An energy-based AMG coarsening strategy

Numerical Linear Algebra with Applications

Volumn 13, Issue 2-3, 2006, Pages 133-148

  Brannick, J ^a   Brezina, M ^a   MacLachlan, S ^a   Manteuffel, T ^a   McCormick, S ^a   Ruge, J ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

AMG; Multigrid; Multigrid coarsening

Indexed keywords

EID: 33645348260     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.480     Document Type: Article

References (27)

1. Brandt A, McCormick SF, Ruge JW. Algebraic multigrid (AMG) for sparse matrix equations. In Sparsity and Its Applications, Evans DJ (ed.). Cambridge University Press: Cambridge, 1984.
2. Ruge JW, Stüben K. Algebraic multigrid (AMG). In Multigrid Methods, McCormick SF (ed.). Frontiers in Applied Mathematics, vol. 3. SIAM: Philadelphia, PA, 1987; 73-130.
3. Adams M, Brezina M, Hu J, Tuminaro R. Parallel multigrid smoothing: polynomial versus Gauss-Seidel. Journal of Computational Physics 2003; 188:593-610.
4. Bochev P, Garasi C, Hu J, Robinson A, Tuminaro R. An improved algebraic multigrid method for solving Maxwell's equations. SIAM Journal on Scientific Computing 2003; 25(2):623-642.
5. Brezina M, Falgout R, MacLachlan S, Manteuffel T, McCormick S, Ruge J. Adaptive smoothed aggregation (αSA). SIAM Journal on Scientific Computing 2004; 25(6): 1896-1920.
6. Stüben K. An introduction to algebraic multigrid. In Multigrid, Trottenberg U, Oosterlee C, Schuller A (eds). Academic Press: San Diego, CA, 2001; 413-528.
7. Tuminaro R, Tong C. Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines. In SuperComputing 2000 Proceedings, Donnelley J (ed.), 2000.
8. Yang U. On the use of relaxation parameters in hybrid smoothers. Numerical Linear Algebra with Applications 2004; 11:155-172.
9. Cleary A, Falgout R, Henson V, Jones J. Coarse-grid selection for parallel algebraic multigrid. In Proceedings of the Fifth International Symposium on Solving Irregularly Structured Problems in Parallel, Lecture Notes in Computer Science, vol. 1457. Springer: New York, 1998; 104-115.
10. De Sterck H, Yang U, Heys J. Reducing complexity in parallel algebraic multigrid preconditioners. SIAM Journal on Matrix Analysis and Applications, 2004, also available as LLNL Technical Report UCRL-JRNL-206780, to appear.
11. Henson V, Yang U. BoomerAMG: a parallel algebraic multigrid solver and preconditioner. Applied Numerical Mathematics 2002; 41:155-177.
12. Livne O. Coarsening by compatible relaxation. Numerical Linear Algebra with Applications 2004; 11(2):205-227.
13. Brezina M, Falgout R, MacLachlan S, Manteuffel T, McCormick S, Ruge J. Adaptive algebraic multigrid. SIAM Journal on Scientific Computing 2006; 27:1261-1286.
14. Brannick J, Zikatanov L. Algebraic multigrid methods based on compatible relaxation and energy minimization. In Proceedings of the 16th International Conference on Domain Decomposition Methods. Springer: New York, 2005, to appear.
15. Brezina M, Cleary A, Falgout R, Henson V, Jones J, Manteuffel T, McCormick S, Ruge J. Algebraic multigrid based on element interpolation (AMGe). SIAM Journal on Scientific Computing 2000; 22:1570-1592.
16. Chartier T, Falgout R, Henson V, Jones J, Manteuffel T, McCormick S, Ruge J, Vassilevski P. Spectral AMGe (pAMGe). SIAM Journal on Scientific Computing 2003; 25:1-26.
17. Vaněk P, Mandel J, Brezina M. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 1996; 56:179-196.
18. Meurant GA. Numerical experiments with algebraic multilevel preconditioners. Electronic Transactions on Numerical Analysis 2001; 12:1-65.
19. Brandt A. General highly accurate algebraic coarsening. Electronic Transactions on Numerical Analysis 2000; 10:1-20.
20. Brannick J. Adaptive algebraic multigrid coarsening strategies. Ph.D. Dissertation, University of Colorado, Boulder, Colorado, U.S.A., 2005.
21. Falgout RD, Vassilevski PS. On generalizing the AMG framework. SIAM Journal on Numerical Analysis 2004; 42(4): 1669-1693.
22. Chow E. An unstructured multigrid method based on geometric smoothness. Numerical Linear Algebra with Applications 2003; 10:401-421.
23. Bröker O. Parallel multigrid methods using sparse approximate inverses. Ph.D. Dissertation, Swiss Federal Institute of Technology, Zurich, Switzerland, 2003.
24. Grote M, Huckle T. Parallel preconditioning with sparse approximate inverses. SIAM Journal on Scientific Computing 1997; 18(3):838-853.
25. Briggs WL, Henson VE, McCormick SF. A Multigrid Tutorial (2nd edn). SIAM Books: Philadelphia, 2000.
26. Ashby SF, Manteuffel TA, Saylor PE. A taxonomy for conjugate gradient methods. SIAM Journal on Numerical Analysis 1990; 27:1542-1568.
27. Cleary AJ, Falgout RD, Henson VE, Jones JE, Manteuffel TA, McCormick SF, Miranda GN, Ruge JW. Robustness and scalability of algebraic multigrid. SIAM Journal on Scientific Computing 2000; 21(5): 1886-1908.