schwarz alternating method for the case of many subregions
    • Dept. Comp. Sci., Courant Inst., NYU
    • Dryja, M., and Widlund, O.B. (1987). An additive variant of the Schwarz alternating method for the case of many subregions. Technical Report TR 339, Dept. Comp. Sci., Courant Inst., NYU.
    • (1987) Technical Report , vol.TR 339
    • Dryja, M.1    Widlund, O.B.2
  • 12
    • 0011007773 scopus 로고    scopus 로고
    • Parallel multi-level solvers for spectral element methods
    • Ilin, A.V. and Scott, L.R. (eds.), Third Int. Conference on Spectral and High Order Methods
    • Fischer, P.F. (1996). Parallel multi-level solvers for spectral element methods. In Ilin, A.V. and Scott, L.R. (eds.), Third Int. Conference on Spectral and High Order Methods, Houston Journal of Mathematics, pp. 595-604.
    • (1996) Houston Journal of Mathematics , pp. 595-604
    • Fischer, P.F.1
  • 13
    • 0031145109 scopus 로고    scopus 로고
    • An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations
    • Fischer, P.F. (1997). An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations. J. Comput. Phys. 133, 84-101.
    • (1997) J. Comput. Phys. , vol.133 , pp. 84-101
    • Fischer, P.F.1
  • 14
    • 0042071939 scopus 로고    scopus 로고
    • Spectral element methods for transitional flows in complex geometries
    • Fischer, P.F., Kruse, G.W., and Loth, F. (2002). Spectral element methods for transitional flows in complex geometries. J. Sci. Comput. 17, 81-98.
    • (2002) J. Sci. Comput. , vol.17 , pp. 81-98
    • Fischer, P.F.1    Kruse, G.W.2    Loth, F.3
  • 15
    • 0041750046 scopus 로고    scopus 로고
    • An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows
    • Bjørstad, P. and Luskin, M. (eds.), Springer, Berlin
    • Fischer, P.F., Miller, N.I., and Tufo, H.M. (2000). An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows. In Bjørstad, P. and Luskin, M. (eds.), Parallel Solution of Partial Differential Equations, Springer, Berlin, pp. 158-180.
    • (2000) Parallel Solution of Partial Differential Equations , pp. 158-180
    • Fischer, P.F.1    Miller, N.I.2    Tufo, H.M.3
  • 16
    • 0028450352 scopus 로고
    • Spectral element methods for large scale parallel Navier-Stokes calculations
    • Fischer, P.F., and Rønquist, E.M. (1994). Spectral element methods for large scale parallel Navier-Stokes calculations. Comput. Methods Appl. Mech. Engrg. 116, 69-76.
    • (1994) Comput. Methods Appl. Mech. Engrg. , vol.116 , pp. 69-76
    • Fischer, P.F.1    Rønquist, E.M.2
  • 18
    • 38249027646 scopus 로고
    • Line relaxation for spectral multigrid methods
    • Heinrichs, W. (1988). Line relaxation for spectral multigrid methods. J. Comput. Phys. 77, 166-182.
    • (1988) J. Comput. Phys. , vol.77 , pp. 166-182
    • Heinrichs, W.1
  • 19
    • 84968475596 scopus 로고
    • Improved condition number for spectral methods
    • Heinrichs, W. (1989). Improved condition number for spectral methods. Math. Comp. 53, 103-119.
    • (1989) Math. Comp. , vol.53 , pp. 103-119
    • Heinrichs, W.1
  • 20
    • 34250966014 scopus 로고
    • Direct solution of partial difference equations by tensor product methods
    • Lynch, R.E., Rice, J.R., and Thomas, D.H. (1964). Direct solution of partial difference equations by tensor product methods. Numer. Math. 6, 185-199.
    • (1964) Numer. Math. , vol.6 , pp. 185-199
    • Lynch, R.E.1    Rice, J.R.2    Thomas, D.H.3
  • 23
    • 0025416211 scopus 로고
    • Two-level domain decomposition preconditioning for the p-version finite element method in three dimensions
    • Mandel, J. (1990). Two-level domain decomposition preconditioning for the p-version finite element method in three dimensions. Int. J. Numer. Methods Eng. 29, 1095-1108.
    • (1990) Int. J. Numer. Methods Eng. , vol.29 , pp. 1095-1108
    • Mandel, J.1
  • 24
    • 0000527799 scopus 로고
    • Domain decomposition preconditioning for p-version finite elements with high aspect ratios
    • Mandel, J., and Lett, G.S. (1991). Domain decomposition preconditioning for p-version finite elements with high aspect ratios. Appl. Numer. Math. 8, 411-425.
    • (1991) Appl. Numer. Math. , vol.8 , pp. 411-425
    • Mandel, J.1    Lett, G.S.2
  • 25
    • 0023982322 scopus 로고
    • On the use of deflation to improve the convergence of conjugate gradient iteration
    • Mansfield, L. (1988). On the use of deflation to improve the convergence of conjugate gradient iteration. Comm. in Appl. Numer. Meth. 4, 151-156.
    • (1988) Comm. in Appl. Numer. Meth. , vol.4 , pp. 151-156
    • Mansfield, L.1
  • 26
    • 0023331865 scopus 로고
    • Deflation of conjugate gradients with application to boundary value problems
    • Nicolaides, R.A. (1987). Deflation of conjugate gradients with application to boundary value problems. SIAM J. Numer. Anal. 24, 355-365.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 355-365
    • Nicolaides, R.A.1
  • 27
    • 85013126603 scopus 로고
    • Spectral methods for problems in complex geometry
    • Orszag, S.A. (1980). Spectral methods for problems in complex geometry. J. Comput. Phys. 37, 70-92.
    • (1980) J. Comput. Phys. , vol.37 , pp. 70-92
    • Orszag, S.A.1
  • 29
    • 0001511946 scopus 로고
    • Preconditioning Legendre spectral collocation approximations to elliptic problems
    • Parter, S.V., and Rothman, E.E. (1995). Preconditioning Legendre spectral collocation approximations to elliptic problems. SIAM J. Numer. Anal. 32, 333-385.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 333-385
    • Parter, S.V.1    Rothman, E.E.2
  • 30
    • 0346246272 scopus 로고    scopus 로고
    • Overlapping Schwarz methods for unstructured spectral elements
    • Pavarino, L.F., and Warburton, T. (2000). Overlapping Schwarz methods for unstructured spectral elements. J. Comput. Phys. 160, 298-317.
    • (2000) J. Comput. Phys. , vol.160 , pp. 298-317
    • Pavarino, L.F.1    Warburton, T.2
  • 31
    • 0000337361 scopus 로고    scopus 로고
    • A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions
    • Pavarino, L.F., and Widlund, O.B. (1996). A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions. SIAM J. Numer. Anal. 33, 1303-1335.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1303-1335
    • Pavarino, L.F.1    Widlund, O.B.2
  • 33
    • 0026993282 scopus 로고
    • A domain decomposition method for elliptic boundary value problems: Application to unsteady incompressible fluid flow
    • Keyes, D.E., Chan, T.F., Meurant, G., Scroggs, J.S., and Voigt, R.G. (eds.), SIAM, Philadelphia
    • Rønquist, E.M. (1992). A domain decomposition method for elliptic boundary value problems: application to unsteady incompressible fluid flow. In Keyes, D.E., Chan, T.F., Meurant, G., Scroggs, J.S., and Voigt, R.G. (eds.), Fifth Int. Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, pp. 545-557.
    • (1992) Fifth Int. Symposium on Domain Decomposition Methods for Partial Differential Equations , pp. 545-557
    • Rønquist, E.M.1
  • 34
    • 0042387044 scopus 로고    scopus 로고
    • A domain decomposition solver for the steady Navier-Stokes equations
    • Ilin, A.V., and Scott, L.R. (eds.), Third Int. Conference on Spectral and High Order Methods
    • Rønquist, E.M. (1996). A domain decomposition solver for the steady Navier-Stokes equations. In Ilin, A.V., and Scott, L.R. (eds.), Third Int. Conference on Spectral and High Order Methods, Houston Journal of Mathematics, pp. 469-485.
    • (1996) Houston Journal of Mathematics , pp. 469-485
    • Rønquist, E.M.1
  • 35
    • 0000784858 scopus 로고
    • Spectral element multigrid, I:. Formulation and numerical results
    • Rønquist, E.M., and Patera, A.T. (1987). Spectral element multigrid, I:. Formulation and numerical results. J. Sci. Comput. 2, 389-406.
    • (1987) J. Sci. Comput. , vol.2 , pp. 389-406
    • Rønquist, E.M.1    Patera, A.T.2
  • 36
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Saad, Y., and Schultz, M.H. (1986). GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856-869.
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 37
    • 0034190393 scopus 로고    scopus 로고
    • A finite element multigrid preconditioner for chebyshev-collocation methods
    • Shen, J. E., Wang, F., and Xu, J. (2000). A finite element multigrid preconditioner for chebyshev-collocation methods. Appl. Numer. Math. 33, 471-477.
    • (2000) Appl. Numer. Math. , vol.33 , pp. 471-477
    • Shen, J.E.1    Wang, F.2    Xu, J.3
  • 38
    • 0002043336 scopus 로고    scopus 로고
    • Efficient Chebyshev-Legendre Galerkin methods for elliptic problems
    • Ilin, A.V., and Scott, L.R. (eds.), Third Int. Conference on Spectral and High Order Methods
    • Shen, J.E. (1996). Efficient Chebyshev-Legendre Galerkin methods for elliptic problems. In Ilin, A.V., and Scott, L.R. (eds.), Third Int. Conference on Spectral and High Order Methods, Houston Journal of Mathematics, pp. 233-239.
    • (1996) Houston Journal of Mathematics , pp. 233-239
    • Shen, J.E.1
  • 41
    • 0006606983 scopus 로고    scopus 로고
    • Fast parallel direct solvers for coarse-grid problems
    • Tufo, H.M., and Fischer, P.F. (2001). Fast parallel direct solvers for coarse-grid problems. J. Parallel Distrib. Comput. 61, 151-177.
    • (2001) J. Parallel Distrib. Comput. , vol.61 , pp. 151-177
    • Tufo, H.M.1    Fischer, P.F.2
  • 42
    • 0038892823 scopus 로고
    • Spectral multigrid methods for elliptic equations
    • Zang, T.A., Wong, Y.S., and Hussaini, M.Y. (1982). Spectral multigrid methods for elliptic equations. J. Comput. Phys. 48, 485-501.
    • (1982) J. Comput. Phys. , vol.48 , pp. 485-501
    • Zang, T.A.1    Wong, Y.S.2    Hussaini, M.Y.3
  • 43
    • 0040670821 scopus 로고
    • Spectral multigrid methods for elliptic equations II
    • Zang, T.A., Wong, Y.S., and Hussaini, M.Y. (1984). Spectral multigrid methods for elliptic equations II. J. Comput. Phys. 54, 489-507.
    • (1984) J. Comput. Phys. , vol.54 , pp. 489-507
    • Zang, T.A.1    Wong, Y.S.2    Hussaini, M.Y.3


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