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

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.
Authors:
; ;
Publication Date:
OSTI Identifier:
22230775
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 246; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; BOUNDARY CONDITIONS; CONVERGENCE; EQUATIONS; FUNCTIONALS; INTEGRALS; MATHEMATICAL SOLUTIONS; MINIMIZATION; PERTURBATION THEORY; REFRACTIVE INDEX