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

PROJECT TITLE :

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

ABSTRACT:

A brand new formulation of the partial part equivalent circuit (PEEC) methodology is presented, that is like minded to be combined with compression and matrix–vector product acceleration techniques. In particular, cashing in on the rank-deficiency of the magnetic and electrical field couplings, the adaptive cross approximation (ACA) technique is firstly, adopted to compress PEEC interaction matrices, particularly partial inductances and coefficients of potential matrices. Differently from the utilization of ACA in conjunction with the method of moments, in this study, magnetic and electrical field couplings are kept distinct, so permitting to efficiently compress each 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 thus that matrix–vector merchandise involving the interaction matrices can be significantly accelerated in virtue of their compression, thus resulting in terribly good speed-ups when using iterative solvers like the generalised methodology 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.

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