Computation of waveguide scattering matrix near thresholds. Issue 8 (11th June 2017)

• Record Type: Journal Article
• Authors: Kabardov, M. M.; Plamenevskii, B. A.; Sharkova, N. M.
• Is Part Of: Applicable analysis. Volume 96:Issue 8(2017)
• Page Start: 1295
• Page End: 1302
• Publication Date: 2017-06-11
• Subjects: Helmholtz equation -- scattering matrix -- threshold -- augmented wave space; 65M99 -- 65N99 -- 65Z99; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1188287
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : A waveguide occupies infinite strip with one or several narrows on a two-dimensional (2D) plane and is governed by the Helmholtz equation with Dirichlet boundary condition. On the waveguide continuous spectrum, which coincides with a half-axis, a scattering matrix is defined. At each point of the continuous spectrum this matrix has finite size, which changes at thresholds. The thresholds form a sequence of positive numbers increasing to infinity. Approximate calculation of the scattering matrix in a threshold vicinity requires special treatment. We discuss and compare two methods of numerical approximation to the scattering matrix near a threshold.