A hierarchical wavefront method for LU-SGS

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.