Efficient implementation of conduction modes for modelling skin effect

We present an efficient approach for computing the impedance matrix of a system of conductors, in the quasi-magneto static domain, suitable for frequency analysis well above the skin effect threshold. The method is based on the current decomposition in terms of conduction modes (CM) rather than the widespread filament decomposition. The memory gains using CM were already known to be large. Our main contribution is to improve the efficiency so as to achieve performance ratios that are significantly better than those resulting from using filament decomposition for the same accuracy. As the frequency increases the improvements become noteworthy. These gains result from optimally rendering two dimensional integration approaches involving the Coulomb Green function in combination with linear combinations of exponentials to the particular landscape of each of the constituent terms.