论文标题
RBF-FD和其他无网格数值方法的平行域离散算法解决PDE
Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs
论文作者
论文摘要
在本文中，我们提出了一种新型的平行尺寸独立于节点定位算法，该算法能够生成具有可变密度的节点，适用于无网格的数值分析。基于泊松盘采样的非常有效的顺序算法并行用于共享内存计算机，例如带有多核处理器的现代工作站。该平行算法使用其数据分为两个级别的全局空间索引方法，从而实现了有效的多线程实现。添加引导程序使该算法能够使用任何数量的并行线程，同时保持其顺序变体。我们在六个复合物的2和3维域上演示了算法性能，这些域是非矩形形状的，或具有变化的淋巴间距或两者兼而有之。我们对算法进行运行时分析，以证明其达到高速加速的能力，无论域如何，并显示了16个处理器内核在实验硬件上的缩放程度。我们还根据域形状的影响，点位置质量和各种并行化开销来分析算法。
In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on Poisson disc sampling is parallelized for use on shared-memory computers, such as modern workstations with multi-core processors. The parallel algorithm uses a global spatial indexing method with its data divided into two levels, which allows for an efficient multi-threaded implementation. The addition of bootstrapping enables the algorithm to use any number of parallel threads while remaining as general as its sequential variant. We demonstrate the algorithm performance on six complex 2- and 3-dimensional domains, which are either of non-rectangular shape or have varying nodal spacing or both. We perform a run-time analysis of the algorithm, to demonstrate its ability to reach high speedups regardless of the domain and to show how well it scales on the experimental hardware with 16 processor cores. We also analyse the algorithm in terms of the effects of domain shape, quality of point placement, and various parallelization overheads.
