Friendly fast poisson solver preconditioning technique for 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 paper presents a Fast Poisson Solver (FPS) preconditioned method for unstructured power grids with unideal boundary conditions. Unstructured power grids are transformed to structured grids, which can be modeled as Poisson blocks by analytic formulation. The analytic formulation of transformed structured grids is adopted as an analytic preconditioner for original unstructured grids, in which the analytic preconditioner can be considered as a sparse approximate inverse technique. By combining this analytic preconditioner with robust conjugate gradient method, we demonstrate that this approach is totally robust for extremely large scale power grid simulations. Theoretical proof and experimental results show that iterations of our proposed method will hardly increase with the increasing of grid size as long as the pads density and the distribution range of metal conductance value have been decided. We demonstrate that the run efficiency of our approach is much higher than classical incomplete Cholesky factorization preconditioned conjugate gradient solver and random walk-based hybrid solver.