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Resonant Scattering and Generation of WavesNumerical Experiments

Resonant Scattering and Generation of Waves: Numerical Experiments [In this chapter, we present a selection of results from our fund of numerical experiments. We methodically focus on the approach based upon the numerical solution of the system (3.17) of nonlinear Hammerstein integral equations, as described in Chaps. 3 and 6. The finite element method from Chap. 5 has also been implemented and successfully tested (Angermann, Yatsyk, Int J Electromagn Waves Electron Syst 13(12), 15–30, 2008, [1]) (Hoff, Numerische Simulation der Oberwellengeneration in nichtlinearen elektromagnetischen Diffraktionsproblemen. Diploma thesis (supervisor: L. Angermann), Department of Mathematics, Clausthal University of Technology, 2014, [2]). Since the obtained approximations to the solution of the boundary value problem (1.66) were largely comparable to the numerical results for the system (3.17) and thus did not provide any other (or even new) findings, we have omitted a similarly detailed description and discussion of the finite element results. Nevertheless, we have included a few comments on these results.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Resonant Scattering and Generation of WavesNumerical Experiments

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing AG, part of Springer Nature 2019
ISBN
978-3-319-96300-6
Pages
123 –186
DOI
10.1007/978-3-319-96301-3_7
Publisher site
See Chapter on Publisher Site

Abstract

[In this chapter, we present a selection of results from our fund of numerical experiments. We methodically focus on the approach based upon the numerical solution of the system (3.17) of nonlinear Hammerstein integral equations, as described in Chaps. 3 and 6. The finite element method from Chap. 5 has also been implemented and successfully tested (Angermann, Yatsyk, Int J Electromagn Waves Electron Syst 13(12), 15–30, 2008, [1]) (Hoff, Numerische Simulation der Oberwellengeneration in nichtlinearen elektromagnetischen Diffraktionsproblemen. Diploma thesis (supervisor: L. Angermann), Department of Mathematics, Clausthal University of Technology, 2014, [2]). Since the obtained approximations to the solution of the boundary value problem (1.66) were largely comparable to the numerical results for the system (3.17) and thus did not provide any other (or even new) findings, we have omitted a similarly detailed description and discussion of the finite element results. Nevertheless, we have included a few comments on these results.]

Published: Jul 27, 2018

Keywords: Nonlinear Hammerstein Integral Equations; Nonlinear Dielectric Permittivity; Eigen Fields; Preset Field; Incident Field

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