  Large scale circuit simulation, such as power delivery network analysis, has become increasingly challenge in the VLSI design verification flow. Power delivery network can be simulated by both SPICE-type circuit-based model and eletromagnetics-based model when full-wave accuracy is desired. In the early time of the time domain finite element simulation for integrated circuit, the modes having the highest eigenvalues supported by the numerical system will be excited. Because of the band limited source, after the early time, the modes having a resonance frequency well beyond the input frequency band will die down, and all physically important high-order modes and DC mode will show up and become dominant. Among these modes, the DC mode is the last one to show up. Although the convergence criterion is not applied on the DC mode, the existence of DC mode in the field solution will deteriorate the convergence rate of the first several high order modes. Therefore, this paper first analyzed the mathematic characteristics of the DC mode and proposed a rigorous and fast solution to extract the DC mode from the numerical system in order to speed up the convergence rate. Experimental results demonstrated the robustness and superior performance of this method. 
Fast and Rigorous DC Solution in Finite Element Method for Integrated   Circuit Analysis