On the preconditioner of conjugate gradient method — A power grid simulation perspective

Abstract

Preconditioned Conjugate Gradient (PCG) method has been demonstrated to be effective in solving large-scale linear systems for sparse and symmetric positive definite matrices. One critical problem in PCG is to design a good preconditioner, which can significantly reduce the runtime while keeping memory usage efficient. Universal preconditioners are simple and easy to construct, but their effectiveness is highly problem-dependent. On the other hand, domain-specific preconditioners that explore the underlying physical meaning of the matrices usually work better, but are difficult to design. In this paper, we study the problem in the context of power grid simulation, and develop a novel preconditioner based on the power grid structure through simple circuit simulations. Experimental results show 43% reduction in the number of iterations and 23% speedup over existing universal preconditioners.