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New Parallel Sparse Direct Solvers for Multicore Architectures
Scientific Computing Department, STFC Rutherford Appleton Laboratory, Harwell Oxford, OX11 0QX, UK
* Author to whom correspondence should be addressed.
Received: 9 August 2013; in revised form: 16 October 2013 / Accepted: 21 October 2013 / Published: 1 November 2013
Abstract: At the heart of many computations in science and engineering lies the need to efficiently and accurately solve large sparse linear systems of equations. Direct methods are frequently the method of choice because of their robustness, accuracy and potential for use as black-box solvers. In the last few years, there have been many new developments, and a number of new modern parallel general-purpose sparse solvers have been written for inclusion within the HSL mathematical software library. In this paper, we introduce and briefly review these solvers for symmetric sparse systems. We describe the algorithms used, highlight key features (including bit-compatibility and out-of-core working) and then, using problems arising from a range of practical applications, we illustrate and compare their performances. We demonstrate that modern direct solvers are able to accurately solve systems of order 106 in less than 3 minutes on a 16-core machine.
Keywords: sparse matrices; sparse linear systems; symmetric systems; direct solvers; multifrontal; supernodal; bit-compatibility; Fortran 95; OpenMP; parallel
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MDPI and ACS Style
Hogg, J.; Scott, J. New Parallel Sparse Direct Solvers for Multicore Architectures. Algorithms 2013, 6, 702-725.
Hogg J, Scott J. New Parallel Sparse Direct Solvers for Multicore Architectures. Algorithms. 2013; 6(4):702-725.
Hogg, Jonathan; Scott, Jennifer. 2013. "New Parallel Sparse Direct Solvers for Multicore Architectures." Algorithms 6, no. 4: 702-725.