计算机科学 ›› 2022, Vol. 49 ›› Issue (6): 108-118.doi: 10.11896/jsjkx.210300259
汪晋, 刘江
WANG Jin, LIU Jiang
摘要： 在科学计算和工程领域,大型稀疏线性方程组的求解非常常见,目前已经有许多迭代方法和预处理技术被用于求解这类方程。DILU预处理技术类似于ILU,是开源计算流体力学软件OpenFOAM中重要的预处理技术,但未在OpenFOAM以外的领域引起关注,目前也没有完整的GPU实现。比较了DILU和ILU预处理技术对稳定双共轭梯度法(BiCGStab)加速的效果,以及它们在构造预处理子上的开销,结果表明,DILU在加速效果上不逊于ILU且在稳定性上优于ILU。在GPU并行实现方面,DILU可以使用分层并行和无全局同步并行两种并行策略,详细讨论了DILU预处理技术在这两种策略下的实现方法,给出了相关的算法和参考代码,然后比较了在两种并行策略下DILU预处理技术的性能。数值实验结果表明,在实践中两种并行策略各有优劣,可以根据实际表现进行选择。另外比较了GPU和CPU执行的DILU预处理技术,GPU在性能上具有明显优势,在线性方程组求解上存在性能瓶颈的程序可以移植到GPU平台以提升性能。
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