Vector problem of electromagnetic wave diffraction by a system of inhomogeneous volume bodies, thin screens, and wire antennas

References

• Durand M. Layer potentials and boundary value problems for the helmholtz equation in the complement of a thin obstacle. Math. Methods Appl. Sci. 1983;5:389–421.
   Google Scholar
• Colton D, Kress R. Integral equation method in scattering theory. New York (NY): Wiley; 1984.
   Google Scholar
• Costabel M, Stephan E. A direct boundary integral equation method for transmission problems. J. Math. Anal. Appl. 1985;106:367–413.
   Web of Science ®Google Scholar
• Stephan EP. Boundary integral equations for screen problems in ℝ3. Integral Equ. Potential Theory. 1987;10:236–257.
   Web of Science ®Google Scholar
• Costabel M. Boundary integral operators on Lipschitz domains: elementary results. SIAM J. Math. Anal. 1988;19:613–626.
   Web of Science ®Google Scholar
• Kress R. Linear integral equations. Vol. 82, Applied mathematical sciences. New York: Springer Verlag New York Inc.; 1989.
   Google Scholar
• Kirsch A, Lechleiter A. The operator equations of Lippmann-Schwinger type for acoustic and electromagnetic scattering problems in L\textsubscript{2}. Appl. Anal. 2010;88:807–830.
   Web of Science ®Google Scholar
• Costabel M, Darrigrand E, Kone E. Volume and surface integral equations for electromagnetic scattering by a dielectric body. J. Comput. Appl. Math. 2010;234:1817–1825.
   Web of Science ®Google Scholar
• Ilinskii AS, Kravtsov VV, Sveshnikov AG. Matematicheskie modeli elektrodinamiki [Mathematical Models of Electrodynamics]. Moscow: Vysshaya Shkola; 1991.
   Google Scholar
• Ilinsky AS, Smirnov YuG. Electromagnetic wave diffraction by conducting screens. Utrecht: VPS; 1998.
   Google Scholar
• Samokhin AB. Integral equations and iteration methods in electromagnetic scattering. Utrecht: DeGruyter; 2001.
   Google Scholar
• Smirnov YuG. Convergence of the Galerkin methods for equation with elliptic operators on subspaces and solving the electric field equation. Comput. Math. Math. Phys. 2007;47:126–135.
   Google Scholar
• Valovik DV, Smirnov YG. Pseudodifferential operator method in a problem of the diffraction of an electromagnetic wave on a dielectric body. Differ. Equ. 2012;48:517–523.
   Web of Science ®Google Scholar
• Strishkov VA. Asymptotic correctness of the integral equations of electrodynamics in the thin-wire approximation. USSR Comput. Math. Math. Phys. 1989;29:90–93. doi:10.1016/0041-5553(89)90012-8.
   Web of Science ®Google Scholar
• Poljak D, Roje V. Finite element technique for solving time-domain Hallen integral equation. In: Tenth International Conference on Antennas and Propagation, Edinburgh, UK (Conf. Publ. No. 436). Vol. 1; 1997. doi:10.1049/cp:19970243.
   Google Scholar
• Kevanishvili GS. On the theory of Hallen integral equation. In: Proceedings of the 5th International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory DIPED - 2000, Tbilisi; 2000. doi:10.1109/DIPED.2000.889993
   Google Scholar
• Fikioris G, Wu TT. On the application of numerical methods to Hallen’s equation. Antennas Propag. 2001;49:383–392. doi:10.1109/8.918612.
   Web of Science ®Google Scholar
• Bogle A, Kempel L, Nyquist D. Conversion of MFIE for radiation and scattering by a slot in a PEC parallel-plate configuration to a Hallen equation. In: Antennas and Propagation Society International Symposium, Albuquerque, NM. 2006. doi:10.1109/APS.2006.1711222.
   Google Scholar
• Medvedik MYu, Smirnov YuG, Tsupak AA. Scalar problem of plane wave diffraction by a system of non-intersecting screens and inhomogeneous bodies. Comput. Math. Math. Phys. 2014;54:1280–1292.
   Web of Science ®Google Scholar
• Smirnov YuG. Tsupak AA. Method of integral equations in the scalar problem of diffraction on a system consisting of a "Soft" and a "Hard" screen and an inhomogeneous body. Differ. Equ. 2014;50:1150–1160.
   Web of Science ®Google Scholar
• Smirnov YuG, Tsupak AA. Integrodifferential equations of the vector problem of electromagnetic wave diffraction by a system of non-intersecting screens and inhomogeneous bodies. Adv. Math. Phys. 2015;2015:1–6. Article ID 945965. doi:10.1155/2015/945965.
   Web of Science ®Google Scholar
• Medvedik MY, Smirnov YG. Subhierarchical method for solving problems of diffraction of electromagnetic waves by a dielectric body in a rectangular waveguide. J. Commun. Technol. Electron. 2011;56:947–952.
   Web of Science ®Google Scholar
• Medvedik MY, Smirnov YG. Ellipticity of the electric field integral equation for absorbing media and the convergence of the Rao--Wilton--Glisson method. Comput. Math. Math. Phys. 2014;54:114–122.
   Web of Science ®Google Scholar
• Rao SM, Wilton DR, Glisson AW. Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antennas Propag. 1982;AP-30:409–418.
   Web of Science ®Google Scholar