An Iterative Scheme for Solving a Lippmann-Schwinger Nonlinear Integral Equation by the Galerkin Method

The purpose of this study is to solve a nonlinear integral equation describing the propagation of electromagnetic waves in a body located in free space. The boundary-value problem for the Helmholtz equation is reduced to the solution of the integral equation. An iterative method of creating a nonlinear medium inside a body with a dielectric structure is constructed. The problem is solved numerically. The size of the matrix obtained in the calculation exceeds 30 000 elements. The internal convergence of the iterative method is shown. The plots illustrating the field distribution in the nonlinear body are presented. The numerical method has been proposed and implemented.

Automated summary

The purpose of this study is to solve a nonlinear integral equation describing the propagation of electromagnetic waves in a body located in free space. The boundary-value problem for the Helmholtz equation is reduced to the solution of the integral equation. An iterative method of creating a nonlinear medium inside a body with a dielectric structure is constructed. The problem is solved numerically, and the internal convergence of the iterative method is shown. The plots illustrating the field distribution in the nonlinear body are presented.