Nonlinear Integral Equations in Modeling and Simulation of Electromagnetic Fields

Nonlinear integral equations serve as vital tools for creating electromagnetic field models of compound media systems. The Nystrom method serves as a numerical technique that applies quadrature rules to integral equation discretization for efficient solution of nonlinear electromagnetic field problems. A system of nonlinear algebraic equations results from converting integral problems using this approach which allows both accurate solutions and computational efficiency. The feature extraction process involving electromagnetic field data requires the Wavelet Transform which enables scientists to perform multi-resolution analyses and detect effective frequency components. The combination of Nystrom method with wavelet and feature extraction applications provides accurate solutions for use in wave propagation along with plasma physics and nonlinear optics applications. This method proves itself as a new computational alternative to finite element or boundary element methods because it produces better precision alongside enhanced efficiency. The performance of the Nystrom method in large-scale electromagnetic simulations requires additional research to develop adaptive strategies for quadrature methods.