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Application of a complete radiation boundary condition for the Helmholtz equation in locally perturbed waveguides. (English) Zbl 1428.78021

Summary: This paper deals with an application of a complete radiation boundary condition (CRBC) for the Helmholtz equation in locally perturbed waveguides. The CRBC, one of efficient high-order absorbing boundary conditions, has been analyzed in straight waveguides in [T. Hagstrom and S. Kim, Numer. Math. 141, No. 4, 917–966 (2019; Zbl 1412.65187)]. In this paper, we apply CRBC to the Helmholtz equation posed in locally perturbed waveguides and establish the well-posedness of the problem and convergence of CRBC approximate solutions. The new CRBC proposed in this paper improves the one studied in [loc. cit.] in two aspects. The first one is that the new CRBC involves more damping parameters with the same computational cost as that of CRBC in [loc. cit.], which results in 50% smaller reflection errors. The second one is that the new CRBC takes a Neumann terminal condition of three term recurrence relations of auxiliary variables instead of a Dirichlet terminal condition used in [loc. cit.] so that it can treat cutoff modes effectively. Finally, we present numerical experiments illustrating the convergence theory.

MSC:

78A50 Antennas, waveguides in optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

Citations:

Zbl 1412.65187

Software:

deal.ii
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References:

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