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Persistent URL http://purl.org/net/epubs/work/66493
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Record Id 66493
Title Achieving bit compatibility in sparse direct solvers (corrected)
Abstract In some applications that rely on the numerical solution of linear systems it can be important that the computed results are reproducible. When designing a parallel sparse direct solver the goal of effciency potentially con icts with that of achieving bit-by-bit identical results. This paper focuses on two approaches to achieving bit compatibility independently of the number of processors the solver is run on. The first, use of a fixed summation order, is demonstrated as a practical solution for multifrontal solvers. This is due to the low number of summands involved in the multifrontal assembly operations. The second is based on using extended precision. An analysis is presented that demonstrates that the use of extended precision alone is insu cient to ensure bit compatibility because of rounding discontinuities. An algorithm is presented to detect possibly problematic summations, allowing alternate approaches to be used only when needed. The large number of summands encountered in supernodal algorithms makes them suitable for extended precision summation. A multifrontal solver and a supernodal solver from the HSL mathematical software library are used to explore the performance and feasibility of the two approaches on linear systems arising from practical applications.
Organisation STFC , SCI-COMP , SCI-COMP-CM
Keywords parallel , multifrontal , sparse linear systems , direct solver , supernodal , bit compatible
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Preprints RAL-P-2012-005-corr. 2013. RAL-P-2012-005-corr.pdf 2013