高阶网格在GPU上的通用场评估
General Field Evaluation in High-Order Meshes on GPUs
AI总结：
本文提出一种在GPU上高效评估高阶网格中任意点场值的方法，结合全局/局部映射、边界框和带信任域的牛顿法，支持四边形、六面体及表面网格，应用于网格间传递和粒子追踪。
摘要：
在有限/谱元网格中任意点进行稳健且可扩展的函数评估，是查询偏微分方程解在感兴趣点处的值、比较不同网格之间的解以及进行拉格朗日粒子追踪所必需的。这是一个具有挑战性的问题，特别是对于通过MPI并行划分的高阶非结构化网格，因为它需要识别与给定点重叠的单元并计算相应的参考空间坐标。我们提出了一种稳健且高效的技术，用于在包含四边形和六面体的大规模高阶网格中进行通用场评估。在所提出的方法中，结合全局划分和处理器局部映射，首先确定候选MPI秩的列表，然后局部确定可能包含给定点的候选单元。接下来，逐单元边界框进一步缩减候选单元列表。最后，使用带信任域的牛顿法来确定重叠单元及相应的参考空间坐标。由于基于GPU的架构在加速使用张量积单元的网格计算分析中变得流行，我们开发了专门的核函数以在GPU上利用所提出的方法。该方法还扩展到支持在表面网格上进行通用场评估。论文最后通过展示所提方法在各种应用中的使用来结束，从r-自适应过程中的网格到网格传递到拉格朗日粒子追踪。
英文摘要：
Robust and scalable function evaluation at any arbitrary point in the finite/spectral element mesh is required for querying the partial differential equation solution at points of interest, comparison of solution between different meshes, and Lagrangian particle tracking. This is a challenging problem, particularly for high-order unstructured meshes partitioned in parallel with MPI, as it requires identifying the element that overlaps a given point and computing the corresponding reference space coordinates. We present a robust and efficient technique for general field evaluation in large-scale high-order meshes with quadrilaterals and hexahedra. In the proposed method, a combination of globally partitioned and processor-local maps are used to first determine a list of candidate MPI ranks, and then locally candidate elements that could contain a given point. Next, element-wise bounding boxes further reduce the list of candidate elements. Finally, Newton's method with trust region is used to determine the overlapping element and corresponding reference space coordinates. Since GPU-based architectures have become popular for accelerating computational analyses using meshes with tensor-product elements, specialized kernels have been developed to utilize the proposed methodology on GPUs. The method is also extended to enable general field evaluation on surface meshes. The paper concludes by demonstrating the use of proposed method in various applications ranging from mesh-to-mesh transfer during r-adaptivity to Lagrangian particle tracking.
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。
