论文标题
空气代数多机，用于时空杂交不连续的盖尔金离散（ - 扩散）
AIR algebraic multigrid for a space-time hybridizable discontinuous Galerkin discretization of advection(-diffusion)
论文作者
论文摘要
本文研究了近似理想限制（AIR）代数多机的效率，鲁棒性和可伸缩性，作为对流率主导的流量的可时空杂交不连续的盖尔金（HDG）离散化的全面解决方案的预处理。这项研究的动机是，$（d+1）$ - 尺寸和空气中的时间依赖性的对流扩散方程可将其视为“稳定”的对流扩散问题 - 对于稳定的对流统计问题而言是强大的求解器。数值示例证明了空气作为对固定和时间依赖性域的对流扩散问题的预处理的有效性，同时均逐一和全面的时空离散化，以及在均匀和时空自适应网格的培训的背景下。仔细观察空气中产生的几何结构，这也解释了为什么空气可以在对流和双曲线问题上提供强大的，可扩展的时空收敛性，而大多数多层次并行时间方案都在此类问题上挣扎。
This paper investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a space-time hybridizable discontinuous Galerkin (HDG) discretization of advection-dominated flows. The motivation for this study is that the time-dependent advection-diffusion equation can be seen as a "steady" advection-diffusion problem in $(d+1)$-dimensions and AIR has been shown to be a robust solver for steady advection-dominated problems. Numerical examples demonstrate the effectiveness of AIR as a preconditioner for advection-diffusion problems on fixed and time-dependent domains, using both slab-by-slab and all-at-once space-time discretizations, and in the context of uniform and space-time adaptive mesh refinement. A closer look at the geometric coarsening structure that arises in AIR also explains why AIR can provide robust, scalable space-time convergence on advective and hyperbolic problems, while most multilevel parallel-in-time schemes struggle with such problems.
