메뉴 건너뛰기




Volumn 21, Issue 5, 2000, Pages 1886-1908

Robustness and scalability of algebraic multigrid

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; INTERPOLATION; LARGE SCALE SYSTEMS; PARALLEL PROCESSING SYSTEMS; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS);

EID: 0033710185     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827598339402     Document Type: Article
Times cited : (143)

References (36)
  • 1
    • 0000014842 scopus 로고
    • The multi-grid methods for the diffusion equation with strongly discontinuous coefficients
    • R. E. ALCOUFFE, A. BRANDT, J. E. DENDY JR., AND J. W. PAINTER, The multi-grid methods for the diffusion equation with strongly discontinuous coefficients, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 430-454.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 430-454
    • Alcouffe, R.E.1    Brandt, A.2    Dendy J.E., Jr.3    Painter, J.W.4
  • 3
    • 0001940743 scopus 로고
    • The algebraic multilevel iteration methods - Theory and applications
    • Plovdiv, Bulgaria, 1993, VSI, Zeist, The Netherlands
    • O. AXELSSON AND M. NEYTCHEVA, The algebraic multilevel iteration methods - Theory and applications, in Proceedings of the Second International Colloquium in Numerical Analysis, Plovdiv, Bulgaria, 1993, VSI, Zeist, The Netherlands, 1993, pp. 13-23.
    • (1993) Proceedings of the Second International Colloquium in Numerical Analysis , pp. 13-23
    • Axelsson, O.1    Neytcheva, M.2
  • 4
    • 0000523893 scopus 로고    scopus 로고
    • A class of hybrid algebraic multilevel preconditioning methods
    • Z.-Z. BAI, A class of hybrid algebraic multilevel preconditioning methods, Appl. Numer. Math., 19 (1996), pp. 389-399.
    • (1996) Appl. Numer. Math. , vol.19 , pp. 389-399
    • Bai, Z.-Z.1
  • 5
    • 0042677173 scopus 로고    scopus 로고
    • A unified framework for the construction of various algebraic multilevel preconditioning methods
    • University of Nijmegen, Nijmegen, The Netherlands
    • Z.-Z. BAI AND O. AXELSSON, A unified framework for the construction of various algebraic multilevel preconditioning methods, in AMLI'96: Proceedings of the Conference on Algebraic Multilevel Iteration Methods with Applications, Vol. 1, University of Nijmegen, Nijmegen, The Netherlands, 1996, pp. 63-76.
    • (1996) AMLI'96: Proceedings of the Conference on Algebraic Multilevel Iteration Methods with Applications , vol.1 , pp. 63-76
    • Bai, Z.-Z.1    Axelsson, O.2
  • 6
    • 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
  • 7
    • 0000000860 scopus 로고
    • Guide to multigrid development
    • Multigrid Methods, W. Hackbusch and U. Trottenberg, eds., Springer-Verlag, Berlin
    • A. BRANDT, Guide to multigrid development, in Multigrid Methods, W. Hackbusch and U. Trottenberg, eds., Lecture Notes in Mathematics 960, Springer-Verlag, Berlin, 1982, pp. 220-312.
    • (1982) Lecture Notes in Mathematics , vol.960 , pp. 220-312
    • Brandt, A.1
  • 9
    • 0003230568 scopus 로고
    • Multigrid techniques: 1984 guide with applications to fluid dynamics
    • Gesellschaft für Mathematik und Datenverarbeitung, St. Augustin
    • A. BRANDT, Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, GMD-Studien 85, Gesellschaft für Mathematik und Datenverarbeitung, St. Augustin, 1984.
    • (1984) GMD-Studien , vol.85
    • Brandt, A.1
  • 10
    • 0001927250 scopus 로고
    • Algebraic multigrid theory: The symmetric case
    • A. BRANDT, Algebraic multigrid theory: The symmetric case, Appl. Math. Comput., 19 (1986), pp. 23-56.
    • (1986) Appl. Math. Comput. , vol.19 , pp. 23-56
    • Brandt, A.1
  • 12
    • 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 Applications, D. J. Evans, ed., Cambridge University Press, Cambridge, UK, 1985, pp. 257-284.
    • (1985) Sparsity and Its Applications , pp. 257-284
    • Brandt, A.1    Mccormick, S.F.2    Ruge, J.W.3
  • 14
    • 0012123163 scopus 로고
    • Algebraic multigrid methods and the schur complement
    • W. Hackbusch, ed., Vieweg, Braunschweig
    • W. DAHMEN AND L. ELSNER, Algebraic multigrid methods and the Schur complement, in Robust Multi-Grid Methods, Notes on Numerical Fluid Mechanics 23, W. Hackbusch, ed., Vieweg, Braunschweig, 1989, pp. 58-68.
    • (1989) Robust Multi-Grid Methods, Notes on Numerical Fluid Mechanics , vol.23 , pp. 58-68
    • Dahmen, W.1    Elsner, L.2
  • 16
    • 0008356447 scopus 로고
    • Interpolation and related coarsening techniques for the algebraic multigrid method
    • Multigrid Methods IV, Proceedings of the Fourth European Multigrid Conference, Amsterdam, 1993, Birkhäuser, Basel
    • G. GOLUBOVICI AND C. POPA, Interpolation and related coarsening techniques for the algebraic multigrid method, in Multigrid Methods IV, Proceedings of the Fourth European Multigrid Conference, Amsterdam, 1993, Internat. Ser. Numer. Math. 116, Birkhäuser, Basel, 1994, pp. 201-213.
    • (1994) Internat. Ser. Numer. Math. , vol.116 , pp. 201-213
    • Golubovici, G.1    Popa, C.2
  • 17
    • 0031073092 scopus 로고    scopus 로고
    • Additive multilevel-preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs
    • T. GRAUSCHOPF, M. GRIEBEL, AND H. REGLER, Additive multilevel-preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs, Appl. Numer. Math., 23 (1997), pp. 63-96.
    • (1997) Appl. Numer. Math. , vol.23 , pp. 63-96
    • Grauschopf, T.1    Griebel, M.2    Regler, H.3
  • 18
    • 38249030345 scopus 로고
    • A note on the vectorization of algebraic multigrid algorithms
    • R. HEMPEL AND C. P. THOMPSON, A note on the vectorization of algebraic multigrid algorithms, Appl. Math. Comput., 26 (1988), pp. 245-256.
    • (1988) Appl. Math. Comput. , vol.26 , pp. 245-256
    • Hempel, R.1    Thompson, C.P.2
  • 19
    • 0002255549 scopus 로고
    • Convergence of algebraic multigrid methods for symmetric positive definite matrices with weak diagonal dominance
    • W. Z. HUANG, Convergence of algebraic multigrid methods for symmetric positive definite matrices with weak diagonal dominance, Appl. Math. Comput., 46 (1991), pp. 145-164.
    • (1991) Appl. Math. Comput. , vol.46 , pp. 145-164
    • Huang, W.Z.1
  • 20
    • 0024878671 scopus 로고
    • Algebraic multigrid domain decomposition methods
    • Y. A. KUZNETSOV, Algebraic multigrid domain decomposition methods, Soviet J. Numer. Anal. Math. Modeling, 4 (1989), pp. 361-392.
    • (1989) Soviet J. Numer. Anal. Math. Modeling , vol.4 , pp. 361-392
    • Kuznetsov, Y.A.1
  • 21
    • 0002570353 scopus 로고
    • Overlapping domain decomposition methods for FE-problems with elliptic singular perturbed operators
    • R. Glowinski, Y. A. Kuznetsov, G. Meurant, J. Périaux, and O. Widlund, eds., SIAM, Philadelphia
    • Y. A. KUZNETSOV, Overlapping domain decomposition methods for FE-problems with elliptic singular perturbed operators, in Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Proceedings in Applied Mathematics 51, R. Glowinski, Y. A. Kuznetsov, G. Meurant, J. Périaux, and O. Widlund, eds., SIAM, Philadelphia, 1991, pp. 223-241.
    • (1991) Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Proceedings in Applied Mathematics , vol.51 , pp. 223-241
    • Kuznetsov, Y.A.1
  • 22
    • 0022107991 scopus 로고
    • Multigrid methods for variational problems: General theory for the V-cycle
    • S. F. MCCORMICK, Multigrid methods for variational problems: General theory for the V-cycle, SIAM J. Numer. Anal., 22 (1985), pp. 634-643.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 634-643
    • Mccormick, S.F.1
  • 24
    • 0343507120 scopus 로고
    • On smoothing properties of SOR relaxation for algebraic multigrid method
    • C. POPA, On smoothing properties of SOR relaxation for algebraic multigrid method, Stud. Cerc. Mat., 5 (1989), pp. 399-406.
    • (1989) Stud. Cerc. Mat. , vol.5 , pp. 399-406
    • Popa, C.1
  • 25
    • 0343071073 scopus 로고
    • A simple parallel algebraic multigrid
    • IOS Press, Washington, D.C.
    • G. ROBINSON, A simple parallel algebraic multigrid, in Occam and the Transputer, IOS Press, Washington, D.C., 1991, pp. 62-75.
    • (1991) Occam and the Transputer , pp. 62-75
    • Robinson, G.1
  • 27
    • 0001326593 scopus 로고
    • Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG)
    • The Institute of Mathematics and its Applications Conference Series, D. J. Paddon and H. Holstein, eds., Clarendon Press, Oxford
    • J. W. RUGE AND K. STÜBEN, Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG), in Multigrid Methods for Integral and Differential Equations, The Institute of Mathematics and its Applications Conference Series, D. J. Paddon and H. Holstein, eds., Clarendon Press, Oxford, 1985, pp. 169-212.
    • (1985) Multigrid Methods for Integral and Differential Equations , pp. 169-212
    • Ruge, J.W.1    Stüben, K.2
  • 29
    • 0002621183 scopus 로고
    • Algebraic multigrid (AMG): Experiences and comparisons
    • K. STÜBEN, Algebraic multigrid (AMG): Experiences and comparisons, Appl. Math. Cornput., 13 (1983), pp. 419-452.
    • (1983) Appl. Math. Cornput. , vol.13 , pp. 419-452
    • Stüben, K.1
  • 30
    • 0001822668 scopus 로고
    • Multigrid methods: Fundamental algorithms, model problem analysis and applications
    • W. Hackbusch and U. Trottenberg, eds., Springer-Verlag, Berlin
    • K. STÜBEN AND U. TROTTENBERG, Multigrid methods: Fundamental algorithms, model problem analysis and applications, in Multigrid Methods, Lecture Notes in Mathematics 960, W. Hackbusch and U. Trottenberg, eds., Springer-Verlag, Berlin, 1982, pp. 1-176.
    • (1982) Multigrid Methods, Lecture Notes in Mathematics , vol.960 , pp. 1-176
    • Stüben, K.1    Trottenberg, U.2
  • 32
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid based on smoothed aggregation for second and fourth order problems
    • P. VANĚK, J. MANDEL, AND M. BREZINA, Algebraic multigrid based on smoothed aggregation for second and fourth order problems, Computing, 56 (1996), pp. 179-196.
    • (1996) Computing , vol.56 , pp. 179-196
    • Vaněk, P.1    Mandel, J.2    Brezina, M.3
  • 33
    • 0003515955 scopus 로고
    • Algebraic multignd on unstructured meshes
    • Center for Computational Mathematics, University of Colorado at Denver, Denver, CO
    • P. VANĚK, J. MANDEL, AND M. BREZINA, Algebraic Multignd on Unstructured Meshes, UCD/CCM Report 34, Center for Computational Mathematics, University of Colorado at Denver, Denver, CO, 1994; also available online at http://www-math.cudenver.edu/ccmreports/rep34.ps.gz.
    • (1994) UCD/CCM Report , vol.34
    • Vaněk, P.1    Mandel, J.2    Brezina, M.3
  • 34
    • 24244454533 scopus 로고    scopus 로고
    • Solving a two-dimensional Helmholtz problem by algebraic multigrid
    • Center for Computational Mathematics, University of Colorado at Denver, Denver, CO
    • P. VANĚK, J. MANDEL, AND M. BREZINA, Solving a Two-Dimensional Helmholtz Problem by Algebraic Multigrid, UCD/CCM Report 110, Center for Computational Mathematics, University of Colorado at Denver, Denver, CO, 1997; also available online at http://www-math.cudenver.edu/ccmreports/rep110.ps.gz.
    • (1997) UCD/CCM Report , vol.110
    • Vaněk, P.1    Mandel, J.2    Brezina, M.3
  • 35
    • 0003608177 scopus 로고    scopus 로고
    • Convergence of algebraic multigrid based on smoothed aggregation
    • Center for Computational Mathematics, University of Colorado at Denver, Denver, CO
    • P. VANĚK, J. MANDEL, AND M. BREZINA, Convergence of Algebraic Multigrid Based on Smoothed Aggregation, UCD/CCM Report 126, Center for Computational Mathematics, University of Colorado at Denver, Denver, CO, 1998; also available online at http://www-math.cudenver.edu/ccmreports/rep126.ps.gz.
    • (1998) UCD/CCM Report , vol.126
    • Vaněk, P.1    Mandel, J.2    Brezina, M.3
  • 36
    • 0043143072 scopus 로고    scopus 로고
    • An energy-minimizinginterpolation for robust multigrid methods
    • Department of Mathematics, UCLA, Los Angeles
    • W. L. WAN, T. F. CHAN, AND B. SMITH, An energy-minimizinginterpolation for robust multigrid methods, UCLA CAM Report 98-6, Department of Mathematics, UCLA, Los Angeles, 1998.
    • (1998) UCLA CAM Report , vol.98 , Issue.6
    • Wan, W.L.1    Chan, T.F.2    Smith, B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.