Fast Poisson solver preconditioned method for robust power grid analysis
Jianlei Yang, Yici Cai, Qiang Zhou, Jin Shi · 2011
Robust and efficient algorithms for power grid analysis are crucial for both VLSI design and optimization. Due to the increasing size of power grids IR drop analysis has be-come more computationally challenging both in runtime and memory consumption. This work presents a fast Poisson solver preconditioned method for unstructured power grid with unideal boundary conditions. In fact, by taking the ad-vantage of analytical formulation of power grids this analyt-ical preconditioner can be considered as sparse approximate inverse technique. By combining this analytical precondi-tioner with robust conjugate gradient method, we demon-strate that this approach is totally robust for extremely large scale power grid simulations. Experimental result-s have shown that iterations of our proposed method will hardly increase with grid size increasing once the pads den-sity and the range of metal resistances value distribution have been decided. We demonstrated that this approach solves an unstructured power grid with 2.56M nodes in only 1/3 iterations of classical ICCG solver, and achieves almost 20X speedups over the classical ICCG solver on runtime.