A parallel linear system solver for circuit simulation problems

Abstract

This paper presents a parallel mixed direct/iterative method for solving linear systems Ax = b arising from circuit simulation. The systems are solved by a block LU factorization with an iterative method for the Schur complement. The Schur complement is a small and rather dense matrix. Direct LU decomposition of the Schur complement takes too much time in order to achieve reasonable speedup results. Our iterative method for the Schur complement is often much faster than the direct LU approach. Moreover, the iterative method is better parallelizable. This results in a fast sequential and well parallelizable method.