We introduce several parallel algorithms operating on a distributed forest of adaptive quadtrees/octrees. They are targeted at large-scale applications relying on data layouts that are more complex than required for standard finite elements, such as hp -adaptive Galerkin methods, particle tracking and semi-Lagrangian schemes, and in-situ post-processing and visualization. Specifically, we design algorithms to derive an adapted worker forest based on sparse data, to identify owner processes in a top-down search of remote objects, and to allow for variable process counts and per-element data sizes in partitioning and parallel file I/O. We demonstrate the algorithms’ usability and performance in the context of a particle tracking example that we scale to 21e9 particles and 64Ki MPI processes on the Juqueen supercomputer, and we describe the construction of a parallel assembly of variably sized spheres in space creating up to 768e9 elements on the Juwels supercomputer.

中文翻译：

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AMR 和非标准数据访问的并行树算法

我们介绍了几种在自适应四叉树/八叉树的分布式森林上运行的并行算法。它们针对依赖于比标准有限元所需的数据布局更复杂的大规模应用程序，例如生命值- 自适应 Galerkin 方法、粒子跟踪和半拉格朗日方案，以及原位后处理和可视化。具体来说，我们设计算法以基于稀疏数据派生适应的工作森林，在远程对象的自上而下搜索中识别所有者进程，并在分区和并行文件 I/ 中允许可变进程计数和每个元素的数据大小O。我们在粒子跟踪示例的上下文中展示了算法的可用性和性能，我们在 Juqueen 超级计算机上扩展到 21e9 粒子和 64Ki MPI 进程，并描述了在空间中构建可变大小球体的并行组装，创建高达 768e9 Juwels 超级计算机上的元素。