Science at the intersection of data, modelling, and computation

Abstract

In meshless methods, clouds of points irregularly distributed are widely used in discretizing computational domains and are usually unavoidable to accommodate complex geometries. However, the irregularity of points has been reported to be negative effect on the GPU memory access pattern, which results in low performance in GPU computations. In order to remedy this negative effect, a multi-layered point reordering (MLPRO) approach is proposed in this paper for GPU-based meshless implementations. Layer structures based on the virtual connections between central and satellite points in meshless clouds are constructed and used to reorder the points in a layer-by-layer manner. Besides, point reordering inside each thread warp, which is rarely concerned in GPU implementations, is further considered by proposing a supplemental group satellite reordering to form a modified MLPRO approach. Furthermore, by defining virtual connectivity matrixes of meshless clouds of points in the whole computational domain, the effect of reordering mentioned to the data localities can be visibly observed to have a comprehensive view of the improvement of point locality. Supersonic flows in a rectangular channel are firstly selected to test the effect extent of irregularity of meshless points to the GPU performance by increasing the percentage of irregular points occupied in the computational domain. Then flows over two- and three-dimensional aerodynamic configurations are simulated to show the performances of the reordering approaches presented. Numerical results show that significant enhancements of GPU speedups can be achieved for all test cases, particularly for the three-dimensional M6 wing and RAE wing-body combination cases with up to 2.5× further speedups, which is meaningful for simulations with large-scale irregular meshless clouds of points.