Performance of the Generalized Minimum Residual (GMRES) Iterative Solution for the Magnetic Field Integral Equation

[1] The paper discusses a generalized minimum residual (GMRES) iterative solution of the magnetic field integral equation (MFIE) applied to frequency domain scattering problems at medium and high frequencies. First, the performance of the original MFIE is studied, for the perfectly electrically conducting (PEC) sphere. It is shown that the residual error and the solution error do not correlate with each other. Whereas the solution error has already reached a limiting value or even increases, the residual error continues to decrease very fast, typically exponentially. Second, the MFIE is combined with the normal projection of the primary integral equation for the surface magnetic field. Such a technique does not increase the computational complexity of the MFIE. At the same time, it gives a termination criterion for GMRES iterations since the residual error of the combined equation has a typical saturation behavior. In the saturation zone, the residual error and the solution error have approximately the same small value (a typical relative RMS error for the sphere is 1%). A very similar saturation behavior of the residual error has been observed for other tested PEC scatterers including a cube, a cylinder, and a sphere with one segment cut off (the so-called cat eye) at different frequencies. of the generalized minimum residual (GMRES) iterative solution for the magnetic field integral equation,