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

Journal Article · Thu Aug 01 00:00:00 EDT 2013 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2013.03.047· OSTI ID:22230775

Ciraolo, Giulio; Gargano, Francesco; Sciacca, Vincenzo

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.

• OSTI ID: 22230775
• Journal Information: Journal of Computational Physics, Vol. 246; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
APPROXIMATIONS
BOUNDARY CONDITIONS
CONVERGENCE
EQUATIONS
FUNCTIONALS
INTEGRALS
MATHEMATICAL SOLUTIONS
MINIMIZATION
PERTURBATION THEORY
REFRACTIVE INDEX