Localizing Sparse Direct Solvers for Circuit Simulations

We report results obtained using a preconditioned fast iterative solver to model electrostatic circuit problems. The method of moments is used to discretize integral equation-based formulations of the underlying circuit problem. A compressed representation of the system matrix is obtained using the fast multipole method, and the resulting linear system is solved using a preconditioned iterative method. Preconditioners are constructed from a class of localization-based sparse direct solvers, and numerical performance is reported for realistic applications. The impact of incorporating a multilevel matrix binormalization method is also examined, and resulting tradeoffs are discussed.