Evaluation of Integrals Related to the Magnetic Field Integral Equation Over Bilinear Quadrilaterals

Abstract

We present a new method for computing the impedance matrix elements in the method of moments for geometries described by bilinear quadrilaterals (BQ) and for higher-order basis functions (HOBF). Our method is restricted to the Magnetic Field Integral Equation (MFIE) and focuses on the self-elements of the impedance matrix and elements for which the observation point (OP) is near the integration BQ. The method is based on the simple idea of analytical integration along one of the BQ's parameters and numerical integration along the remaining one. For the singular (or nearly so) part of the integral, we show through analysis and examples that our method can provide precision up to fifteen significant digits (SD).