Abstract
Efficient evaluation of partial inductance is an important computational stage in standard and FFT-accelerated partial element equivalent circuit (PEEC) methods and related volume-integral formulations. This work characterizes Gaussian quadrature (GQ) for partial-inductance evaluation between uniform cuboid cells on regular grids, where interactions are specified by relative displacements, to establish accuracy and evaluation-cost baselines and guidance for GQ order selection. The study considers systematically varied cuboid dimensions and relative displacements over a benchmark domain with the longest cuboid dimension fixed to 1 m, allowing results to be transferred to other physical dimensions through scaling. GQ accuracy is assessed against high-accuracy closed-form reference values evaluated using variable-precision arithmetic, while evaluation costs are characterized separately. The results establish the dependence of maximum absolute relative error and evaluation cost on separation distance, quadrature order, cell dimensions, and relative-displacement direction. Distance-dependent switching criteria are established for selecting the lowest GQ order that satisfies a prescribed accuracy requirement, with transverse cell dimensions providing an additional refinement. The resulting characterization provides a baseline for GQ-based partial-inductance evaluation and a practical basis for selecting the evaluation order according to accuracy and cost requirements.