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DOI 10.5286/raltr.2018012
Persistent URL http://purl.org/net/epubs/work/40018255
Record Status Checked
Record Id 40018255
Title A new sparse symmetric indefinite solver using a posteriori threshold pivoting
Abstract The factorization of sparse symmetric indefinite systems is particularly challenging since pivoting is required to maintain stability of the factorization. Pivoting techniques generally offer limited parallelism and are associated with significant data movement hindering the scalability of these methods. Variants of the Threshold Partial Pivoting (TPP) algorithm for example have been often used because of its numerical robustness but standard implementations exhibit poor parallel performance. On the other hand, some methods trade stability for performance on parallel architectures such as the Supernode BunchKaufman (SBK) used in the PARDISO solver. In this case, however, the factors obtained might not be used to accurately compute the solution of the system. For this reason we have designed a task-based LDLT factorization algorithm based on a new pivoting strategy called A Posteriori Threshold Pivoting (APTP) that is much more suitable for modern multicore architectures and has the same numerical robustness as the TPP strategy. We implemented our algorithm in a new version of the SPRAL Sparse Symmetric Indefinite Direct Solver (SSIDS) which initially supported GPU-only factorization. We have used OpenMP 4 task features to implement a multifrontal algorithm with dense factorizations using the novel APTP, and we show that it performs favourably compared to the state-of-the-art solvers HSL MA86, HSL MA97 and PARDISO both in terms of performance on a multicore machine and in terms of numerical robustness. Finally we show that this new solver is able to make use of GPU devices for accelerating the factorization on heterogeneous architectures.
Organisation STFC , SCI-COMP
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Licence Information: Creative Commons Attribution 4.0 International (CC BY 4.0)
Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2018-012. STFC, 2018. RAL-TR-2018-012.pdf 2018