Adaptive-cross-approximation-based acceleration of transient analysis of quasi-static partial element equivalent circuits

A new formulation of the partial element equivalent circuit (PEEC) method is presented, which is well suited to be combined with compression and matrix-vector product acceleration techniques. In particular, taking advantage of the rank-deficiency of the magnetic and electric field couplings, the adaptive cross approximation (ACA) technique is firstly, adopted to compress PEEC interaction matrices, namely partial inductances and coefficients of potential matrices. Differently from the use of ACA in conjunction with the method of moments, in this study, magnetic and electric field couplings are kept distinct, thus allowing to efficiently compress both magnetic and electric field interaction matrices. Secondly, the compressed matrices are used to accelerate the transient analysis of PEEC circuits. Indeed, Kirchoff voltage and current laws are enforced to PEEC circuits so that matrix-vector products involving the interaction matrices can be significantly accelerated in virtue of their compression, thus leading to very good speed-ups when using iterative solvers like the generalised method of residuals algorithm. Numerical results demonstrate the validity, accuracy and performance of the proposed approach in terms of both memory usage saving and transient analysis speed-up.