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Application of Collocation Method During the Solution of Boundary-Value Problem for an Open Elliptical Dielectric Waveguide


A. V. Danilov, V. V. Ermoshin, A. V. Nazarov

Collocation method for open elliptical dielectric waveguide is considered. The statement of the boundary electrodynamic problem for this guiding structure is presented. Correlation theory is used, to the choice of collocation points. Test of the program to search for solutions of dispersion equation was verified by limiting process to open circular dielectric waveguide and comparison with results which was obtained by the adaptive collocation method. It’s shown that uniform distribution of collocation nodes provided fast convergence of root dispersion equation, but this distribution is not provided satisfactory fulfillment of boundary condition at all cross-section of structure. Mismatch of tangential components of electromagnetic field at boundary is fewer if the correlation methodic to choice distribution of collocation nodes is used and convergence solution of dispersion equation is improved. Carried out researches allow to draw a conclusion that methodic to choice distribution of collocation points based on the correlation theory methods application is availability during the electro dynamical analysis of the open guiding structures.
May 29, 2020

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