Algebraic multigrid based on computational molecules, 1: Scalar elliptic problems

Computing (Vienna/New York)

Volumn 77, Issue 1, 2006, Pages 57-75

  Kraus, J K ^a,b   Schicho, J ^a,b  

^a Johann Radon Institute for Computational and Applied Mathematics ^*

^b JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

Algebraic multigrid; Coarse grid selection; Edge matrices; Interpolation weights

Indexed keywords

ALGEBRAIC MULTIGRID; COARSE-GRID SELECTION; EDGE MATRICES; INTERPOLATION WEIGHTS;

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; INTERPOLATION; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS);

MATRIX ALGEBRA;

EID: 32544440613     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-005-0147-x     Document Type: Article

References (26)

1. Axelsson, O.: Iterative solution methods. Cambridge University Press 1994.
2. Brandt, A.: Algebraic multigrid theory: the symmetric case. Preliminary Proc. Int. Multigrid Conf., Copper Mountain, CO, 1983.
3. Brandt, A.: Algebraic multigrid theory: the symmetric case. Appl. Math. Comput. 19, 23-56 (1986).
4. Brandt, A., McCormick, S. F., Ruge, J. W.: Algebraic multigrid (AMG) for automatic multigrid solutions with applications to geodetic computations. Report, Inst. for Computational Studies, Fort Collins, CO, 1982.
5. Brandt, A., McCormick, S. F., Ruge, J. W.: Algebraic multigrid (AMG) for sparse matrix equations. In: Sparsity and its applications (D. J. Evans, ed.). Cambridge: Cambridge University Press 1985, pp. 257-284.
6. Brezina, M., Cleary, A. J., Falgout, R. D., Henson, V. E., Jones, J. E., Manteuffel, T. A., McCormick, S. F., Ruge, J. W.: Algebraic multigrid based on element interpolation (AMGe). SIAM J. Sci. Comput. 22, 1570-1592 (2000).
7. Briggs, W. L., Henson, V. E., McCormick, S. F.: A multigrid tutorial, 2nd edition. Philadelphia: SIAM Books 2001.
8. Chan, T. F., Vanek, P.: Detection of strong coupling in algebraic multigrid solvers. In: Multigrid methods VI, vol. 14. Berlin: Springer 2000, pp. 11-23.
9. Chartier, T., Falgout, R. D., Henson, V. E., Jones, J. Manteuffel, T., McCormick, S., Ruge, J., Vassilevski, P. S.: Spectral AMGe (ρAMGe). SIAM J. Sci. Comput. 25, 1-26 (2004).
10. Cleary, A. J., Falgout, R. D., Henson, V. E., Jones, J. E., Manteuffel, T. A., McCormick, S. F., Miranda, G. N., Ruge, J. W.: Robustness and scalability of algebraic multigrid. SIAM J. Sci. Stat. Comput. 21, 1886-1908 (2000).
11. Falgout, R. D., Vassilevski, P. S.: On generalizing the algebraic multigrid framework. SIAM J. Numer. Anal. 42, 1669-1693 (2004).
12. Haase, G., Langer, U., Reitzinger, S., Schöberl, J.: Algebraic multigrid methods based on element preconditioning. Int. J. Comp. Math. 78, 575-598 (2004).
13. Henson, V. E., Vassilevski, P.: Element-free AMGe: general algorithms for computing the interpolation weights in AMG. SIAM J. Sci. Comput. 23, 629-650 (2001).
14. Jones, J. E., Vassilevski, P.: AMGe based on element agglomeration. SIAM J. Sci. Comput. 25, 109-133 (2001).
15. Kraus, J. K.: On the utilization of edge matrices in algebraic multigrid. Lecture Notes in Computer Science. Proc. 5th Int. Conf. on "Large-Scale Scientific Computations", Sozopol, Bulgaria, June 6-10, 2005 (to appear).
16. Langer, U., Reitzinger, S., Schicho, J.: Symbolic methods for the element preconditioning technique. In: Proc. SNSC Hagenberg (Langer, U., Winkler, F., eds.). Springer 2002.
17. Mandel, J., Brezina, M., Vaněk, P.: Energy optimization of algebraic multigrid bases. Computing 62, 205-228 (1999).
18. Ruge, J. W., Stüben, K.: Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG). In: Multigrid methods for integral and differential equations (Paddon, D. J., Holstein, H., eds.). The Institute of Mathematics and Its Applications Conference Series. Oxford: Clarendon Press 1985, pp. 169-212.
19. Ruge, J. W., Stüben, K.: Algebraic multigrid (AMG). In: Multigrid methods. Frontiers in Applied Mathematics, Vol. 3 (McCormick, S.F., ed.). Philadelphia: SIAM 1987, pp. 73-130.
20. Schöberl, J.: NETGEN - an advancing front 2D/3D-mesh generator based on abstract rules. Comput. Visual. Sci. 41-52 (1997).
21. Stüben, K.: Algebraic multigrid (AMG): experiences and comparisons. Appl. Math. Comput. 13, 419-452 (1983).
22. Tuminaro, R. S., Tong, C.: Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines. Report, Sandia National Laboratories, 2000.
23. Varga, R. S.: Matrix iterative analysis. Prentice-Hall 1962.
24. Vaněk, P., Brezina, M., Mandel, J.: Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math. 88, 559-579 (2001).
25. Vaněk, P., Mandel, J., Brezina, M.: Algebraic multigrid based on smoothed aggregation for second-and fourth-order problems. Computing 56, 179-196 (1996).
26. Wan, W. L., Chan, T. F., Smith, B.: An energy-minimizing interpolation for robust multigrid methods. Siam J. Sci. Comput. 21, 1632-1649 (2000).