The Galerkin Method Based on Triangular Sinusoidal Currents for Electromagnetic Scattering by Arbitrarily Conducting Surfaces

The Galerkin moment method based on triangular sinusoidal currents is proposed. Its basis function is a modified version of Rao-Wilton-Glisson (RWG) vector basis function when the meshed triangles are modeled by bilinear interpolated parametric surfaces under particular oblique linear local coordinates. Because of the adoption of sinusoidal factor in the current basis function, the fourfold impedance integrals reduce into double integrals, while the double potential integrals reduce into only one dimensional integrals. The integrand of the remaining double impedance integral involves complex exponential integrals, which does not bring any computation benefit to the total quadrature time for the moment. However, the remaining one-dimensional potential integrals make it rather effective to do scattering modal analysis or near-zone energy flow analysis after solving the matrix equation. In either scene, there is a requirement for frequent calculation of the near- or far-zone fields of complex surface objects. The proposed method is applied to scattering problems of conducting square plate and sphere illuminated by a plane wave. The computed surface currents agree very well with results via RWG Galerkin method, and the method also has a little superior convergence rate.