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A matrix-free two-grid preconditioner for solving boundary integral equations in electromagnetism. (English) Zbl 1095.78010
In this paper there are presented some multipole techniques for solving boundary integral equations in electromagnetism. The author uses a sparse approximate inverse as a smoother for an algebraic two-grid cycle where the inter-grids operators are based on spectral information from the preconditioned matrix. The sparse approximate inverse is computed from the near-field part of the dense coefficient matrix and the pattern is prescribed in advance by using physical information. The numerical results on small and medium size problems from radar cross section calculations illustrate this method.

MSC:
78M25 Numerical methods in optics (MSC2010)
65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
65N38 Boundary element methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
78A45 Diffraction, scattering
78A50 Antennas, waveguides in optics and electromagnetic theory
Software:
HSL
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References:
[1] Alléon, G., Amram, S., Durante, N., Homsi, P., Pogarieloff, D., Farhat, C.: Massively parallel processing boosts the solution of industrial electromagnetic problems: High performance out-of-core solution of complex dense systems. In: Proc. 8th SIAM Conf. on Parallel (M. Heath, V. Torczon, G. Astfalk, P. E. Bjørstad, A. H. Karp, C. H. Koebel, V. Kumar, R. F. Lucas, L. T. Watson, D. E. Womble, eds.), Minneapolis, Minnesota, USA. Philadelphia: SIAM 1997.
[8] Canning, F. X.: The impedance matrix localization (IML) method for moment-method calculations. IEEE Antennas and Propagation Magazine 1990.
[11] Carpentieri, B., Giraud, L., Gratton, S.: Additive and multiplicative two-level spectral preconditioning for general linear systems. Technical Report TR/PA/04/38, CERFACS, Toulouse, France, 2004 · Zbl 1145.65023
[17] Edelman, A.: Records in dense linear algebra [online, cited 27 April 2005]. Available from: http://www-math.mit.edu/edelman/records.html.
[25] HSL. A collection of Fortran codes for large scale scientific computation, 2000. http://www.numerical.rl.ac.uk/hsl.
[28] Lee, J., Lu, C.-C., Zhang, J.: Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics. Technical Report 363-02, Department of Computer Science, University of Kentucky, KY, 2002 · Zbl 1368.78050
[30] Morgan, R. B.: Implicitely restarted GMRES and Arnoldi methods for nonsymmetric systems of equations. SIAM J. Matrix Anal. Appl. 21(4), 1112–1135. · Zbl 0963.65038
[33] Rahola, J.: Experiments on iterative methods and the fast multipole method in electromagnetic scattering calculations. Technical Report TR/PA/98/49, CERFACS, Toulouse, France, 1998
[37] Samant, A. R., Michielssen, E., Saylor, P.:Approximate inverse based preconditioners for 2D dense matrix problems. Technical Report CCEM-11-96, University of Illinois, 1996.
[40] Sylvand, G.: La méthode multipôle rapide en electromagnétisme : performances, parallélisation, applications. PhD thesis, Ecole Nationale des Ponts et Chaussées, 2002
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