Parallel algebraic multigrid methods on distributed memory computers

SIAM Journal on Scientific Computing

Volumn 24, Issue 2, 2003, Pages 410-427

  Haase, Gundolf ^a   Kuhn, Michael ^a   Reitzinger, Stefan ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Algebraic multigrid methods; Distributed memory; Domain decomposition data distribution; Finite element method; Parallel iterative solvers; Parallel multigrid preconditioners

Indexed keywords

ALGORITHMS; DISTRIBUTED COMPUTER SYSTEMS; FINITE ELEMENT METHOD; LINEAR EQUATIONS; LINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

DISTRIBUTED MEMORY COMPUTERS;

NATURAL SCIENCES COMPUTING;

EID: 0037249228     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501386237     Document Type: Article

References (27)

1. A. ANWANDER, M. KUHN, S. REITZINGER, AND C. WOLTERS, A Parallel Algebraic Multigrid Solver for the Finite Element Method Based Source Localization in the Human Brain, Tech. Report 01-21, SFB F013 "Numerical and Symbolic Scientific Computing," Johannes Kepler University Linz, Linz, Austria, 2001. Computing and Visualization in Science, to appear.
2. D. BRAESS, Towards algebraic multigrid for elliptic problems of second order, Computing, 55 (1995), pp. 379-393.
3. 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.
4. C. C. DOUGLAS AND M. B. DOUGLAS, MGNet Bibliography, Department of Mathematics and the Center for Computational Sciences, University of Kentucky, Lexington, KY and Department of Computer Science, Yale University, New Haven, CT, 1991-1999 (last modified on November 6, 1999), http://www.mgnet.org/bib/mgnet.bib.
5. R. FALGOUT, V. E. HENSON, J. E. JONES, AND U. M. YANG, Boomer AMG: A Parallel Implementation of Algebraic Multigrid, Tech. Report UCRL-MI-133583, Lawrence Livermore National Laboratory, Livermore, CA, 1999.
6. G. HAASE, Parallel incomplete Cholesky preconditioned based on the non-overlapping data distribution, Parallel Comput., 24 (1998), pp. 1685-1703.
7. G. HAASE, Parallelization of Numerical Algorithms for PDEs, Teubner, Stuttgart, 1999 (in German).
8. G. HAASE, A parallel AMG for overlapping and non-overlapping domain decomposition, Electron. Trans. Numer. Anal., 10 (2000), pp. 41-55.
9. G. HAASE AND M. KUHN, Preprocessing for 2D FE-BE domain decomposition methods, Comput. Vis. Sci., 2 (1999), pp. 25-35.
10. G. HAASE, M. KUHN, AND U. LANGER, Parallel multigrid 3D Maxwell solvers, Parallel Comput., 27 (2001), pp. 761-775.
11. G. HAASE, M. KUHN, U. LANGER, S. REITZINGER, AND J. SCHÖBERL, Parallel Maxwell solvers, in Proceedings of SCEE, Lect. Notes Comput. Sci. Eng. 18, Springer-Verlag, Berlin, 2001, pp. 71-78.
12. G. HAASE, U. LANGER, AND A. MEYER, The approximate Dirichlet decomposition method I, II, Computing, 47 (1991), pp. 137-167.
13. G. HAASE, U. LANGER, S. REITZINGER, AND J. SCHÖBERL, Algebraic multigrid methods based on element preconditioning, Int. J. Comput. Math., 78 (2001), pp. 575-598.
14. M. JUNG, On the parallelization of multi-grid methods using a non-overlapping domain decomposition data structure, Appl. Numer. Math., 23 (1997), pp. 119-137.
15. G. KARYPIS, K. SCHLOEGEL, AND V. KUMAR, Par Metis, Parallel Graph Partitioning and Sparse Matrix Ordering Library, Version 3.0, Tech. Report, University of Minnesota, Department of Computer Science and Engineering, Minneapolis, MN, 2002.
16. F. KICKINGER, Algebraic multigrid for discrete elliptic second-order problems, in Multigrid Methods V. Proceedings of the 5th European Multigrid Conference, Lect. Notes Comput. Sci. Eng. 3, W. Hackbusch, ed., Springer-Verlag, Berlin, 1998, pp. 157-172.
17. A. KRECHEL AND K. STÜBEN, Parallel algebraic multigrid based on subdomain blocking, Parallel Comput., 27 (2001), pp. 1009-1031.
18. M. KUHN, DDComm - Distributed Data Communication Library, SFB F013 "Numerical and Symbolic Scientific Computing," http://www.sfb013.uni-linz.ac.at., 2000.
19. M. KUHN, U. LANGER, AND J. SCHÖBERL, Scientific computing tools for 3D magnetic field problems, in The Mathematics of Finite Elements and Applications X, J. Whiteman, ed., John Wiley and Sons, New York, 2000, pp. 239-258; also available online from http://www.sfb013.uni-linz.ac.at.
20. K. H. LAW, A parallel finite element solution method, Computer and Structures, 23 (1989), pp. 845-858.
21. A. MEYER, A parallel preconditioned conjugate gradient method using domain decomposition and inexact solvers on each subdomain, Computing, 45 (1990), pp. 217-234.
22. S. REITZINGER, PEBBLES - User's Guide, SFB F013 "Numerical and Symbolic Scientific Computing," http://www.sfb013.uni-linz.ac.at, 1999.
23. S. REITZINGER AND J. SCHÖBERL, An algebraic multigrid method for finite element discretizations with edge elements, Numer. Linear Algebra Appl., 9 (2002), pp. 223-238.
24. J. W. RUGE AND K. STÜBEN, Algebraic multigrid, in Multigrid Methods, S. F. McCormick, ed., Frontiers Appl. Math. 3, SIAM, Philadelphia, 1987, pp. 73-130.
25. J. SCHÖBERL, NETGEN - An advancing front 2D/3D-mesh generator based on abstract. rules, Comput. Vis. Sci., 1 (1997), pp. 41-52.
26. P. VANEK, J. MANDEL, AND M. BREZINA, Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems, Computing, 56 (1996), pp. 179-196.
27. C. WAGNER, On the algebraic construction of multilevel transfer operators, Computing, 65 (2000), pp. 73-95.