One- and two-dimensional scattering analysis using a fast numerical method

Abstract

Most integral equations of the first kind are ill posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number. Solving this system may be difficult or impossible. Since many problems in one-dimensional (1D) and 2D scattering from perfectly conducting bodies can be modelled by linear Fredholm integral equations of the first kind, the main focus of this study is to present a fast numerical method for solving them. This method is based on vector forms for representation of triangular functions. By using this approach, solving the first kind integral equation reduces to solving a linear system of algebraic equations. To construct this system, the method uses sampling of functions. Hence, the calculations are performed very quickly. Its other advantages are the low cost of setting up the equations without applying any projection method such as collocation, Galerkin, etc; setting up a linear system of algebraic equations of appropriate condition number and good accuracy. To show the computational efficiency of this approach, some practical 1D and 2D scatterers are analysed by it.