  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).
