# State-of-The-Art Sparse Direct Solvers

## TL;DR

This paper reviews modern sparse direct solvers, highlighting advances in preprocessing, parallelization, and dense submatrix handling that significantly improve efficiency for circuit simulation problems.

## Contribution

It provides an overview of recent developments in sparse elimination methods, emphasizing preprocessing, parallelism, and dense submatrix detection techniques.

## Key findings

- Enhanced preprocessing improves diagonal dominance and reduces fill-in.
- Parallel processing accelerates sparse elimination.
- Detection of dense submatrices enables efficient dense kernel computations.

## Abstract

In this chapter we will give an insight into 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 for problems arising from circuit simulation, how the improvements in recent years have advanced direct solution methods significantly.