TY - JOUR

T1 - A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains

AU - Sciacca, Vincenzo

AU - Gargano, Francesco

AU - Ciraolo, Giulio

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Applied Mathematics

KW - Computational Mathematics

KW - Helmholtz equation

KW - Minimization of integral functionals

KW - Spectral methods

KW - Transparent boundary conditions

KW - Applied Mathematics

KW - Computational Mathematics

KW - Helmholtz equation

KW - Minimization of integral functionals

KW - Spectral methods

KW - Transparent boundary conditions

UR - http://hdl.handle.net/10447/148960

UR - http://www.springer.com/birkhauser/mathematics/journal/40314

M3 - Article

VL - 34

SP - 1035

EP - 1055

JO - Computational and Applied Mathematics

JF - Computational and Applied Mathematics

SN - 0101-8205

ER -