Tutorial
(Tutorial is Free for All registered participants)

Resonance Phenomena in Electromagnetics:
Mathematical and Numerical Methods, Recent Results and Applications

(Yury SHESTOPALOV, University of Gävle, Sweden)

5 August 2018, 15:30-17:30 hrs (Robert Laidlaw I)

The tutorial provides a concise introduction into mathematical and numerical methods for the analysis of various resonance phenomena in electromagnetics of open structures. Correct mathematical statements and techniques are presented that enable rigorous proofs of the eixstence and analysis of distribution of resonance frequencies and wave propagation constants. A special attention is paid to determination and detailed investigation of complex resonance quantities and phenomena in lossy media. Waves in radially inhomogeneous nonlinear media are considered. The following basic structures are investigated: layered dielectric media in free space and waveguides, fibers and Goubau lines filled with inhomogeneous lossy or nonlinear media. Iteration methods are described that enable explicit calculations of resonance quantities. A review of most recent results is included. The tutorial gives a possibility to deepen and improve the knowledge in basic mathematical subjects relevant to the studies of resonance phenomena. Teaching is accompanied by the necessary calculations performed using MATLAB which will serve as a potential to gain additional skills of working with this computational platform. Layout and content of the tutorial require only basic knowledge in differential equations and complex analysis. The tutorial is supported by a compendium available online and many problems and project tasks to be solved for better learning. Mathematical and numerical methods and results are applied to the analysis of artificial and epsilon-near-zero media and metamaterials.

Yury SHESTOPALOV is now professor of Mathematics at the University of Gävle, Sweden. He accomplished complete university career from teaching assistant to professor and department head at Moscow State University (MSU), Karlstad University and University of Gävle (since 2013). Y. Shestopalov has been continuously teaching (since 1977) all university courses in mathematics. In 1992-1993 he created and then was head of the department of computer science at the MSU Kolmogorov Advanced Education and Science Centre (AESC)—The Kolmogorov School. Y. Shestopalov organized the teaching of computer science, programming, and foundations of applied mathematics, worked out programs and basic courses, textbooks, compendiums, and course materials. As a member of Board of Advisors and then of the Board of Directors Y. Shestopalov initiated the Faculty of Higher Pedagogical Education at MSU. His main scientific results and contributions are within the following areas: spectral theory of operators and its application in mathematical methods for electromagnetics; methods of solution to inverse problems and problems with uncertain data; wave propagation in nonlinear media and nonlinear operator equations; integral equations, partial differential equations; numerical methods, optimization, applied computer codes, software and program packages. Among his recent achievements are complete description of the spectrum of waves in a broad class of inhomogeneously filled waveguides and mathematical theory of inverse waveguide problems. Y. Shestopalov has authored and co-authored five books, also published in USA and UK, more than 60 articles in peer-reviewed journals and in total more than 200 scientific works. He supervised several PhD works; among his disciples there are active professors in mathematics, applied mathematics and electrical engineering. Y. Shestopalov performs international cooperation as visiting professor and coheads international research projects with several institutions in Sweden, USA, Japan, Germany, Finland, Russia, and Ukraine. Since 1977 Y. Shestopalov organized more than 20 and participated in more than 60 international conferences and symposia; he is Vice-Chairman of Progress in Electromagnetics Research Symposium and Programme Committee member of several URSI conferences.