Two iterative methods for solving the volumetric singular equation for a nonlinear diffraction problem in a semi-infinite rectangular waveguide

Abstract

Background. The purpose of the study is to construct a nonlinear electromagnetic field inside the waveguide. We assume that the body is located in a semi-infinite rectangular waveguide and that an electromagnetic field propagates inside the body. Iterative algorithms based on solving a volumetric nonlinear singular integral equation are proposed and described. Numerical results are presented. Materials and methods. The boundary value problem for the system of Maxwell's equations is reduced to a volume singular integral equation. An iterative method for creating a nonlinear medium inside a body with a dielectric structure is constructed. Results. The problem is solved numerically. The size of the matrix obtained in the calculation is about 15,000 elements. The internal convergence of the iterative method is shown. Graphs are shown illustrating the field distribution inside a nonlinear body. Conclusions. A numerical method for finding wave numbers that make it possible to create a nonlinear field is proposed and implemented.

Keywords

• boundary value problem
• maxwell’s system of equations
• nonlinear volumetric singular integral equation
• numerical method
• collocation method