TY - JOUR

T1 - A method for approximate computation of waveguide scattering matrices

AU - Plamenevskii, Boris A.

AU - Poretskii, Aleksandr S.

AU - Sarafanov, Oleg V.

N1 - Funding Information: This work was supported by the Russian Science Foundation (grant no. 17-11-01126). Publisher Copyright: © 2020 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/6

Y1 - 2020/6

N2 - A waveguide occupies a domain in an (n + 1)-dimensional Euclidean space which has several cylindrical outlets to infinity. Three classes of waveguides are considered: those of quantum theory, of electromagnetic theory, and of elasticity theory, described respectively by the Helmholtz operator, the Maxwell system, and the system of equations for an elastic medium. It is assumed that the coefficients of all problems stabilize exponentially at infinity, to functions that are independent of the axial variable in the corresponding cylindrical outlet. Each row of the scattering matrix is given approximately by minimizing a quadratic functional. This functional is constructed by use of an elliptic boundary value problem in a bounded domain obtained by cutting the cylindrical outlets of the waveguide at some distance R. The existence and uniqueness of a solution is proved for each of the three types of waveguides. The minimizers converge exponentially fast as functions of R, as R → ∞, to rows of the scattering matrix.

AB - A waveguide occupies a domain in an (n + 1)-dimensional Euclidean space which has several cylindrical outlets to infinity. Three classes of waveguides are considered: those of quantum theory, of electromagnetic theory, and of elasticity theory, described respectively by the Helmholtz operator, the Maxwell system, and the system of equations for an elastic medium. It is assumed that the coefficients of all problems stabilize exponentially at infinity, to functions that are independent of the axial variable in the corresponding cylindrical outlet. Each row of the scattering matrix is given approximately by minimizing a quadratic functional. This functional is constructed by use of an elliptic boundary value problem in a bounded domain obtained by cutting the cylindrical outlets of the waveguide at some distance R. The existence and uniqueness of a solution is proved for each of the three types of waveguides. The minimizers converge exponentially fast as functions of R, as R → ∞, to rows of the scattering matrix.

KW - Helmholtz operator

KW - Maxwell system

KW - Scattering matrix

KW - Theory of elasticity

KW - Waveguide

UR - http://www.scopus.com/inward/record.url?scp=85092364853&partnerID=8YFLogxK

U2 - 10.1070/RM9850

DO - 10.1070/RM9850

M3 - Article

AN - SCOPUS:85092364853

VL - 75

SP - 509

JO - Russian Mathematical Surveys

JF - Russian Mathematical Surveys

SN - 0036-0279

IS - 3

ER -