Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis for Propagation and Radiation Problems

TL;DR

This paper introduces a simple, flexible algorithm for finding complex roots and poles of analytic functions over arbitrary regions, using phase analysis and adaptive meshing, with applications in electromagnetic wave propagation.

Contribution

It presents a novel, intuitive method based on phase analysis and discretized Cauchy's principle for efficiently locating roots and poles in complex regions.

Findings

Effective for various analytic functions and shapes

Supports adaptive mesh for improved accuracy

Validated with numerical tests on electromagnetic structures

Abstract

A flexible and effective algorithm for complex roots and poles finding is presented. A wide class of analytic functions can be analyzed, and any arbitrarily shaped search region can be considered. The method is very simple and intuitive. It is based on sampling a function at the nodes of a regular mesh, and on the analysis of the function phase. As a result, a set of candidate regions is created and then the roots/poles are verified using a discretized Cauchy's argument principle. The accuracy of the results can be improved by the application of a self-adaptive mesh. The effectiveness of the presented technique is supported by numerical tests involving different types of structures, where electromagnetic waves are guided and radiated. The results are verified, and the computational efficiency of the method is examined.