An Improvement of Global Complex Roots and Poles Finding Algorithm for Propagation and Radiation Problems

An improvement of the recently developed global roots finding algorithm has been proposed. The modification allows to shorten the computational time by reducing the number of function calls. Moreover, both versions of the algorithms (standard and modified) have been tested for numerically defined functions obtained from spectral domain approach and field matching method. The tests have been performed for three simple microwave structures (open waveguides and conformal antenna resonator). The results have been verified and the increase of efficiency for the improved version of the algorithm has been confirmed.

[1]  Piotr Kowalczyk,et al.  Efficient Complex Root Tracing Algorithm for Propagation and Radiation Problems , 2017, IEEE Transactions on Antennas and Propagation.

[2]  Jerzy Mazur,et al.  An Analysis of Probe-Fed Rectangular Patch Antennas With Multilayer and Multipatch Configurations on Cylindrical Surfaces , 2014, IEEE Transactions on Antennas and Propagation.

[3]  Kin-Lu Wong,et al.  Analysis of a cylindrical-rectangular microstrip structure with an airgap , 1994 .

[4]  R. Lech Calculation of Resonance in Planar and Cylindrical Microstrip Structures Using a Hybrid Technique , 2018, IEEE Transactions on Antennas and Propagation.

[5]  Piotr Kowalczyk,et al.  On root finding algorithms for complex functions with branch cuts , 2017, J. Comput. Appl. Math..

[6]  L. Trefethen,et al.  Robust rational interpolation and least-squares , 2011 .

[7]  J. N. Lyness,et al.  A Numerical Method for Locating the Zeros of an Analytic Function , 1967 .

[8]  Elias N. Glytsis,et al.  Multilayer waveguides: efficient numerical analysis of general structures , 1992 .

[9]  Arnold Schönhage,et al.  The fundamental theorem of algebra in terms of computational complexity - preliminary report , 1982 .

[10]  W. Press Numerical recipes in Fortran 77 : the art of scientific computing : volume 1 of fortran numerical recipes , 1996 .

[11]  D. Owen Handbook of Mathematical Functions with Formulas , 1965 .

[12]  Piotr Kowalczyk,et al.  Propagation in the Open Cylindrical Guide of Arbitrary Cross Section With the Use of Field Matching Method , 2018, IEEE Transactions on Antennas and Propagation.

[13]  Wojciech Marynowski,et al.  An Analysis of Elliptical-Rectangular Multipatch Structure on Dielectric-Coated Confocal and Nonconfocal Elliptic Cylinders , 2015, IEEE Transactions on Antennas and Propagation.

[14]  James R. Pinkert,et al.  An Exact Method for Finding the Roots of a Complex Polynomial , 1976, TOMS.