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Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |

Home > Vol. 42 > pp. 261-286
## An Exact Perturbative Formulation of the Dielectric Integral Equations for Lossy InterfacesBy B. A. Davis and R. J. Adams
Abstract:
In modeling scattering from lossy surfaces, the surface is often approximated as a perfect electric conductor (PEC). However, when loss and wave penetration become important, the IBC model is typically employed and is adequate for many numerical simulations. However, the IBC's range of validity is considered unclear and an accurate quantification of its error is difficult. Consequently, other more exact implementations are necessary, such as integral equation methods. In this paper, a novel numerical implementation of the exact dielectric integral equations has been developed for scattering from a two-dimensional (2D), lossy dielectric interface. The formulation presented herein combines the coupled integral equations to form a single equation. This equation is easily interpreted as the magnetic field integral equation (MFIE) for a 2D, PEC surface with a perturbative term related to the finite conductivity of the surface. The advantage of this perturbation approach is that for ocean and other high loss surfaces, the solution is expected to be rapidly convergent with respect to other approaches and will reproduce the correct result even for surfaces with small curvature radii. Test cases demonstrate increased convergence with increased loss and increased contrast for perpendicular polarization. However with parallel polarization, convergence problems are uncovered and are associated with the Brewster angle effect.
2. Holliday, D., L. L. DeRaad Jr., and G. J. St-Cyr, "Forwardbackward: Anew method for computing lowgrazing scattering," 3. Adams, R. J., "A class of robust and efficient iterative methods for wave scattering problems," 4. Adams, R. J. and G. S. Brown, "A combined field approach to scattering from infinite elliptical cylinders using the method of ordered multiple interactions," 5. Adams, R. J., B. A. Davis, and G. S. Brown, 6. Davis, B. A., "Propagation and scattering of waves by terrain features," 7. Poggio, A. J. and E. K. Miller, "Integral equation solutions of three dimensional scattering problems," 8. Marx, E., 9. Kleinman, R. E. and P. A. Martin, "On single integral equations for the transmission problem in acoustics," 10. Glisson, A. W., "An integral equation for electromagnetic scattering from homogeneous dielectric bodies," 11. Morita, N., N. Kumagai, and J. R. Mautz, 12. Adams, R. J., "R. J. and G. S. Brown. Stabilisation procedure for electric field integral equation," 13. Adams, R. J. and B. A. Davis, 14. Mitzner, K. M., "An integral equation approach to scattering from a body of finite conductivity," 15. Wang, ``Limits, "Limits and validity of the impedance boundary condition on penetrable surfaces," 16. Harrington, R. F., 17. West, J. C., "Low-grazing scattering from breaking water waves using an impedance boundary mm/gtd approach," |

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