Sparse direct solution on parallel computers.

*(English)*Zbl 06987052
Al-Baali, Mehiddin (ed.) et al., Numerical analysis and optimization. Selected papers based on the presentations at the 4th international conference, NAO-IV, Muscat, Oman, January 2–5, 2017. Cham: Springer (ISBN 978-3-319-90025-4/hbk; 978-3-319-90026-1/ebook). Springer Proceedings in Mathematics & Statistics 235, 67-98 (2018).

This paper discusses designing algorithms and software for solving sparse systems using direct methods on parallel computers. After discussing the solution of large sparse symmetric positive definite systems, the authors use a runtime system to express and execute a DAG (directed acyclic graphs)-based Cholesky factorization. The runtime system plays the role of a software layer between the application and the architecture and handles the management of task dependencies as well as task scheduling and maintaining data coherency. The software is implemented using the OpenMP standard and the runtime systems StarPU and PaRSEC. The performance is demonstrated on a multicore architecture. The case of symmetric indefinite matrix is also considered. For highly unsymmetrical systems, a completely different approach based on developing a parallel version of a Markowitz threshold ordering is used where some of the algorithmic challenges involved are discussed. Finally, using a hybrid direct-iterative solver that combines the better of the two approaches that enables the solution of even larger problems in parallel is described.

For the entire collection see [Zbl 1402.65005].

For the entire collection see [Zbl 1402.65005].

Reviewer: T. C. Mohan (Chennai)

##### MSC:

65Y05 | Parallel numerical computation |