  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.
