Virtual screening: a step towards a sparse partial inductance matrix

We extend the partial inductance concept by replacing the magnetic interaction between open filaments i and j by that between filament j and a (finite) closed loop, formed by connecting the endpoints of a filament pair (i-i/sup l/). The secondary filament i/sup l/ is constructed by radial projection of filament i onto a cylindrical shell around filament j. We show that, although individual partial inductance values are modified, the inductive behaviour of the full circuit is invariant. Mutual inductances of distant filaments are particularly reduced, because the far field of a conductor loop falls off much faster than that of a single filament. Therefore, it is expected that subsequent removal of such transformed off-diagonal elements from the partial inductance matrix has less effect on the overall inductive properties, so our method provides a tool to enhance robustness under matrix sparsification. We call our method "virtual screening", because the screening filaments (i/sup l/) are not physically present. Symmetry of the inductance matrix is presented for orthogonal networks only. We also present an extension of our method to a more general class of shells. This allows a detailed comparison of the virtual screening method and the "potential shift-truncate method", introduced with spherical equipotential shells (B. Krauter and L.T. Pileggi, 1995) and extended to ellipsoidal equipotential shells (M. Beattie et al., 1998). We find strong similarities, but also differences. An interesting result is the fact that the virtual screening method with tubular shells applied to orthogonal networks can be interpreted as a generalization of the potential shift-truncate method to non-equipotential shells, which also implies that preservation of stability is guaranteed.