The power grid transient simulation in linear time based on 3D alternating-direction-implicit method

The rising power consumption and clock frequency of VLSI technology demand robust and stable power delivery. Extensive transient simulations on large scale power delivery structures are required to analyze power delivery fluctuation caused by dynamic IR-, and Ldi/dt drop as well as package and on-chip resonance. This paper develops a novel and efficient transient simulation algorithm for the power distribution networks. The 3D TLM-ADI (Transmission-Line-Modeling Alternating-Direction-Implicit) method, first models the power delivery structure as a three dimensional transmission line shunt node structure and transfers those equations to the Telegraph equation. Finally, we solve it by the alternating direction implicit method. The 3D TLM-ADI method, with linear runtime and memory requirement, is also unconditionally stable which ensures that the time-steps are not limited by any stability requirement. Numerical experimental results show that the 3D TLM-ADI method is not only over 300,000 times faster than SPICE but also extremely memory saving and accurate.