Optimizing the Accelerated Recursive Doubling Algorithm for Block Tridiagonal Systems of Equations

Technical Report · Sat Aug 01 04:00:00 EDT 2020

DOI:https://doi.org/10.2172/1648916· OSTI ID:1648916

Joshipura, Muktaka ^[1]; Seal, Sudip K. ^[1]

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1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

The need to solve block tridiagonal systems with hundreds or thousands of right-hand sides for the same block tridiagonal matrix is common in a variety of disciplines. To meet this need, the Accelerated Recursive Doubling Algorithm was developed. After a right-hand side independent phase, the algorithm allows for the quick, online calculation of solutions for different right-hand sides. In this work, we present methods to optimize the Accelerated Recursive Doubling Algorithm in memory usage and computation time in a hybrid parallelization model. The right-hand side independent phase of the naïve implementation takes ≥ 11/3 the amount of memory required to store the tridiagonal matrix, while our implementation reduces the fraction to ≈ 5/3 . The right-hand side dependent phase of the naïve implementation takes ≥ 6 times the amount of memory required to store the right-hand side, while our implementation reduces the fraction to ≈ 3. The computation time for the independent phase is reduced to ≈ 2/3 times that of the naïve implementation, while the computation time for the dependent phase is reduced to ≈ 5/9 . With increasing numbers of shared-memory threads q on every distributed processing element, we have O(q) theoretical speedup.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1648916
• Report Number(s): ORNL/LTR-2020/40
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING