A numerical method for the solution of electromagnetic wave diffraction problems on perfectly conducting screens
The author reconsiders the electromagnetic diffraction problems connected with perfectly conducting screens and presents a numerical method in which the key step consists of the approximation by Gaussian functions. The solution of the problem is reduced, as usual, to the determination of the density of surface current, say \(J(x)\), induced on the screen at a set of appropriately chosen surface nodes, namely \(\{x^{(j)}\}\). To this end he approximates the current densities in question by Gaussian functions concentrated on the planes tangent to the screen at the node points, namely \[ J(x)\Omega(x)\approx \sum_j J^{(j)} \varphi_j(x) \omega_j(x). \] Here \(\Omega(x)\) denotes the delta-function concentrated on the screen while \(\omega_j(x)\) stands for the delta-function concentrated on the plane tangent to the screen at the point \(x^{(j)}\). As to \(\varphi_j(x)\), it is defined by \[ \varphi_j(x)= {1\over\pi D}\exp\Biggl(-{|x- x^{(j)}|\over Dh^2}\Biggr), \] where \(D\) is the dimension of the problem (\(D= 2\) or \(D=3\)) while \(h\) is the distance between the consecutive nodes.
scientific article; zbMATH DE number 1763681