We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.

Ciraolo, G., Gargano, F., & Sciacca, V. (2013). A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional. JOURNAL OF COMPUTATIONAL PHYSICS, 246, 78-95 [10.1016/j.jcp.2013.03.047].

A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

CIRAOLO, Giulio;GARGANO, Francesco;SCIACCA, Vincenzo
2013

Abstract

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.
Settore MAT/05 - Analisi Matematica
Settore MAT/07 - Fisica Matematica
http://www.sciencedirect.com/science/article/pii/S0021999113002258
Ciraolo, G., Gargano, F., & Sciacca, V. (2013). A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional. JOURNAL OF COMPUTATIONAL PHYSICS, 246, 78-95 [10.1016/j.jcp.2013.03.047].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/71623
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