X - Null-field method in electromagnetic theory

Abstract

This chapter discusses the analysis of electromagnetic scattering using the null-field method (NFM) with discrete sources. The chapter focuses on the exterior and the transmission boundary-value problems. It begins by constructing projection methods for the general null-field equations. Next, it presents the conventional null-field method with discrete sources for solving the exterior Maxwell problem. The efficiency of the conventional null-field method, in comparison to other projection methods, is investigated from a computational point of view. The chapter discusses the use of Tikhonov regularization and presents some numerical results. It considers the conventional null-field method for solving the transmission problem. For the sake of completeness the different formulations of the method that serves as input for our computer simulations is listed. The chapter then proceeds to establishing the expression of the transition matrix and investigate general constraints of the transition matrix such as symmetry and unitarity. It will demonstrate that the use of distributed sources rather than a localized source improves the symmetry of the transition matrix. Finally, it presents some computer simulations. These include scattering by particles with large size parameters, particles with extreme geometries, cubs, ellipsoids, and rough particles.