We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains (Ciraolo et al. in J Comput Phys 246:78–95, 2013) where the index of refraction is not required to be constant at infinity. The approach is based on the minimization of an integral functional, which arises from an integral formulation of the radiation condition at infinity. In this paper, we implement a Fourier–Chebyshev collocation method to study some convergence properties of the numerical algorithm; in particular, we give numerical evidence of some convergence estimates available in the literature (Ciraolo in Helmholtz equation in unbounded domains: some convergence results for a constrained optimization problem, 2013) and study numerically the minimization problem at low and mid-high frequencies. Numerical examples in some relevant cases are also shown.

Ciraolo, G., Gargano, F., Sciacca, V. (2015). A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains. COMPUTATIONAL AND APPLIED MATHEMATICS, 34(3), 1035-1055 [10.1007/s40314-014-0164-5].

A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains

CIRAOLO, Giulio;GARGANO, Francesco;SCIACCA, Vincenzo
2015-01-01

Abstract

We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains (Ciraolo et al. in J Comput Phys 246:78–95, 2013) where the index of refraction is not required to be constant at infinity. The approach is based on the minimization of an integral functional, which arises from an integral formulation of the radiation condition at infinity. In this paper, we implement a Fourier–Chebyshev collocation method to study some convergence properties of the numerical algorithm; in particular, we give numerical evidence of some convergence estimates available in the literature (Ciraolo in Helmholtz equation in unbounded domains: some convergence results for a constrained optimization problem, 2013) and study numerically the minimization problem at low and mid-high frequencies. Numerical examples in some relevant cases are also shown.
2015
http://www.springer.com/birkhauser/mathematics/journal/40314
Ciraolo, G., Gargano, F., Sciacca, V. (2015). A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains. COMPUTATIONAL AND APPLIED MATHEMATICS, 34(3), 1035-1055 [10.1007/s40314-014-0164-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/148960
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