Analysis of shielding enclosures using the multilevel plane wave time domain algorithm

While both integral and differential equation based time domain solvers have been known to the CEM community for many years, the latter are usually chosen for analyzing EMI/EMC problems. This is due to the fact that classical time domain integral equation solvers, such as the marching-on-in-time (MOT) method, suffer from a high computational complexity. Indeed, the memory requirements and the computational cost associated with the MOT method scale as O(N/sub S//sup 2/) and O(N/sub T/N/sub S//sup 2/), where N/sub T/ is the duration of the simulation in terms of time steps and N/sub S/ is the number of spatial unknowns. To reduce these costs, the multilevel plane wave time domain algorithm (MLPWTD) was introduced previously; this algorithm reduces the memory requirements and computational cost to O(N/sub T/N/sub S/) and O(N/sub T/N/sub S/ log/sup 2/ N/sub S/), respectively. This paper illustrates the application of the MLPWTD solver to the analysis of radiation characteristics of wires and perfect electrically conducting (PEC) modules on motherboard configurations that reside in shielding enclosures. Numerical results are presented that demonstrate the efficacy and applicability of the algorithm to the analysis of complex structures.