A load balancing parallel algorithm for solving large-scale tridiagonal linear systems

Min Tian; Shan Qiao; Junjie Wang; Wei Du

doi:10.1117/12.2626438

21 December 2021 A load balancing parallel algorithm for solving large-scale tridiagonal linear systems

Min Tian, Shan Qiao, Junjie Wang, Wei Du

Proceedings Volume 12156, International Conference on Algorithms, High Performance Computing, and Artificial Intelligence (AHPCAI 2021); 1215602 (2021) https://doi.org/10.1117/12.2626438
Event: International Conference on Algorithms, High Performance Computing, and Artificial Intelligence (AHPCAI 2021), 2021, Sanya, China

Abstract

Solving large-scale sparse linear systems is a critical problem in scientific and engineering computing. Partial differential equations can solve problems in many fields. They can be transformed into large-scale linear systems with a series of methods, and the parallel solution of tridiagonal linear systems is one of them. The solution of linear systems is very time-consuming in most of the problems, accounting for more than half of the total time. Load balancing can reduce process time for waiting and improves computational efficiency, and it is the focus of many algorithms. The article is based on Stone's proposed recursive doubling algorithm, an improved algorithm for solving tridiagonal linear systems using the full-recursive-doubling communication model and the Möbiu transform. The improved algorithm can calculate the million-dimensional linear systems. Numerical experiments show that compared with ordinary parallel algorithms, the improved algorithm shows up to 2x improvement than the original version, and some results even show up to 3x. In addition, the load-balancing performance has been greatly improved, and the time difference of the processes is 1/7 of the original version. The improved algorithm has a good load balancing, and the running time of each process is not much different, avoiding process waiting and resource wastage.

Citation Download Citation

Min Tian, Shan Qiao, Junjie Wang, and Wei Du "A load balancing parallel algorithm for solving large-scale tridiagonal linear systems", Proc. SPIE 12156, International Conference on Algorithms, High Performance Computing, and Artificial Intelligence (AHPCAI 2021), 1215602 (21 December 2021); https://doi.org/10.1117/12.2626438

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KEYWORDS

Computing systems

Partial differential equations

Algorithm development

Chromium

Computer simulations

Data processing

Matrices

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