AMG by element agglomeration and constrained energy minimization interpolation

Numerical Linear Algebra with Applications

Volumn 13, Issue 9, 2006, Pages 771-788

  Kolev, Tzanio V ^a   Vassilevski, Panayot S ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Algebraic multigrid; Element agglomeration; Minimal energy interpolation; Vector preserving interpolation

Indexed keywords

EID: 33750744063     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.494     Document Type: Article

References (20)

1. Brezina M, Cleary AJ, Falgout RD, Henson JE, Jones JE, Manteuffel TA, McCormick SF, Ruge JW. Algebraic multigrid based on element interpolation (AMGe). SIAM Journal on Scientific Computing 2000; 22:1570-1592.
2. Jones JE, Vassilevski PS. AMGe based on element agglomerations. SIAM Journal on Scientific Computing 2001; 23:109-133.
3. Chartier T, Falgout R, Henson VE, Jones J, Manteuffel T, McCormick S, Ruge J, Vassilevski PS. Spectral AMGe (pAMGe). SIAM Journal on Scientific Computing 2003; 25:1-26.
4. Chartier T, Falgout R, Henson VE, Jones J, Manteuffel T, McCormick S, Ruge J, Vassilevski PS. Spectral element agglomerate AMGe. Proceedings of 16th International Conference of Domain Decomposition Methods. Lecture Notes in Computational Science and Engineering. Springer: Berlin, New York University, 2005; in press.
5. Vassilevski PS. Sparse matrix element topology with application to AMG and preconditioning. Numerical Linear Algebra with Applications 2002; 9:429-444.
6. Wan WL, Chan TF, Smith B. An energy-minimizing interpolation for robust multigrid methods. SIAM Journal on Scientific Computing 2000; 21:1632-1649.
7. Wagner C. On the algebraic construction of multilevel transfer operators. Computing 2000; 65:73-95.
8. Xu J, Zikatanov LT. On an energy minimizing basis in algebraic multigrid methods. Computing and Visualization in Science 2004; 7:121-127.
9. Vassilevski PS, Zikatanov LT. Multiple vector preserving interpolation mappings in algebraic multigrid. SIAM Journal on Matrix Analysis and Applications 2005-2006; 27:1040-1055.
10. Brezina M, Falgout R, MacLachlan S, Manteuffel T, McCormick S, Ruge J. Adaptive smoothed aggregation (aSA). SIAM Journal on Scientific Computing 2004; 25:1896-1924.
11. Brezina M, Falgout R, MacLachlan S, Manteuffel T, McCormick S, Ruge J. Adaptive algebraic multigrid. SIAM Journal on Scientific Computing 2006; 27:1261-1286.
12. Mandel J. Balancing domain decomposition. Communications in Applied Numerical Methods 1993; 9:233-241.
13. Falgout RD, Vassilevski PS. On generalizing the algebraic multigrid framework. SIAM Journal on Numerical Analysis 2004; 42:1669-1693.
14. Falgout RD, Vassilevski PS, Zikatanov LT. On two-grid convergence estimates. Numerical Linear Algebra with Applications 2005; 12:471-494.
15. METIS: Family of Multilevel Partitioning Algorithms, and ParMETIS: Parallel Graph Partitioning. Available online at http://www-users.cs.umn.edu/ karypis/metis/
16. Wabro M. AMGe - coarsening strategies and application to the Oseen equations. SIAM Journal on Scientific Computing 2006; 27:2077-2097.
17. Henson VE, Yang UM. BoomerAMG: a parallel algebraic multigrid solver and preconditioner. Applied Numerical Mathematics 2002; 41:155-177
18. (Also available as LLNL Technical Report UCRL-JC-141495).
19. Vaněk P, Mandel J, Brezina M. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 1996; 3:179-196.
20. Adams M, Brezina M, Hu J, Tuminaro R. Parallel multigrid smoothing: polynomial versus Gauss-Seidel. Journal of Computational Physics 2003; 188:593-610.