非均匀域的扩散合成加速，与空洞兼容
Diffusion synthetic acceleration for heterogeneous domains, compatible with voids
摘要：
求解S $_N$输运方程的标准方法是使用具有扩散合成加速（DSA）的源迭代。虽然这种方法在许多问题上得到了广泛的应用和有效的，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上。对于大规模并行模拟，关键是（i）预处理源迭代快速收敛，以及（ii）DSA预处理器的动作可以使用快速，可扩展的求解器（如代数多重网格（AMG））来应用。对于异构域，这两种兴趣可能是不一致的。特别是，存在DSA扩散离散化，可以使用AMG快速求解，但它们并不总是产生鲁棒/快速收敛的较大的源迭代。相反，存在鲁棒的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这些算子的动作。此外，目前很少有确定性输运的解决方案的方法是兼容的空隙。本文提出了一种新的非均匀DSA预处理器，它只对光学厚子域进行预处理。由此产生的方法证明了强大的各种异质输运问题，包括一个线性化的黑腔网格惯性约束聚变。此外，预处理器的动作容易使用$\mathcal{O}(1)$ AMG迭代来计算，{传输迭代的收敛通常需要比当前最先进的"全DSA“少的$2-5\times$迭代，并且所提出的方法与空隙是平凡兼容的。对于黑腔问题，用$5-10$ AMG迭代法对小于3%的网格单元进行预处理，得到了快速收敛的结果。
英文摘要：
A standard approach to solving the S$_N$ 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 (i) preconditioned source iteration converges rapidly, and (ii) 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 $\mathcal{O}(1)$ AMG iterations, {convergence of the transport iteration typically requires $2-5\times$ less 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 $5-10$ AMG iterations.
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