Application of wavelets on the interval to the analysis of thin-wire antennas and scatterers

An analysis of thin-wire antennas and scatterers using orthogonal wavelets on interval [0,1] is presented. The thin-wire version of the electric-field integral equation (EFLE) is solved by the hybrid wavelet expansion and boundary element method (HWBM). Maps between the curved solution domains and the interval [0,1] are established by using the geometrical representation of the boundary element method (BEM). By virtue of these maps, bases over the curved solution domains are derived from orthogonal wavelets on [0,1] that are used to expand the unknown current over the wires. The utilization of the wavelets on [0,1] circumvents the difficulties in the application of the wavelets on the real line to finite-domain problems and has no periodicity constraint to the unknown function that is usually imposed by the periodic wavelets. Numerical examples are provided for a variety of thin-wire antennas and scatterers.