The boundary-value problem for the transport equation with purely Compton scattering.
Anikonov, D.S., Konovalova, D.S. (2005)
Sibirskij Matematicheskij Zhurnal
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Anikonov, D.S., Konovalova, D.S. (2005)
Sibirskij Matematicheskij Zhurnal
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G. A. Viano (1985)
Recherche Coopérative sur Programme n°25
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Armin Lechleiter, Dinh-Liem Nguyen (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter....
Xavier Claeys, Ralf Hiptmair (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
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Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations...
Xavier Claeys, Ralf Hiptmair (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations...
A. Martin (1974)
Recherche Coopérative sur Programme n°25
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Richard Melrose, Maciej Zworski (1994)
Journées équations aux dérivées partielles
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V. Chiadò Piat, M. Codegone (2003)
RACSAM
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In this paper, we consider a family of scattering problems in perforated unbounded domains Ω. We assume that the perforation is contained in a bounded region and that the holes have a ?critical? size. We study the asymptotic behaviour of the outgoing solutions of the steady-state scattering problem and we prove that an extra term appears in the limit equation. Finally, we obtain convergence results for scattering frequencies and solutions.