Features of Asymptotic Method Implementation for Electromagnetic Scattering Problem in Material with Chaotically Distributed Inclusions

The electromagnetic (EM) scattering problem on a set of randomly distributed particles in a homogeneous material is solved by an analytical-numerical asymptotic method. This is possible due to the assumption of small particles. The analytical part of the solution consists of deriving an approximate formula for a system of linear algebraic equations (SLAE) with respect to the values of an unknown auxiliary function. The numerical solution of the auxiliary SLAE allows us to solve the initial scattering problem and to derive an explicit formula for the magnetic permeability of the resulting inhomogeneous material. The software implementation features of the proposed method are described in detail, including heterogeneous region geometry simulation, complexity, and computation time for individual key formulas. Optimal method selection for direct problem solving in terms of computational resources is an essential prerequisite for the successful solution of the inverse problem, since heuristic algorithms require multiple solutions to direct problems with different input parameters. Numerical data indicate the possibility of obtaining a more diverse distribution of magnetic permeability in the resulting heterogeneous material compared to regular and chaotic methods of particle embedding.