Algorithms for Parallel Generic hp -Adaptive Finite Element Software
Algorithms for Parallel Generic hp -Adaptive Finite Element Software
复制标题
并行通用 hp 自适应有限元软件算法
DOI：
10.1145/3603372
复制
发表时间：
2023
影响因子：
2.7
通讯作者：
Bangerth, Wolfgang
中科院分区：
文献类型：
--
作者：
Fehling, Marc;Bangerth, Wolfgang
HP自适应有限元方法可以独立选择每个单元的网格大小(H)和多项式次数(P)，长期以来一直被认为比单独使用h或rp自适应方法具有更好的理论收敛特性。然而，它没有被广泛使用，至少部分原因是底层算法的困难和缺乏广泛使用的实现。当与连续有限元一起使用时尤其如此。在这里，我们讨论在分布式存储的并行机上全面和通用地实现HP自适应有限元方法所必需的算法。特别是，我们将提出一种适用于连续有限元空间的自由度唯一计数的多阶段算法，描述加权负载平衡的考虑因素，并讨论进程之间可变大小数据的传输。我们用数值例子说明了我们的算法的性能，并证明了它们可以合理地扩展到至少16,384个消息通道接口进程。
Thehp-adaptive finite element method—where one independently chooses the mesh size (h) and polynomial degree (p) to be used on each cell—has long been known to have better theoretical convergence properties than eitherh- orp-adaptive methods alone. However, it is not widely used, owing at least in part to the difficulty of the underlying algorithms and the lack of widely usable implementations. This is particularly true when used with continuous finite elements.Herein, we discuss algorithms that are necessary for a comprehensive and generic implementation ofhp-adaptive finite element methods on distributed-memory, parallel machines. In particular, we will present a multistage algorithm for the unique enumeration of degrees of freedom suitable for continuous finite element spaces, describe considerations for weighted load balancing, and discuss the transfer of variable size data between processes. We illustrate the performance of our algorithms with numerical examples and demonstrate that they scale reasonably up to at least 16,384 message passage interface processes.We provide a reference implementation of our algorithms as part of the open source librarydeal.II.