A block QMR method for computing multiple simultaneous solutions to complex symmetric systems

SIAM Journal on Scientific Computing

Volumn 17, Issue 1, 1996, Pages 263-274

  Boyse, William E ^a   Seidl, Andrew A ^a  

^a LOCKHEED MARTIN   (United States)

Author keywords

Block Lanczos algorithm; Complex symmetric matrices; Maxwell's equations; Preconditioner; QMR

Indexed keywords

EID: 0001266838     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/0917019     Document Type: Article

References (18)

1. W. E. BOYSE, D. R. LYNCH, K. D. PAULSEN, AND G. N. MINERBO, Nodal based finite element modeling of Maxwell's equations, IEEE Trans. Antennas Propagation, 40 (1992), pp. 642-651.
2. W. E. BOYSE AND A. A. SEIDL, A hybrid finite element method for near bodies of revolution, IEEE Trans. Magnetics, 27 (1991), pp. 3833-3840.
3. _, Convergence acceleration by preconditioning a block quasi minimum residual method for a finite element formulation of electromagnetic scattering, in URSI Symposium Digest, Chicago, Illinois, 1992, IEEE-APS/URSI/NEM Joint Symposium, p. 172.
4. _, An iterative solver for multiple right hand sides based on the block Lanczos algorithm, in URSI Symposium Digest, Chicago, Illinois, 1992, IEEE-APS/URSI/NEM Joint Symposium, p. 173.
5. _, A hybrid finite element method for 3-D scattering using nodal and edge elements, IEEE Trans. Antennas Propagation, 42 (1994), pp. 1436-1442.
6. A. CHATTERJEE, J. M. JIN, AND J. L. VOLAKIS, Edge-based finite elements and vector ABC's applied to 3-D scattering, IEEE Trans. Antennas Propagation, 41 (1993), pp. 221-226.
7. J. D'ANGELO AND I. D. MAYERGOYZ, RF scattering and radiation by using a decoupled Helmholtz equation approach, IEEE Trans. Magnetics, 29 (1993), pp. 2040-2042.
8. R. W. FREUND, Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 425-448.
9. R. W. FREUND, M. H. GUTKNECHT, AND N. M. NACHTIGAL, An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, Part I, Tech. report 90.45, RIACS, NASA Ames Research Center, November 1990.
10. A. GEOROE AND J. W. LIU, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1981.
11. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1983.
12. R. F. HARRINGTON, Field Computation by Moment Methods, Macmillan, New York, 1968.
13. J. R. MAUTZ AND R. F. HARRINGTON, H-field, E-field, and combined-field solutions for conducting bodies of revolution, Arch. Elektron. Ubertragungstech. (Electron. Comm.), 32 (1978), pp. 159-164.
14. D. P. O'LEARY, The block conjugate gradient algorithm and related methods, Linear Algebra Appl., 29 (1980). pp. 293-322.
15. _, Parallel implementation of the block conjugate gradient algorithm, Parallel Comput., 5 (1987), pp. 127-139.
16. S. PISSANETZKY, Sparse Matrix Technology, Academic Press, Inc., New York, 1984.
17. Y. SAAD, ILUT: A dual threshold incomplete LU factorization, Res. report UMSI92/38, University of Minnesota Supercomputer Institute, Minneapolis, MN, March 1992.
18. D. P. YOUNG, R. G. MELVIN, F. T. JOHNSON, J. E. BUSSOLETTI, L. B. WIGTON, AND S. S. SAMANT, Application of sparse matrix solvers as effective preconditioned, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 1186-1199.