Keywords:-
Article Content:-
Abstract
Article introduces an extension of the approximating functions method, a particular case of the finite element method (FEM) with interpolating functions in the form of Lagrange polynomials of a special form, to solve electrodynamics problems in a planar waveguide with constant polarization in the spatial-temporal domain using the Volterra integral equation method. The main goal of the article is to expand the area of applicability of this method to three-dimensional problems in a planar waveguide with constant polarization, as well as to obtain general interpolation expressions in analytical form, which will be used to construct a system of nonlinear equations for solving specific problems.
References:-
References
Y. Shifman, Y. Leviatan, "On the use of spatio-temporal multiresolution analysis in method of moments solutions of transient electromagnetic scattering," IEEE Trans. on Antennas and Propagation, vol.49, pp. 1123, 2001.
M. R. Gomez, A. Salinas, A. R. Bretones, "Time-Domain Integral Equation Methods For Transient Analysis," IEEE Antennas and Propagation Magazine, vol. 34, pp. 15-24, 1992.
A. G. Nerukh, N. K. Sakhnenko, T. Benson, P. Sewell, Non-stationary electromagnetics (Singapore: Pan Stanford Publishing Ltd., 2013).
A. Nerukh, and T. Benson, Non-Stationary Electromagnetics: An Integral Equations Approach (2nd ed.) (Jenny Stanford Publishing, 2018), https://doi.org/10.1201/9780429027734.
J. N. Reddy, An Introduction to the Finite Element Method (Third ed. (McGraw-Hill, 2005).
J. Jin, The Finite Element Method in Electromagnetics (NY: Wiley 1993).
J. F. Lee, R. Lee, A. Cangellaris, "Time-Domain Finite-Element Methods," IEEE Trans. Antennas Propagat, vol. 45, pp. 430–442, 1997.
D. Anish, A. Dasgupta, G. Sarkar, "A new set of orthogonal functions and its application to the analysis of dynamic systems," Journal of the Franklin Institute, vol. 343, pp. 1–26, 2006.
K. Maleknejad, H. Almasieh, M. Roodaki, "Triangular functions (TF) method for the solution of nonlinear Volterra–Fredholm integral equations," Commun Nonlinear Sci Numer Simulat, vol. 10, pp. 10-12, 2010.
D. Zolotariov, A. Nerukh, "Extension of the approximation functions method for 2D nonlinear Volterra integral equations," Applied Radioelectronics, vol. 10, no. 1, pp. 39- 44, 2011.
A. Nerukh, D. Zolotariov and T. Benson, "The approximating functions method for nonlinear Volterra integral equations," Opt Quant Electron, vol. 47, pp. 2565–2575, 2015, https://doi.org/10.1007/s11082-015-0141-2.
D. Zolotariov, "The New Modification Of The Approximating Functions Method For Cloud Computing," International Journal Of Mathematics And Computer Research, vol. 9, no. 9, pp. 2376-2380, 2021, https://doi.org/10.47191/ijmcr/v9i9.01.
D. Zolotariov, "The mechanism for creation of event-driven applications based on Wolfram Mathematica and Apache Kafka," Innovative Technologies and Scientific Solutions for Industries, vol. 15, no. 1, pp. 53–58, 2021, https://doi.org/10.30837/ITSSI.2021.15.053.
D. Zolotariov, "The platform for creation of event-driven applications based on Wolfram Mathematica and Apache Kafka," Innovative Technologies and Scientific Solutions for Industries, vol. 16, no. 2, pp. 12–18, 2021, https://doi.org/10.30837/ITSSI.2021.16.012.
D. Zolotariov, A. Nerukh, "The study of application of approximating functions method for problems in a planar waveguide with non-magnetic media with losses," (publishing)
Yu.A. Brychkov, O. I. Marichev, A.P. Prudnikov, Tables of Indefinite Integrals: A Handbook (Russia: Fizmatlit, 2003) (In Russian).
Downloads
Citation Tools
Most read articles by the same author(s)
- Denis Zolotariov, About One Approach to Deploying an API Gateway Development Environment , International Journal Of Mathematics And Computer Research: Vol 10 No 4 (2022): VOLUME 10 ISSUE 04