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DOE OSTI · 1648916

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

Joshipura, Muktaka·Seal, Sudip K.
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Abstract

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.

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BibTeXRIS

Joshipura, Muktaka, Seal, Sudip K.. 2020-08-01. Optimizing the Accelerated Recursive Doubling Algorithm for Block Tridiagonal Systems of Equations. https://doi.org/10.2172/1648916

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