In this chapter we will give an insight into modern sparse elimination meth-
ods. 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 multi-threaded level–3 BLAS. We will
demonstrate for problems arising from circuit simulation how the improvement in
recent years have advanced direct solution methods significantly.
Parallel Algorithms in Computational Science&Engineering - Parallelism as Enabling Technology in CSE Applications