Application of the wavelets in 2D and 3D scattering or radiation problems

Abstract

Wavelets technique is applied for solving of 2D and 3D Dirichlet, Neumann and mix boundary problems. The developed method utilizes Haar or linear Battle-Lemarie wavelets functions and Fredholm integral equations (-or a system of the Fredholm integral equations) of fist kind with smooth or singular kernels and developed new method of "prolonged" boundary conditions. The results of the wavelet technique's using are illustrated by calculations of the scattering pattern by dielectric (-or perfect conducting) cylinder with complicated cross sections, ellipsoid of revolution, perfect conducting screens, single and dual-reflector antennas (both kD = I and kD >> 1 regions). The problems of accuracy, choosing auxiliary surfaces are discussed.