메뉴 건너뛰기




Volumn 34, Issue 4, 2012, Pages

Aggregation-based algebraic multigrid for convection-diffusion equations

Author keywords

Aggregation; Convection diffusion; Convergence analysis; Linear systems; Multigrid

Indexed keywords

DIFFUSION IN LIQUIDS; EIGENVALUES AND EIGENFUNCTIONS; HEAT CONVECTION; ITERATIVE METHODS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 84866354380     PISSN: 10648275     EISSN: 10957200     Source Type: Journal    
DOI: 10.1137/110835347     Document Type: Article
Times cited : (182)

References (47)
  • 1
    • 20044390432 scopus 로고    scopus 로고
    • Numerical solution of saddle point problems
    • M. BENZI, G. H. GOLUB, AND J. LIESEN, Numerical solution of saddle point problems, Acta Numer., 14 (2005), pp. 1-137.
    • (2005) Acta Numer. , vol.14 , pp. 1-137
    • Benzi, M.1    Golub, G.H.2    Liesen, J.3
  • 3
    • 0029488033 scopus 로고
    • Towards algebraic multigrid for elliptic problems of second order
    • D. BRAESS, Towards algebraic multigrid for elliptic problems of second order, Computing, 55 (1995), pp. 379-393.
    • (1995) Computing , vol.55 , pp. 379-393
    • Braess, D.1
  • 4
    • 0002438068 scopus 로고
    • Algebraic multigrid (AMG) for sparse matrix equations
    • D. J. Evans, ed., Cambridge University Press, Cambridge, UK
    • A. BRANDT, S. F. MCCORMICK, AND J. W. RUGE, Algebraic multigrid (AMG) for sparse matrix equations, in Sparsity and Its Application, D. J. Evans, ed., Cambridge University Press, Cambridge, UK, 1984, pp. 257-284.
    • (1984) Sparsity and its Application , pp. 257-284
    • Brandt, A.1    Mccormick, S.F.2    Ruge, J.W.3
  • 8
    • 0027641332 scopus 로고
    • Multi-level iterative technique and aggregation concept with semi-analytical preconditioning for solving boundary-value problems
    • V. E. BULGAKOV, Multi-level iterative technique and aggregation concept with semi-analytical preconditioning for solving boundary-value problems, Comm. Numer. Methods Engrg., 9 (1993), pp. 649-657.
    • (1993) Comm. Numer. Methods Engrg. , vol.9 , pp. 649-657
    • Bulgakov, V.E.1
  • 10
    • 0003090969 scopus 로고
    • Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
    • P. M. DE ZEEUW, Matrix-dependent prolongations and restrictions in a blackbox multigrid solver, J. Comput. Appl. Math., 33 (1990), pp. 1-27.
    • (1990) J. Comput. Appl. Math. , vol.33 , pp. 1-27
    • De Zeeuw, P.M.1
  • 11
    • 0000555209 scopus 로고
    • Black box multigrid for nonsymmetric problems
    • J. E. DENDY, Black box multigrid for nonsymmetric problems, Appl. Math. Comput., 13 (1983), pp. 261-283.
    • (1983) Appl. Math. Comput. , vol.13 , pp. 261-283
    • Dendy, J.E.1
  • 12
    • 0000011239 scopus 로고
    • Variational iterative methods for non-symmetric systems of linear equations
    • S. C. EISENSTAT, H. C. ELMAN, AND M. H. SCHULTZ, Variational iterative methods for non-symmetric systems of linear equations, SIAM J. Numer. Anal., 20 (1983), pp. 345-357.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 345-357
    • Eisenstat, S.C.1    Elman, H.C.2    Schultz, M.H.3
  • 14
    • 77953131795 scopus 로고    scopus 로고
    • Performance of parallel AMG-preconditioners in CFD-codes for weakly compressible flows
    • M. EMANS, Performance of parallel AMG-preconditioners in CFD-codes for weakly compressible flows, Parallel Comput., 36 (2010), pp. 326-338.
    • (2010) Parallel Comput. , vol.36 , pp. 326-338
    • Emans, M.1
  • 15
    • 0034144751 scopus 로고    scopus 로고
    • Residual-minimizing Krylov subspace methods for stabilized discretizations of convection-diffusion equations
    • O. G. ERNST, Residual-minimizing Krylov subspace methods for stabilized discretizations of convection-diffusion equations, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1079-1101.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 1079-1101
    • Ernst, O.G.1
  • 18
    • 0036211804 scopus 로고    scopus 로고
    • AMGe based on element agglomeration
    • J. E. JONES AND P. S. VASSILEVSKI, AMGe based on element agglomeration, SIAM J. Sci. Comput., 23 (2001), pp. 109-133.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 109-133
    • Jones, J.E.1    Vassilevski, P.S.2
  • 19
    • 0037233450 scopus 로고    scopus 로고
    • A multigrid method based on graph matching for convection-diffusion equations
    • H. KIM, J. XU, AND L. ZIKATANOV, A multigrid method based on graph matching for convection-diffusion equations, Numer. Linear Algebra Appl., 10 (2003), pp. 181-195.
    • (2003) Numer. Linear Algebra Appl. , vol.10 , pp. 181-195
    • Kim, H.1    Xu, J.2    Zikatanov, L.3
  • 20
    • 20044388272 scopus 로고    scopus 로고
    • GMRES convergence analysis for a convection-diffusion model problem
    • J. LIESEN AND Z. STRAKOŠ, GMRES convergence analysis for a convection-diffusion model problem, SIAM J. Sci. Comput., 26 (2005), pp. 1989-2009.
    • (2005) SIAM J. Sci. Comput. , vol.26 , pp. 1989-2009
    • Liesen, J.1    Strakoš, Z.2
  • 21
    • 55549120903 scopus 로고    scopus 로고
    • Algebraic multigrid solvers for complex-valued matrices
    • S. P. MACLACHLAN AND C. W. OOSTERLEE, Algebraic multigrid solvers for complex-valued matrices, SIAM J. Sci. Comput., 30 (2008), pp. 1548-1571.
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 1548-1571
    • Maclachlan, S.P.1    Oosterlee, C.W.2
  • 23
    • 55549139507 scopus 로고    scopus 로고
    • Analysis of aggregation-based multigrid
    • A. C. MURESAN AND Y. NOTAY, Analysis of aggregation-based multigrid, SIAM J. Sci. Comput., 30 (2008), pp. 1082-1103.
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 1082-1103
    • Muresan, A.C.1    Notay, Y.2
  • 24
    • 79954552462 scopus 로고    scopus 로고
    • Algebraic analysis of aggregation-based multigrid
    • A. NAPOV AND Y. NOTAY, Algebraic analysis of aggregation-based multigrid, Numer. Linear Algebra Appl., 18 (2011), pp. 539-564.
    • (2011) Numer. Linear Algebra Appl. , vol.18 , pp. 539-564
    • Napov, A.1    Notay, Y.2
  • 25
    • 84861387731 scopus 로고    scopus 로고
    • An algebraic multigrid method with guaranteed convergence rate
    • A. NAPOV AND Y. NOTAY, An algebraic multigrid method with guaranteed convergence rate, SIAM J. Sci. Comput., 34 (2012), pp. A1079-A1109.
    • (2012) SIAM J. Sci. Comput. , vol.34
    • Napov, A.1    Notay, Y.2
  • 27
    • 0034397438 scopus 로고    scopus 로고
    • A robust algebraic multilevel preconditioner for non symmetric M-matrices
    • Y. NOTAY, A robust algebraic multilevel preconditioner for non symmetric M-matrices, Numer. Linear Algebra Appl., 7 (2000), pp. 243-267.
    • (2000) Numer. Linear Algebra Appl. , vol.7 , pp. 243-267
    • Notay, Y.1
  • 28
    • 77955681191 scopus 로고    scopus 로고
    • An aggregation-based algebraic multigrid method
    • Y. NOTAY, An aggregation-based algebraic multigrid method, Electron. Trans. Numer. Anal., 37 (2010), pp. 123-146.
    • (2010) Electron. Trans. Numer. Anal. , vol.37 , pp. 123-146
    • Notay, Y.1
  • 29
    • 72449145877 scopus 로고    scopus 로고
    • Algebraic analysis of two-grid methods: The nonsymmetric case
    • Y. NOTAY, Algebraic analysis of two-grid methods: The nonsymmetric case, Numer. Linear Algebra Appl., 17 (2010), pp. 73-97.
    • (2010) Numer. Linear Algebra Appl. , vol.17 , pp. 73-97
    • Notay, Y.1
  • 31
    • 21244493692 scopus 로고    scopus 로고
    • Convergence analysis of a multigrid method for a convection-dominated model problem
    • M. A. OLSHANSKII AND A. REUSKEN, Convergence analysis of a multigrid method for a convection-dominated model problem, SIAM J. Numer. Anal., 42 (2004), pp. 1261-1291.
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 1261-1291
    • Olshanskii, M.A.1    Reusken, A.2
  • 32
    • 0001927801 scopus 로고    scopus 로고
    • An evaluation of parallel multigrid as a solver and a preconditioner for singularly perturbed problems
    • C. W. OOSTERLEE AND T. WASHIO, An evaluation of parallel multigrid as a solver and a preconditioner for singularly perturbed problems, SIAM J. Sci. Comput., 19 (1998), pp. 87-110.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 87-110
    • Oosterlee, C.W.1    Washio, T.2
  • 33
    • 0033708934 scopus 로고    scopus 로고
    • Krylov subspace acceleration of nonlinear multigrid with application to recirculating flows
    • C. W. OOSTERLEE AND T. WASHIO, Krylov subspace acceleration of nonlinear multigrid with application to recirculating flows, SIAM J. Sci. Comput., 21 (2000), pp. 1670-1690.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 1670-1690
    • Oosterlee, C.W.1    Washio, T.2
  • 34
    • 21444442790 scopus 로고    scopus 로고
    • A multigrid method based on incomplete Gaussian elimination
    • A. REUSKEN, A multigrid method based on incomplete Gaussian elimination, Numer. Linear Algebra Appl., 3 (1996), pp. 369-390.
    • (1996) Numer. Linear Algebra Appl. , vol.3 , pp. 369-390
    • Reusken, A.1
  • 35
    • 0036556997 scopus 로고    scopus 로고
    • Convergence analysis of a multigrid method for convection-diffusion equations
    • A. REUSKEN, Convergence analysis of a multigrid method for convection-diffusion equations, Numer. Math., 91 (2002), pp. 323-349.
    • (2002) Numer. Math. , vol.91 , pp. 323-349
    • Reusken, A.1
  • 37
    • 55049118140 scopus 로고    scopus 로고
    • A new Petrov-Galerkin smoothed aggregation preconditioner for nonsymmetric linear systems
    • M. SALA AND R. S. TUMINARO, A new Petrov-Galerkin smoothed aggregation preconditioner for nonsymmetric linear systems, SIAM J. Sci. Comput., 31 (2008), pp. 143-166.
    • (2008) SIAM J. Sci. Comput. , vol.31 , pp. 143-166
    • Sala, M.1    Tuminaro, R.S.2
  • 38
    • 0003338384 scopus 로고    scopus 로고
    • Multigrid, U. Trottenberg, C. W. Oost-erlee, and A. Schüller, eds., Academic Press, London Appendix A
    • K. STÜBEN, An introduction to algebraic multigrid, in Multigrid, U. Trottenberg, C. W. Oost-erlee, and A. Schüller, eds., Academic Press, London, 2001, pp. 413-532, Appendix A.
    • (2001) An Introduction to Algebraic Multigrid , pp. 413-532
    • Stüben, K.1
  • 42
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid based on smoothed aggregation for second and fourth order elliptic problems
    • P. VANĚK, J. MANDEL, AND M. BREZINA, Algebraic multigrid based on smoothed aggregation for second and fourth order elliptic problems, Computing, 56 (1996), pp. 179-196.
    • (1996) Computing , vol.56 , pp. 179-196
    • Vaněk, P.1    Mandel, J.2    Brezina, M.3
  • 44
    • 0036227289 scopus 로고    scopus 로고
    • On three-grid Fourier analysis for multigrid
    • R. WIENANDS AND C. W. OOSTERLEE, On three-grid Fourier analysis for multigrid, SIAM J. Sci. Comput., 23 (2001), pp. 651-671.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 651-671
    • Wienands, R.1    Oosterlee, C.W.2
  • 45
    • 36348995518 scopus 로고    scopus 로고
    • Analysis and comparison of geometric and algebraic multigrid for convection-diffusion equations
    • C.-T. WU AND H. C. ELMAN, Analysis and comparison of geometric and algebraic multigrid for convection-diffusion equations, SIAM J. Sci. Comput., 28 (2006), pp. 2208-2228.
    • (2006) SIAM J. Sci. Comput. , vol.28 , pp. 2208-2228
    • Wu, C.-T.1    Elman, H.C.2
  • 46
    • 0001258894 scopus 로고    scopus 로고
    • Coarse-grid correction for nonelliptic and singular perturbation problems
    • I. YAVNEH, Coarse-grid correction for nonelliptic and singular perturbation problems, SIAM J. Sci. Comput., 19 (1998), pp. 1682-1699.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1682-1699
    • Yavneh, I.1
  • 47
    • 0001720471 scopus 로고    scopus 로고
    • Fast multigrid solution of the advection problem with closed characteristics
    • I. YAVNEH, C. H. VENNER, AND A. BRANDT, Fast multigrid solution of the advection problem with closed characteristics, SIAM J. Sci. Comput., 19 (1998), pp. 111-125.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 111-125
    • Yavneh, I.1    Venner, C.H.2    Brandt, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.