paper 150204064654

Published: 2015-07-09

Block LU Preconditioner for the Electric Field Integral Equation

Stanislav L. Stavtsev

Institute of Numerical Mathematics, Russian Academy of Sciences, Russia

Homepage

Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)1523-1527

Abstract

Boundary element discretizations are used in many fields of science and engineering, for example, to solve the problem of electromagnetic scattering with electric field integral equation (EFIE). To solve the EFIE on surfaces of arbitrary shape, RWG functions are traditionally used. The matrices arising from the discretization of integral equations can be adequately approximated with low-rank matrices using the mosaic-skeleton method. However, to solve the problem of scattering with a large wave size of the object, we have to solve a large system with n ∼ 105 –106 . Systems of linear equations with matrices of this order are solved iteratively (GMRES). For a large wave size, the matrix is ill-conditioned and we have to use a preconditioner. In this paper, the number of iterations in the GMRES method is reduced by building a block LU preconditioner. The numerical experiments have revealed that the preconditioner makes it possible to solve the problem of electromagnetic scattering on objects with a larger wave size.

Citation

Stanislav L. Stavtsev, "Block LU Preconditioner for the Electric Field Integral Equation," Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)1523-1527

References

1. Colton, D. L. and R. Kress, Integral Equation Method in Scattering Theory, Wiley, New York, 1983. Google Scholar

2. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scaterring by surfaces of arbitrary shape," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 3, 409-418, 1982.
doi:10.1109/tap.1982.1142818 Google Scholar

3. Song, J. M. and W. C. Chew, "Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetics scattering," Microwave Opt. Tech. Lett., Vol. 10, No. 1, 14-19, 1995.
doi:10.1002/mop.4650100107 Google Scholar

4. Stavtsev, S. L. and E. E. Tyrtyshnikov, "Application of Mosaic-Skeleton approximations for solving EFIE," PIERS Proceedings, 1901-1904, Moscow, 2009. Google Scholar

5. Tyrtyshnikov, E. E., "Incomplete cross apprixmation in the Mosaic-Skeleton method," Computing, Vol. 64, No. 4, 367-380, 2000. Google Scholar

6. Stavtsev, S. L., "Application of the method of incomplete cross approximation to a nonstationary problem of vortex rings dynamics," Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 27, No. 3, 303-320, 2012.
doi:10.1515/rnam-2012-0017 Google Scholar

7. Saad, Y. and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM J. Sci. Stat. Comput., 856-869, 1986.
doi:10.1137/0907058 Google Scholar

8. Guo, H., J. Hu, J. Yin, and Z. Nie, "An improved Calderon preconditioner for electric field integral equation," Asia Pacific Microwave Conference, APMC 2009, 92-95, 2009. Google Scholar

9. Chai, W. and D. Jiao, "An LU decomposition based direct integral equation solver of linear complexity and higher-order accuracy for large-scale interconnect extraction," IEEE Transactions on Advanced Packaging, Vol. 33, No. 4, 794-803, 2010.
doi:10.1109/tadvp.2010.2053537 Google Scholar

10. Bebendorf, M., "Hierarchical LU decomposition-based preconditioners for BEM," Computing, Vol. 74, 225-247, 2005.
doi:10.1007/s00607-004-0099-6 Google Scholar