Abstract
The Maxwell system is considered in a waveguide with perfectly conducting boundary having several cylindrical outlets to infinity. A minimizer of a quadratic functional serves as an approximation to a row of the scattering matrix. To construct such a functional, we solve an auxiliary boundary value problem in the bounded domain obtained by cutting off, at a distance R, the waveguide outlets to infinity. As R tends to infinity, the minimizer a(R, k) tends at exponential rate to the corresponding row of the scattering matrix.
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References
S. A. Nazarov and B. A. Plamenevsky, Elliptic Problems in Domains with Piecewise Smooth Boundaries, de Gruyter Expositions in Mathematics, vol. 13, Walter de Gruyter & Co., Berlin, 1994.
B. A. Plamenevskii and A. S. Poretskii, Algebra i Analiz, 25:1 (2013), 94–155; English transl.: St. Petersburg Math. J., 25:1 (2014), 63–104.
B. A. Plamenevskii and O. V. Sarafanov, Funkts. Anal. Prilozhen., 48:1 (2014), 61–72; English transl.: Functional Anal. Appl., 48:1 (2014), 49–58.
B. A. Plamenevskii, A. S. Poretskii, and O. V. Sarafanov, Algebra i Analiz, 26:1 (2014), 128–164; English transl.: St. Petersburg Math. J., 26:1 (2015), 91–116.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 49, No. 1, pp. 93–96, 2015
Original Russian Text Copyright © by B. A. Plamenevskii, A. S. Poretskii, and O. V. Sarafanov
The work was supported by grants of St. Petersburg University no. 11.38.666.2013 and RFBR no. 12-01-00247a.
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Plamenevskii, B.A., Poretskii, A.S. & Sarafanov, O.V. On computation of waveguide scattering matrices for the Maxwell system. Funct Anal Its Appl 49, 77–80 (2015). https://doi.org/10.1007/s10688-015-0088-x
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DOI: https://doi.org/10.1007/s10688-015-0088-x