Abstract
We consider different preconditioning techniques of both implicit and explicit form in connection with Krylov methods for the solution of large dense complex symmetric non-Hermitian systems of equations arising in computational electromagnetics. We emphasize in particular sparse approximate inverse techniques that use a static nonzero pattern selection. By exploiting geometric information from the underlying meshes, a very sparse but effective preconditioner can be computed. In particular our strategies are applicable when fast multipole methods are used for the matrix-vector products on parallel distributed memory computers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
M. Benzi, C. D. Meyer, and M. Tůma. A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J. Scientific Computing, 17:1135–1149, 1996.
B. Carpentieri, I. S. Du., and L. Giraud. Sparse pattern selection strategies for robust frobenius norm minimization preconditioners in electromagnetism. Technical Report TR/PA/00/05, CERFACS, Toulouse, France, 1999. To Appear in Numerical Linear Algebra with Applications.
R. W. Freund. A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems. SIAM J. Scientific Computing, 14(2):470–482, 1993.
R. W. Freund and N. M. Nachtigal. QMR: a quasi-minimal residual method for non-hermitian linear systems. Numerische Mathematik, 60(3):315–339, 1991.
M. Grote and T. Huckle. Parallel preconditionings with sparse approximate inverses. SIAM J. Scientific Computing, 18:838–853, 1997.
J. Rahola. Experiments on iterative methods and the fast multipole method in electromagnetic scattering calculations. Technical Report TR/PA/98/49, CERFACS, Toulouse, France, 1998.
S. M. Rao, D. R. Wilton, and A. W. Glisson. Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antennas Propagat., AP-30:409–418, 1982.
Y. Saad and M. H. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Scientific and Statistical Computing, 7:856–869, 1986.
H. A. van der Vorst. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Scientific and Statistical Computing, 13:631–644, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Carpentieri, B., Duff, I.S., Giraud, L. (2001). Robust Preconditioning of Dense Problems from Electromagnetics. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_21
Download citation
DOI: https://doi.org/10.1007/3-540-45262-1_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41814-6
Online ISBN: 978-3-540-45262-1
eBook Packages: Springer Book Archive