Abstract A standard approach to solving the S transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues with DSA preconditioning, particularly on highly heterogeneous domains. For large-scale parallel simulation, it is critical that both (a) preconditioned source iteration converges rapidly and (b) the action of the DSA preconditioner can be applied using fast, scalable solvers, such as algebraic multigrid (AMG). For heterogeneous domains, these two interests can be at odds. In particular, there exist DSA diffusion discretizations that can be solved rapidly using AMG, but they do not always yield robust/fast convergence of the larger source iteration. Conversely, there exist robust DSA discretizations where source iteration converges rapidly on difficult heterogeneous problems, but fast parallel solvers like AMG tend to struggle applying the action of such operators. Moreover, very few current methods for the solution of deterministic transport are compatible with voids. This paper develops a new heterogeneous DSA preconditioner based on only preconditioning the optically thick subdomains. The resulting method proves robust on a variety of heterogeneous transport problems, including a linearized hohlraum mesh related to inertial confinement fusion. Moreover, the action of the preconditioner is easily computed using AMG iterations, convergence of the transport iteration typically requires 2 to 5× fewer iterations than current state-of-the-art “full” DSA, and the proposed method is trivially compatible with voids. On the hohlraum problem, rapid convergence is obtained by preconditioning less than 3% of the mesh elements with five to ten AMG iterations.

中文翻译：

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异质域的扩散合成加速，兼容空洞

摘要 求解 S 输运方程的标准方法是使用带有扩散合成加速 (DSA) 的源迭代。尽管这种方法被广泛使用并且在许多问题上有效，但 DSA 预处理仍然存在一些实际问题，特别是在高度异构的域中。对于大规模并行模拟，至关重要的是 (a) 预处理源迭代快速收敛，以及 (b) 可以使用快速、可扩展的求解器（例如代数多重网格 (AMG)）应用 DSA 预处理器的操作。对于异构域，这两种兴趣可能是不一致的。特别是，存在可以使用 AMG 快速解决的 DSA 扩散离散化，但它们并不总是产生较大源迭代的稳健/快速收敛。反过来，存在稳健的 DSA 离散化，其中源迭代在困难的异构问题上快速收敛，但像 AMG 这样的快速并行求解器往往难以应用此类算子的动作。此外，目前确定性输运的解决方法很少与空隙兼容。本文基于仅预处理光学厚子域开发了一种新的异构 DSA 预处理器。由此产生的方法在各种异质传输问题上证明是稳健的，包括与惯性约束融合相关的线性化空腔网格。此外，使用 AMG 迭代可以轻松计算预处理器的动作，传输迭代的收敛通常需要比当前最先进的“完整”DSA 少 2 到 5 倍的迭代，并且所提出的方法与空隙非常兼容。在空腔问题上，通过使用五到十次 AMG 迭代对少于 3% 的网格元素进行预处理来获得快速收敛。