Fast poisson solver preconditioned method for robust power grid analysis

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 become 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 advantage of analytical formulation of power grids this analytical preconditioner can be considered as sparse approximate inverse technique. By combining this analytical preconditioner with robust conjugate gradient method, we demonstrate that this approach is totally robust for extremely large scale power grid simulations. Experimental results have shown that iterations of our proposed method will hardly increase with grid size increasing once the pads density 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.