Algebraic multigrid for complex symmetric matrices and applications

Journal of Computational and Applied Mathematics

Volumn 155, Issue 2, 2003, Pages 405-421

  Reitzinger, Stefan ^a   Schreiber, Ute ^b   van Rienen, Ursula ^b  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b UNIVERSITY OF ROSTOCK   (Germany)

Author keywords

Algebraic multigrid; Complex symmetric matrices; Electro quasistatics; Finite integration technique; Krylov subspace methods; Preconditioning technique

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; ITERATIVE METHODS; PROBLEM SOLVING;

COMPLEX SYMMETRIC MATRICES;

MATRIX ALGEBRA;

MATHEMATICAL METHOD;

EID: 0037532453     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00877-4     Document Type: Article

References (32)

1. Axelsson O. Iterative Solution Methods 2nd Edition 1996 Cambridge University Press Cambridge.
2. Braess D. Towards algebraic multigrid for elliptic problems of second order Computing 55 1995 379-393.
3. Brandt A. Generally highly accurate algebraic coarsening Electromagn. Trans. Numer. Anal. 10 2000 1-20.
4. Bunse-Gerstner A. Stoever R. On a conjugate gradient-type method for solving complex symmetric linear systems Linear Algebra Appl. 287 1999 105-123
5. Clemens M. Schuhmann R. van Rienen U. Weiland T. Modern Krylov subspace methods in electromagnetic field computation using the finite integration theorie Appl. Comput. Electromagn. Soc. J. 11 1 1996 70-84
6. Clemens M. Weiland T. Discrete electromagnetics: Maxwell's equations tailored to numerical simulations Internat. Compumag. Soc. Newsletter 8 2 2001 13-20
7. Clemens M. Weiland T. van Rienen U. Comparison of Krylov-type methods for complex linear systems applied to high-voltage problems IEEE Trans. Magn. 34 5 1998 3335-3338.
8. CST GmbH, Büdinger Str. 2a, D-64289 Darmstadt, MAFIA version 4.020.
9. Freund R.W. Nachtigal N.M. An implementation of the QMR method based on coupled two-term recurrences SIAM J. Sci. Comput. 15 1994 297-312
10. G. Haase, U. Langer, S. Reitzinger, J. Schöberl, A general approach to algebraic multigrid, SFB "Numerical and Symbolic Scientific Computing", Technical Report 00-33, Johannes Kepler University Linz, 2000.
11. Hackbusch W. Multigrid Methods and Application 1985 Springer Berlin, Heidelberg, New York
12. W. Hackbusch, Iterative Lösung großer schwachbesetzter Gleichungssysteme, BG Teubner, Stuttgart, 1991.
13. Haus H.A. Melcher J.R. Electromagnetic Fields and Energie 1989 Prentice-Hall Englewood Cliffs, NJ
14. Henson V.E. Vassilevski P.S. Element-free AMGe: general algorithms for computing interpolation weights in AMG SIAM J. Sci. Comput. 23 2001 629-650
15. K. Herrbach, Study of behavior of droplets on polymeric surfaces under electrical stress conditions with the aid of a contact angle measuring system, Report, High Voltage Laboratory, University of Technology, Darmstadt, 2000.
16. Ida N. Bastos J.P.A. Electromagnetics and Calculation of Fields 1997 Springer Berlin
17. Jones J.E. Vassilevski P.S. AMGe based on element agglomeration SIAM J. Sci. Comput. 23 1 2001 109-133
18. S. Keim, D. König, Study of the behavior of droplets on polymeric surfaces under the influence of an applied electrical field, IEEE Conference on Electrical Insulation and Dielectric Phenomena (CEIDP), 1999, pp. 707-710.
19. F. Kickinger, Algebraic multigrid for discrete elliptic second-order problems, Multigrid Methods V, in: W. Hackbusch (Ed.), Proceedings of the Fifth European Multigrid Conference, Springer Lecture Notes in Computational Science and Engineering, Vol. 3, 1998, pp. 157-172.
20. M. Kneuer, Experimentelle Untersuchungen des Verhaltens von Flüssigkeiten auf Isolierstoffoberflächen unter dem Einflußeines elektrischen Feldes, Master's Thesis, High voltage Laboratory, University of Technology, Darmstadt, 2000.
21. Lahaye D. De Gersem H. Vandewalle S. Hameyer K. Algebraic multigrid for complex symmetric systems IEEE Trans. Magn. 36 4 2000 1535-1538
22. McCormick S.F. An algebraic Interpretation of multigrid methods SIAM J. Numer. Anal. 19 3 1982 548-560.
23. Meurant G. Computer solution of large linear systems Studies in Mathematics and its Applications Vol. 28 1999 Elsevier Amsterdam.
24. S. Reitzinger, PEBBLES-User's Guide, Johannes Kepler University Linz, SFB "Numerical and Symbolic Scientific Computing", 1999,
25. S. Reitzinger, Algebraic multigrid methods for large scale element equations, Schriften der Johannes-Kepler-Universität Linz, Reihe C-Technik und Naturwissenschaften, no. 36, Universitätsverlag Rudolf Trauner, 2001.
26. Reitzinger S. Schöberl J. An algebraic multigrid method for finite element discretizations with edge elements Numer. Linear Algebra 9 2002 223-238
27. Ruge J.W. Stüben K. Algebraic multigrid (AMG) McCormick S. Multigrid Methods Frontiers in Applied Mathematics Vol. 5 1986 73 130 SIAM Philadelphia.
28. U. Schreiber, U. van Rienen, S. Keim, Simulation of electric field strength and force density on contaminated h-v insulators, Vol. 18, Springer Lecture Notes in Computational Science and Engineering, 2001, pp. 79-86.
29. U. van Rienen, Numerical methods in computational electrodynamics-linear systems in practical applications, Vol. 12, Springer Lecture Notes in Computational Science and Engineering, 2001.
30. Vanek P. Mandel J. Brezina M. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems Computing 56 1996 179-196.
31. Wagner C. On the algebraic construction of multilevel transfer operators Computing 65 2000 73-95.
32. Weiland T. A discretization method for the solution of Maxwell's equation for six-component fields Electron. Commun. AEÜ 31 3 1977 116-120