A hierarchical wavefront method for LU-SGS. (15th September 2022)

• Record Type: Journal Article
• Authors: Komatsu, Kazuhiko; Hougi, Yuta; Sato, Masayuki; Kobayashi, Hiroaki
• Is Part Of: Computers & fluids. Volume 245(2022)
• Publication Date: 2022-09-15
• Subjects: LU-SGS -- Wavefront -- Hyperplane -- Multi-core vector processors; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2022.105572
• Languages: English
• ISSNs: 0045-7930

Abstract

Abstract: The lower–upper Symmetric-Gauss–Seidel (LU-SGS) method is one of typical implicit methods, especially for an application that requires high convergence and accuracy. However, the data-dependencies among grid points in the LU-SGS method prevent parallelization and vectorization, both of which are important for modern computing systems. As modern computing systems consist of multiple nodes, each of which is equipped with multi-core processors with a vector processing capability, to take advantages of these computing systems, both parallel computing and vector computing are mandatory. This paper proposes a hierarchical wavefront method that combines the wavefront and the hyperplane methods in order to achieve both parallelization and vectorization of the LU-SGS method with block-structured meshes. The evaluation results show that the hierarchical wavefront method is 4.9 times faster than the conventional wavefront method and 24.2 times faster than the hyperplane method. Highlights: Efficient processing of the lower–upper Symmetric-Gauss–Seidel method for modern computing systems. Hierarchical parallel processing and vector processing. Theoretical analysis for the domain decomposition.