An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations

Abstract

The solution of the two-dimensional scattering problem for an homogeneous dielectric cylinder of arbitrary shape is considered. The numerical approach is based on a two-field system of integral equations solved by a Krylov subspace method. To accelerate and to improve the convergence of this solver, an efficient and robust preconditioner, based on the Calderón formulae, is developed. Several numerical simulations, for a wide range of physical parameters, validating the choice of this preconditioner are presented.

Keywords:

• electromagnetic scattering
• dielectric media
• integral equation
• preconditioning techniques
• Calderón formulae

2000 AMS Subject Classification :

• 78A45
• 31A10
• 65F10

Acknowledgements

Parts of this work were begun while the first author was a visiting associate professor at the Applied and Computational Mathematics Department of the California Institute of Technology, Pasadena, USA. The author wishes to thank sincerely Prof. O.P. Bruno for many useful and interesting discussions during the visit and for his friendship and support.