Convergent Galerkin MoM Solution for 2-D H-Scattering from Screens

Abstract

A two-dimensional Neumann problem solution is obtained in the first-kind hypersingular integral equation (HSIE) formulation with the aid of the Galerkin method of moments (GMoM) on the complete orthogonal basis. Convergence and uniqueness of the GMoM solution to the HSIE is proved in the Hilbert space of square integrable functions (L 2 ) for screens with smooth boundary. The exact relationship between actual and residual errors is also obtained, which permits one to calculate an actual error by integrating residual error along the boundary of a scatterer. The condition number increasing problem is solved by making use of proper preconditioning.