Hierarchical Block Multi-Color Ordering：ICCG方法中稀疏三角形解的矢量化和网格化并行排序方法
Hierarchical Block Multi-Color Ordering: A New Parallel Ordering Method for Vectorization and Parallelization of the Sparse Triangular Solver in the ICCG Method
摘要：
本文提出了一种新的并行排序方法来实现稀疏三角形求解器的矢量化和并行化，称为层次块多色排序。在该方法中，并行的向前和向后替换可以被矢量化，同时保留块多色排序的优点，即快速收敛和较少的线程同步。为了在并行ICCG（不完全乔列斯基共轭梯度）求解器中评估所提出的方法，使用五个测试矩阵在三种类型的计算节点上进行了数值测试。数值结果表明，在15个测试用例中，有13个测试用例的性能优于传统的分块和节点多色排序方法，验证了该方法的有效性。
英文摘要：
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 five 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 13 out of 15 test cases, which confirms the effectiveness of the method.
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