An FFT-based approach to including non-ideal ground planes in a fast 3-D inductance extraction program

It is noted that including non-ideal ground planes in 3-D inductance extraction programs is computationally expensive, as the ground plane must be finely discretized to ensure that the current distribution throughout the plane is accurately computed. This makes standard volume-element algorithms unsuitable because they require n ² computation time and storage, where n is the number of filaments into which the ground plane is discretized. In the present work it is noted that, by using a preconditioned iterative method combined with an FFT (fast Fourier transform)-based algorithm to compute the iterates, one can reduce the computation time to effectively n log n, and substantially reduce required storage. Experimental results are presented which show that using the FFT-based approach is more than an order of magnitude faster than computing the iterates explicitly, even on problems with as few as a thousand volume-filaments. The FFT-based algorithm is compared with a GMRES (generalized minimal residual)-style algorithm