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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}
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 -