A Cutting-Edge Parallel Solver for Scalable Power Grid Analysis Using Nested Domain Decomposition

As transistor scaling approaches sub-5 nm technologies, power distribution networks (PDNs) in integrated circuits have grown increasingly complex, with billions to trillions of nodes. Simultaneously, reduced noise margins and increased power density necessitate more accurate and efficient power grid analysis. Traditional methods for solving large-scale PDNs, especially those requiring the solution of sparse linear systems, face significant challenges due to high computational costs. Although domain decomposition methods (DDM) allow for efficient parallel computation, the size of the dense global Schur complement grows excessively large as the number of partitions increases, limiting scalability and imposing substantial computational burdens. This paper introduces an efficient parallel nested domain decomposition solver that incorporates a parallel Schur complement computation strategy and intermediate Schur complement to address these challenges. Experimental results demonstrate that by introducing an intermediate Schur complement, the size of the global Schur complement is significantly reduced, achieving an average $1.70 \times$ speedup in computation, which results in a $1.30 \times$ speedup for the entire solver compared to the conventional DDM parallel solver.