Adaptive smoothed aggregation (αSA)

SIAM Journal on Scientific Computing

Volumn 25, Issue 6, 2004, Pages 1896-1920

  Brezina, M ^a   Falgout, R ^b   Maclachlan, S ^a   Manteuffel, T ^a   Mccormick, S ^a   Ruge, J ^a  

^a UNIVERSITY OF COLORADO   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Adaptive method; Algebraic multigrid (AMG); Generalized smoothed aggregation (SA)

Indexed keywords

ALGEBRA; COMPUTATIONAL COMPLEXITY; FINITE ELEMENT METHOD; GEOMETRY; ITERATIVE METHODS; LINEAR SYSTEMS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS;

ADAPTIVE METHOD; ALGEBRIC MULTIGRIDS (AMG); GENERALIZED SMOOTHED AGGREGATION; SMOOTHED AGGREGATION (SA);

ADAPTIVE SYSTEMS;

EID: 10244278127     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502418598     Document Type: Article

References (23)

1. M. ADAMS, M. BREZINA, J. HU, AND R. TUMINARO, Parallel multigrid smoothing: Polynomial versus Gauss-Seidel, J. Comput. Phys., 188 (2003), pp. 593-610.
2. J. BRAMBLE, J. PASCIAK, J. WANG, AND J. XU, Convergence estimates for multigrid algorithm without regularity assumptions, Math. Comp., 57 (1991), pp. 23-45.
3. A. BRANDT, Lecture given at CASC, Lawrence Livermore National Lab, Livermore, CA, 2001.
4. 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, 1984, pp. 257-284.
5. A. BRANDT AND D. RON, Multigrid solvers and multilevel optimization strategies, in Multilevel Optimization in VLSICAD, Comb. Optim. 14, J. Cong and J. R. Shinnerl, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003, pp. 1-69.
6. M. BREZINA, A. J. CLEARY, R. D. FALGOUT, V. E. HENSON, J. E. JONES, T. A. MANTEUFFEL, S. F. MCCORMICK, AND J. W. RUGE, Algebraic multigrid based on element interpolation (AMGe), SIAM J. Sci. Comput., 22 (2000), pp. 1570-1592.
7. M. BREZINA, R. FALGOUT, S. MACLACHLAN, T. MANTEUFFEL, S. F. MCCORMICK, AND J. W. RUGE, Adaptive Algebraic Multigrid (αAMG), in preparation, 2003.
8. M. BREZINA, C. I. HEBERTON, J. MANDEL, AND P. VANĚK, An Iterative Method with Convergence Rate Chosen A Priori, UCD/CCM report 140, Center for Computational Mathematics, University of Colorado at Denver, Denver, CO, 1999; available online from http://wwwmath.cudenver.edu/ccmreports/rep140.ps.gz.
9. M. BREZINA AND P. VANĚK, A black-box iterative solver based on a two-level Schwarz method, Computing, 63 (1999), pp. 233-263.
10. W. BRIGGS, V. E. HENSON, AND S. F. MCCORMICK, A Multigrid Tutorial, 2nd ed., SIAM, Philadelphia, 2000.
11. T. CHARTIER, Element-Based Alebraic Multigrid (AMGe) and Spectral AMGe, Ph.D. thesis, Univerity of Colorado at Boulder, Boulder, CO, 2001.
12. T. CHARTIER, R. D. FALGOUT, V. E. HENSON, J. E. JONES, T. MANTEUFFEL, S. F. MC-CORMICK, J. W. RUGE, AND P. S. VASSILEVSKI, Spectral AMGe (pAMGe), SIAM J. Sci. Comput., 25 (2003), pp. 1-26.
13. J. FISH AND V. BELSKY, Generalized aggregation multilevel solver, Internat. J. Numer. Methods Engrg., 40 (1997), pp. 4341-4361.
14. S. F. MCCORMICK AND J. W. RUGE, Algebraic multigrid methods applied to problems in computational structural mechanics, in State of the Art Surveys on Computational Mechanics, A. K. Noor and J. T. Oden, eds., ASME, New York, 1989, pp. 237-270.
15. J. W. RUGE, Algebraic multigrid (AMG) for geodetic survey problems, in Proceedings of the International Multigrid Conference, Copper Mountain, CO, 1983.
16. J. W. RUGE, Final Report on AMG02, report, Gesellschaft fuer Mathematik und Datenverarbeitung, St. Augustin, 1985, GMD, contract 5110/022090.
17. J. W. RUGE, Algebraic multigrid applied to systems of partial differential equations, in Proceedings of the International Multigrid Conference, 1985, S. McCormick, ed., North-Holland, Amsterdam, 1986.
18. 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, UK, 1985, pp. 169-212.
19. J. W. RUGE AND K. STÜBEN, Algebraic multigrid (AMG), in Multigrid Methods, Frontiers Appl. Math. 3, S. F. McCormick, ed., SIAM, Philadelphia, 1987, pp. 73-130.
20. P. VANĚK, M. BREZINA, AND J. MANDEL, Convergence of algebraic multigrid based on smoothed aggregation, Numer. Math., 88 (2001), pp. 559-579.
21. P. VANĚK, Acceleration of convergence of a two-level algorithm by smoothing transfer operator, Appl. Math., 37 (1992), pp. 265-274.
22. P. VANĚK, M. BREZINA, AND R. TEZAUR, Two-grid method for linear elasticity on unstructured meshes, SIAM J. Sci. Comput., 21 (1999), pp. 900-923.
23. P. VANĚK, J. MANDEL, AND M. BREZINA, Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems, Computing, 56 (1996), pp. 179-196.