State-of-the-Art Sparse Direct Solvers

Abstract

In this chapter we will give an insight into the development of modern sparse elimination methods. These are driven by a preprocessing phase based on combinatorial algorithms which improve diagonal dominance, reduce fill-in, and improve concurrency to allow for parallel treatment. Moreover, these methods detect dense submatrices which can be handled by dense matrix kernels based on multithreaded level-3 BLAS. We will demonstrate how recent improvements in developing advanced direct solution methods have enabled speeding up parallel circuit simulation without sacrificing accuracy.