On Parallel Sparse LU Factorization: Supernodal Left-Looking Multi-Stage Algorithm

Solution of sparse systems of linear equations by direct methods is widely used in applied problems related to engineering and computational science. Such methods are based on matrix decomposition into the product of triangular factors. Computation of factors (factorization) is the most expensive pa...

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Vydáno v:2023 IEEE 24th International Conference of Young Professionals in Electron Devices and Materials (EDM) s. 1890 - 1894
Hlavní autoři: Karasenko, Ivan I., Gumalevskii, Roman V., Rakitskiy, Anton A.
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 29.06.2023
Témata:
Concurrent computing
elimination tree
Feature extraction
Gaussian elimination
Linear systems
Memory architecture
Memory management
parallel computing
parallel sparse direct solvers
Scientific computing
sparse LU decomposition
Sparse matrices
ISSN:2325-419X
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Shrnutí:Solution of sparse systems of linear equations by direct methods is widely used in applied problems related to engineering and computational science. Such methods are based on matrix decomposition into the product of triangular factors. Computation of factors (factorization) is the most expensive part of direct methods. In this article we consider main principles of sparse LU decomposition method and describe algorithmic and implementation features allowing to achieve high performance on modern shared memory multi-processors architectures. Elimination tree is discussed as a tool for evaluating order of execution and extracting data dependencies in the scope of parallel computations. This paper considers supernodal approach as a key point to exploit efficiency of BLAS Level-3 and LAPACK routines in sparse LU decomposition. Left-looking multi-stage parallel algorithm is proposed to achieve high level of concurrency during factorization. This algorithm aims to improve computational task granularity and load balance at the top of elimination tree structure.
ISSN:2325-419X
DOI:10.1109/EDM58354.2023.10225050