### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 1035-1055 |

Numero di pagine | 21 |

Rivista | Computational and Applied Mathematics |

Volume | 34 |

Stato di pubblicazione | Published - 2015 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

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Risultato della ricerca: Article

*Computational and Applied Mathematics*, vol. 34, pagg. 1035-1055.

}

TY - JOUR

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

AU - Sciacca, Vincenzo

AU - Gargano, Francesco

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 - Helmholtz equation; Minimization of integral functionals; Spectral methods; Transparent boundary conditions; Computational Mathematics; Applied Mathematics

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 -