Accelerated Partial Inductance Evaluation via Cubic Spline Interpolation for the PEEC Method

The partial element equivalent circuit (PEEC) method provides a valuable solution of the Maxwell's equations in both the frequency and time domain. The computation of volume interaction integrals, also if performed in closed form, can be very time-consuming for large problems in which the storage of partial matrices is prohibitive. Iterative solvers allow to overcome this limitation by computing on the fly only matrix rows at each iteration step. For this reason, it is required a fast computation of the partial elements even under quasi-static hypothesis. In this work, an effective methodology for the interpolation in space of the partial inductances required by the PEEC method is developed. The proposed computation is performed through the cubic spline interpolation method, that, under the hypothesis of cubic meshed regions, guarantees always a significant speed-up without loss of the accuracy.