On Parallel Sparse LU Factorization: Supernodal Left-Looking Multi-Stage Algorithm - Karasenko, Ivan I.; Gumalevskii, Roman V.; Rakitskiy, Anton A. (2023 IEEE 24th International Conference of Young Professionals in Electron Devices and Materials (EDM), 2023)
Solution of sparse systems of linear equations by direct methods is widely used in applied problems related to engineering and computational science. Such methods are based on matrix decomposition into the product of triangular factors. Computation of factors (factorization) is the most expensive part of direct methods. In this article we consider main principles of sparse LU decomposition method and describe algorithmic and implementation features allowing to achieve high performance on modern shared memory multi-processors architectures. Elimination tree is discussed as a tool for evaluating order of execution and extracting data dependencies in the scope of parallel computations. This paper considers supernodal approach as a key point to exploit efficiency of BLAS Level-3 and LAPACK routines in sparse LU decomposition. Left-looking multi-stage parallel algorithm is proposed to achieve high level of concurrency during factorization. This algorithm aims to improve computational task granularity and load balance at the top of elimination tree structure.