IX - Discrete sources method in electromagnetic theory

Abstract

This chapter introduces the basic concepts of the discrete sources method (DSM) for solving electromagnetic scattering problems. In the acoustic case, the electromagnetic scattering problem reduces to the approximation problem of the boundary value of the incident field in the “L2”-norm. The technical aspect of the acoustic case is not repeated. Analysis is mainly concentrated on the construction of convergent approximations using the fundamental theorem of discrete approximation. For the impedance boundary-value problem, a somewhat different approach called the “D-matrix” method is presented, as the matrix of the corresponding linear system of equations is dissipative. Also, the dissipativity, the convergence of the approximate solution and the solvability of the linear system of equations using the conservation law of energy is established. Special attention is paid to the discrete sources method with distributed vector multipoles. The mathematical foundation of the method is accompanied by the results of computer simulations. The chapter also discusses the numerical experiments including comparison with other methods and scattering analysis of concave particles, and clusters of particles.