Multiscale decomposition based analysis of PEEC models

The high level of integration has made the analysis and design of integrated circuits and packages increasingly challenging. Hence, there exists an urgent need to reduce the computational complexity of existing numerical methods. The integral equation based method known as the Partial Element Equivalent Circuit (PEEC) method naturally generates an equivalent circuit which can be analyzed in both the time and frequency domains. The enforcement of Kirchoff laws to the equivalent circuit can easily result into a very large set of equations whose solution can be extremely time consuming. In this paper, a new frequency-domain nodal analysis PEEC solver is proposed which is based on the adaptive cross approximation and recursive partitioned matrix inverse formula. The proposed approach provides a significant computational speedup, while preserving the accuracy. The efficiency of the proposed method is demonstrated through its application to a relevant interconnect problem.