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arXiv 2602.16347cs.DC
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负载均衡的并行节点生成用于无网格数值方法

Load Balanced Parallel Node Generation for Meshless Numerical Methods

Jozef Stefan International Postgraduate School(约瑟夫·斯特凡国际研究生院);Institut "Jožef Stefan", Parallel and Distributed Systems Laboratory(约瑟夫·斯特凡研究所,并行与分布式系统实验室)

Jon Vehovar, Miha Rot, Matjaž Depolli, Gregor Kosec

AI总结:

本文提出一种基于Poisson disc采样的并行节点生成算法,通过空间索引和工作分布超树实现负载均衡,减少锁操作,提高无网格方法的并行效率。

摘要:

无网格方法通过在节点处近似微分算子来求解偏微分方程,其中一种生成适合无网格数值分析的节点的算法是基于n维Poisson disc采样方法。该方法能够处理复杂几何并支持可变节点密度,这对于自适应分析至关重要。我们修改该方法以实现并行执行,使用耦合的空间索引和工作分布超树。后者根据节点密度函数预先构建,确保每个叶子代表一个平衡的工作单元。线程在各自前线上推进,并根据需要声明工作超树的叶子,同时避免其他线程已声明的相邻叶子。节点放置约束和部分预构建的空间超树结合在一起,以消除在修改树时锁定树的需要。线程碰撞处理在叶子级别由工作超树管理,大大减少了所需互斥锁获取的次数以进行点插入碰撞检查。我们探讨了所提算法的行为,并将其性能与现有并行化尝试进行比较,并考虑将开发的算法适应分布式系统的要求。

英文摘要:

Meshless methods are used to solve partial differential equations by approximating differential operators at a node as a weighted sum of values at its neighbours. One of the algorithms for generating nodes suitable for meshless numerical analysis is an n-dimensional Poisson disc sampling based method. It can handle complex geometries and supports variable node density, a crucial feature for adaptive analysis. We modify this method for parallel execution using coupled spatial indexing and work distribution hypertrees. The latter is prebuilt according to the node density function, ensuring that each leaf represents a balanced work unit. Threads advance separate fronts and claim work hypertree leaves as needed while avoiding leaves neighbouring those claimed by other threads. Node placement constraints and the partially prebuilt spatial hypertree are combined to eliminate the need to lock the tree while it is being modified. Thread collision handling is managed by the work hypertree at the leaf level, drastically reducing the number of required mutex acquisitions for point insertion collision checks. We explore the behaviour of the proposed algorithm and compare the performance with existing attempts at parallelisation and consider the requirements for adapting the developed algorithm to distributed systems.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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