Abstract
This paper discusses parallelization of the computationally intensive numerical factorization phase of sparse Cholesky factorization on shared memory systems. We propose and compare two parallel algorithms based on the multifrontal method. Both algorithms are implemented in a task-based fashion employing dynamic load balance. The first algorithm associates OpenMP tasks with the nodes of an elimination tree and relies on the OpenMP scheduler. The second algorithm employs a concurrent priority queue to implement balancing. Experimental results on symmetric positive definite matrices from the University of Florida Sparse Matrix Collection show that our implementation is comparable to MUMPS and Intel MKL PARDISO in terms of performance and scaling efficiency on shared memory systems.
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Acknowledgments
The study was partially supported by the RFBR, research project No. 14-01-3145514 and by the grant 02.B.49.21.0003 of The Ministry of education and science of the Russian Federation.
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Lebedev, S., Akhmedzhanov, D., Kozinov, E., Meyerov, I., Pirova, A., Sysoyev, A. (2015). Dynamic Parallelization Strategies for Multifrontal Sparse Cholesky Factorization. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2015. Lecture Notes in Computer Science(), vol 9251. Springer, Cham. https://doi.org/10.1007/978-3-319-21909-7_7
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DOI: https://doi.org/10.1007/978-3-319-21909-7_7
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