Power grid transient simulation in linear time based on transmission-line-modeling alternating-direction-implicit method

The soaring clocking frequency and integration density demand robust and stable power delivery to support tens of millions of transistors switching. To ensure the design quality of power delivery, extensive transient power grid simulations need to be performed during design process. However, the traditional circuit simulation engines are not scaled as well as the complexity of power delivery, as a result, it often takes a long runtime and huge memory requirement to simulate a medium size power grid circuit. We develop and present a new efficient transient simulation algorithm for power distribution. The proposed algorithm, TLM-ADI (transmission-line-modeling alternatingdirection-implicit), first models the power delivery structure as transmission line mesh structure, then solves the transient MNA matrices by the alternating-direction-implicit method. The proposed algorithm, with linear runtime and memory requirement, is also unconditionally stable which ensures that the time-step is not limited by any stability requirement. Extensive experimental results show that the proposed algorithm is not only orders of magnitude faster than SPICE but also extremely accurate.