Boundary-value problems for the Helmholtz equation and their discrete mathematical models

Yu. V. Gandel'

Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, Tome 36 (2010), pp. 36-49.

Résumé

We consider boundary-value problems of mathematical diffraction theory and discuss the possibility of reducing them to boundary hypersingular integral equations and solving them numerically. The analytic technique of parametric representations of pseudodifferential and integral operators and the numerical method of discrete singularities are essentially used. We discuss the reasoning in applying this approach to constructing mathematical models of wave diffraction problems and solving them numerically.

Bibliographie

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[30] Gandel Yu. V., Kononenko A. S., “Mathematical model of a cavity gyrotrons on the basis of hypersingular integral equations”, 10th Int. Conf. on Math. Methods in Electromagnetic Theory, Conf. Proc. (Dnipropetrovsk, Ukraine, September 14–17, 2004), 559–561

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[33] Kononenko A. S., Gandel Yu. V., “Theoretical and numerical investigations of TE and TM modes in coaxial cavity gyrotron”, Proc. of the 36th European Microwave Conf., Manchester, UK, 2006, 1115–1118

[34] Kononenko A. S., Gandel Yu. V., “Mathematical model of ohmic losses in a coaxial cavity gyrotron with a corrugated insert”, Proc. 6th Int. Symp. on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves, Kharkiv, 2007, 292–294

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