Comments on "Fast direct solution of method of moments linear system

In the above-named work a new algorithm is presented for direct (non-iterative) frequency domain method of moments (MoM) calculations based on block-wise compression of the impedance matrix. The storage requirements and computational complexity of the algorithm are claimed to be N^3/2 and N², respectively, if N is the number of unknowns for a MoM surface discretization that is fixed with respect to the wavelength. A more rigorous analysis, explicitly using the asymptotic expression for the number of degrees of freedom (DoF) in the interaction between groups of scatterers, is presented here, showing that this should be N^3/2log N and N²log² N, respectively. The complexity analysis applies to problems that can be formulated as a surface integral equation (SIE) on surfaces in or between homogeneous media, such as a ship or an airplane. It does not apply to volume discretization MoM or multilayer problems. The results presented here are also relevant for block-wise compression methods using iterative solvers, since the compressed impedance matrix is the same. Consequently, the above complexity analysis applies to very large problems, well beyond the reach of even the largest existent computers. For moderate size problems, the "measured" complexity is lower.