发表机构
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在LLNL的ARDRA中结合Hypre，探索降精度DSA加速S_N中子输运，多数场景下不影响加速效果，仅容差严格时可能失效。
AI 中文摘要
生产型离散纵标输运代码的快速求解时间通常需要使用扩散合成加速（DSA）。良好的DSA实现可大幅减少收敛输运解所需的迭代次数，代价是每次迭代需求解一个类扩散线性系统，而更少的输运迭代往往会缩短求解时间。近期研究显示降精度预条件化具有应用前景，只要降精度不会大幅降低待求解高精度线性系统的收敛行为，就能减少时间和内存成本。本文探讨在双精度（64位）下加速输运迭代、同时使用降精度（32位）DSA求解的算法意义：首先实现独立代码，研究平板几何下降精度DSA的理论局限；随后在劳伦斯利弗莫尔国家实验室（LLNL）的离散纵标中性粒子输运代码ARDRA中实现降精度DSA，并结合LLNL的可扩展线性求解器与支持混合精度线性求解的多重网格方法库Hypre；接着求解各类受关注的中子输运问题。研究发现，在多数情况下，降精度DSA与源迭代结合使用时，对DSA的加速特性几乎无影响；但当要求更严格的容差时，降精度DSA可能无法成功加速输运求解，反而会增加求解时间。
英文摘要
Fast solution times in production discrete ordinates transport codes often require the use of diffusion synthetic acceleration (DSA). A good implementation of DSA will substantially reduce the number of iterations to converge the transport solution at the cost of solving a diffusion-like linear system at each iteration. Often fewer transport iterations will lead to smaller times to solution. Recent work has shown the promise of reduced precision preconditioning. Time and memory cost can be decreased as long as the reduced precision does not substantially degrade the convergence behavior of the higher precision linear system being solved. In this paper, we discuss the algorithmic implications of accelerating transport iterations in double precision (64 bit) while using a reduced precision (32 bit) DSA solve. We initially implement a stand alone code to investigate any theoretical limitations of reduced precision DSA in slabs. Then we implement reduced precision DSA in ARDRA, Lawrence Livermore National Laboratory's (LLNL) discrete ordinance neutral particle transport code, coupled with {\it hypre}, LLNL's scalable linear solver and multigrid methods library capable of mixed precision linear solves Then we solve various neutron transport problems of interest. We find that in most circumstances, DSA acceleration in reduced precision has little to no impact on the acceleration properties of DSA when used with source iteration in most circumstances. However, as tighter tolerances are required, reduced precision DSA may fail to successfully accelerate the transport solve and increase time to solution.
Comments10 pages, 7 figures, submitted to ANS M&C 2027
