Modern Krylov subspace methods in electromagnetic field computation using the finite integration theory

Applied Computational Electromagnetics Society Journal

Volumn 11, Issue 1, 1996, Pages 70-84

  Clemens, Markus ^a   Schuhmann, Rolf ^a   Van Rienen, Ursula ^a   Weiland, Thomas ^a  

^a Fg Theor Elektromagnetischer F ^*  (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; INTEGRAL EQUATIONS; INTEGRATION; MATHEMATICAL MODELS; MATRIX ALGEBRA; MAXWELL EQUATIONS;

DISCRETIZATION; FINITE INTEGRATION THEORY; KRYLOV SUBSPACE METHODS;

ELECTROMAGNETIC FIELD THEORY;

EID: 0029779466     PISSN: 10544887     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. O. Axelsson. A survey of preconditioned iterative methods for linear systems of algebraic equations. BIT, 16:166-187, 1985.
2. Oliver Claus and Hans-Joachim Klös, 1994. Private Communications.
3. E. J. Craig. The n-step iteration procedures. Math. Phys., (34):64-73, 1955.
4. Michael Dehler. Numerische Lösung der Maxwellschen Gleichungen auf kreiszylindrischen Gittern. PhD thesis, Technische Hochschule Darmstadt, 1993.
5. Martin Dohlus. Ein Beitrag zur numerischen Berechnung elektromagnetischer Felder im Zeitbereich. PhD thesis, Technische Hochschule Darmstadt, 1992.
6. Stanley C. Eisenstat. Efficient implementation of a class of preconditioned conjugate gradient methods. SIAM Sci. Stat. Comput., 2(1):1-4, March 1981.
7. Roland W. Freund. A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems. SIAM J. Sci. Comput., 14(2):470-482, March 1993.
8. Roland W. Freund and Noel M. Nachtigal. QMR: A quasi-minimal residual method for non-Hermitian matrices. Numer.Math., 60:315-339, 1991.
9. Martin H. Gutknecht. Variants of BICGSTAB for matrices with complex spectrum. SIAM J. Sci. Stat., 14(5):1020-1033, September 1993.
10. Peter Hahne. Zur Numerischen Feldberechnung Zeitharmonischer Elektromagnetischer Felder. PhD thesis, Technische Hochschule Darmstadt, 1992.
11. M. R. Hestenes and E. Stiefel. Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards, 49:409-436, 1952.
12. D. A. H. Jacobs. The Exploitation of Sparsity by Iterative Methods. Sparse matrices and their Uses. I. S. Duff, Springer, 1981. pp. 191-222.
13. Ebrahim M. Kasenally. GMBACK: A generalised minimum backward error algorithm for nonsymmetric linear systems. SIAM J. Sci. Comput., 16(3):698-719, May 1995.
14. The Mafia collaboration. User's Guide MAFIA Version 3.x. CST GmbH, Lauteschlägerstr.38, D-64289 Darmstadt.
15. Ulrike Meier Yang. Preconditioned conjugate gradient methods for nonsymmetric linear systems. Research Report 1210, CSRD, University of Illinois at Urbana Champaign, July 1994.
16. Yousef Saad. Preconditioning techniques for nonsymmetric and indefinite linear systems. Journal of Computational and Applied Mathematics, (24):89-105, 1988.
17. Yousef Saad. Krylov subspace methods on supercomputers. SIAM J. Sci. Stat. Comput., 10(6):1200-1232, 1989.
18. Yousef Saad. ILUT: a dual treshold incomplete LU factorization. Numerical Linear Algebra with Applications, 1(4):387-402, 1994.
19. Yousef Saad and Martin H. Schultz. GMRES: A generalised minimal residual method for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7:856-869, 1986.
20. Gerard L. G. Sleijpen and Diederik R. Fokkema. BICGstab(1) for linear equations involving unsymmetric matrices with complex spectrum. Electronic Transactions on Numerical Analysis, 1:11-32, September 1993.
21. Gerard L. G. Sleijpen, Diederik R. Fokkema, and Henk A. van der Vorst. Generalized Conjugate Gradient Squared. University Utrecht, Department of Mathematics, Preprint No. 851, May 1994.
22. Gerard L. G. Sleijpen and Henk A. van der Vorst. Reliable updated residuals in hybrid Bi-CG methods. University Utrecht, Department of Mathematics, Preprint No. 886, to appear in Computing, November 1994.
23. Gerard L. G. Sleijpen and Henk A. van der Vorst. Maintaining convergence properties of BiCGstab methods in finite precision arithmetic. Numerical Algorithms, 10:203-223, 1995.
24. Gerard L. G. Sleijpen and Henk A. van der Vorst. An overview of approaches for the stable computation of hybrid Bi-CG methods. University Utrecht, Department of Mathematics, Preprint No. 908, to appear in Appl. Numer. Math., March 1995.
25. Peter Sonneveld. CGS, a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 10(1):36-52, November 1989.
26. H. A. van der Vorst and J.B.M. Melissen. A Petrow-Galerkin type method for solving Ax=b, where A is symmetric complex. IEEE Trans.Mag., 26(2):706-708, 1990.
27. Henk A. van der Vorst. Bi-CGStab: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 2(13):631-644, 1992.
28. Ursula van Rienen and Thomas Weiland. Triangular discretization method for the evaluation of RF-fields in cylindrically symmetric cavities. Particle Accelerators, 20:239-267, 1987.
29. Thomas Weiland. A discretization method for the solution of Maxwell's equations for six-component fields. Electronics and Communcations AEÜ, 31:116, 1977.
30. Thomas Weiland. A numerical method for the solution of the eigenvalue problem of longitudinally homogeneous waveguides. Electronics and Communcations AEÜ, 31:308, 1977.
31. Thomas Weiland. Lossy waveguides with arbitrary boundary contour and distribution of material. Electronics and Communcations AEÜ, 33:170, 1979.
32. Thomas Weiland. On the numerical solution of Maxwellian equations and applications. Particle Accelerators, 15:245-291, 1984.
33. Thomas Weiland. On the unique numerical solution of Maxwellian eigenvalue problems in three dimensions. Particle Accelerators, 17:227-242, 1985.
34. Rüdiger Weiss. Error-minimizing Krylov subspace methods. SIAM J. Sci. Comput., 15(3):511-527, May 1994.
35. Harry Yserentant. Preconditioning indefinite discretization matrices. Numer. Math., 54:719-735, 1988.
36. L. Zhuo and F. Walker. Residual smoothing techniques for iterative methods. SIAM J. Sci. Comput., 15(2):297-312, March 1994.