A Fast SIE Solver With Cut Set Analysis and Terminals as Supernodes for Interconnects

A magnetic quasi-static (MQS) surface integral equation (SIE) formulation based on the cut set analysis (CSA) is proposed to extract parameters of interconnects in packages. The surface impedance approximation is used to describe the surface current caused by skin effect at high frequencies. To accurately model arbitrarily shaped structures, triangle meshes are selected to discretize surfaces of interconnects in the proposed formulation. After physically interpreting the discretized matrix equation as a circuit, the CSA is tailored to carefully apply the charge conservation condition. Triangles on each terminal are bounded together as a supernode to enforce currents flowing into/out interconnects. In addition, an efficient preconditioner and the precorrected Fast Fourier Transform (pFFT) are used to accelerate the convergence and matrix-vector product. Four numerical examples were carried out to validate the effectiveness by comparing it with the industrial solver. Our results show that the proposed formulation is accurate, efficient, and flexible to model complex interconnects at high frequencies.