MURPHY -- -- 3D区块结构合用电网科学计算可缩放多分辨率框架 (MURPHY -- A scalable multiresolution framework for scientific computing on 3D block-structured collocated grids)

We present the derivation, implementation, and analysis of a multiresolution adaptive grid framework for numerical simulations on 3D block-structured collocated grids with distributed computational architectures. Our approach provides a consistent handling of non-lifted and lifted interpolating wavelets of arbitrary order demonstrated using second, fourth, and sixth order wavelets, and combines that with standard finite-difference based discretization operators. We first validate that the wavelet family used provides strict and explicit error control when coarsening the grid, that lifting wavelets increase the grid compression rate while conserving discrete moments across levels, and that high-order PDE discretization schemes retain their convergence order even at resolution jumps when combined with sufficiently high order wavelets. We then use a test case of the advection of a scalar to analyze convergence for the temporal evolution of a PDE, which shows that our wavelet-based refinement criterion is successful at controlling the overall error while the coarsening criterion is effective at retaining the relevant information on a compressed grid. Our software exploits the block-structured grid data structure for efficient multi-level operations, and the parallelization strategy relies on a one-sided MPI-RMA communication approach with active PSCW synchronization leading to highly scalable performance on more than 7,000 cores.

翻译：我们提出一个多分辨率适应网格框架的衍生、实施和分析,用于对3D区块结构的合用网格进行数字模拟,用分布式计算结构模拟3D区块结构的合用网格。我们的方法对使用第二、第四和第六级的任意波子展示的非提升和提升的中间波子进行一致的处理,并将这种处理与标准的基于有限差异的离散操作器结合起来。我们首先确认,波子系在变换电网时提供了严格和明确的错误控制,拉动波子会增加电网压缩速度,同时保存不同层次的离散时间,高等级的PDE离散计划甚至在分辨率跳跃时保留其趋同顺序。我们随后使用一个测试案例,用一个斜度分析PDE时间演变的趋同点来分析趋同。这表明,我们基于波子系的精细化标准成功地控制了整体错误,而粗略的标准有效地保留了压缩电网格中的相关信息。我们的软件利用了块结构的电网格数据结构数据结构结构来高效的多层次操作,而高层次的PDE分离战略则依靠动态同步的同步战略,而不是高度的MRMS-A-A-A-CMS-S-S-S-S-P-S-S-S-S-S-S-S-S-S-S-S-P-S-S-S-S-S-S-S-S-S-P-S-S-S-S-S-S-S-S-P-S-S-S-S-S-S-S-S-S-P-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-P-P-P-S-S-S-S-S-S-P-S-P-P-P-P-P-P-P-P-P-P-P-P-S-S-S-S-S-S-P-P-P-P-P-P-P-P-P-P-P-P-P-P-