Hierarchical block multi-color ordering: a new parallel ordering method for vectorization and parallelization of the sparse triangular solver in the ICCG method
Takeshi Iwashita, Senxi Li, Takeshi Fukaya · CCF Transactions on High Performance Computing · 2020
Abstract In this paper, we propose a new parallel ordering method to vectorize and parallelize the sparse triangular solver, which is called hierarchical block multi-color ordering. In this method, the parallel forward and backward substitutions can be vectorized while preserving the advantages of block multi-color ordering, that is, fast convergence and fewer thread synchronizations. To evaluate the proposed method in a parallel ICCG (Incomplete Cholesky Conjugate Gradient) solver, numerical tests were conducted using seven test matrices on three types of computational nodes. The numerical results indicate that the proposed method outperforms the conventional block and nodal multi-color ordering methods in 18 out of 21 test cases, which confirms the effectiveness of the method.