A vectorized multiscale compressed decomposition-based solver for partial element equivalent circuit method

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 that can be analyzed in both the time and frequency domains. The enforcement of Kirchhoff laws to the equivalent circuit may easily result into a very large set of equations whose solution can be extremely time-consuming.In this paper, we propose a vectorized version, over the frequency sweep, of the adaptive cross approximation algorithm. Furthermore, the multiscale block decomposition is applied to the PEEC method, powered by a vectorization strategy and an efficient management of the random access memory. It is found that the proposed use of vectorization and compression techniques in the framework of the multiscale block decomposition results in a significant computational speedup of the frequency-domain analysis of PEEC models. The efficiency and accuracy of the proposed method are demonstrated through its application to two pertinent problems. Copyright (c) 2014 John Wiley & Sons, Ltd.