Fast block-iterative domain decomposition algorithm for IR drop analysis in large power grid

Due to the extremely large sizes of power grids, IR drop analysis has become a computationally challenging problem both in terms of runtime and memory usage. In order to design scalable algorithms to handle ever increasing power-grid sizes, the most promising approach is to use a ¿divide-and-conquer¿ strategy such as domain decomposition. Such an approach not only decomposes a large problem into manageable sub-problems, it also naturally allow a parallel processing solution for further speedup in computation time. As a result, a power-grid analysis algorithm based upon the traditional domain decomposition method has been reported. Unfortunately, the method in has strong limitation on the size of the interfaces between the sub-problems and therefore severely limits its capability in solving very large problems. In this paper, we present a block-iterative domain-decomposition algorithm which effectively combines the advantages of direct solvers and iterative methods. With a carefully chosen domain decomposition strategy, our approach does not suffer from the difficulties. While the algorithm fails to analyze a power grid of 4 millions nodes, our algorithm solves a power grid of 42 millions nodes accurately in 1.5 hours.