Compactly expressing large-scale datasets through Multivariate Functional Approximations (MFA) can be critically important for analysis and visualization to drive scientific discovery. Tackling such problems requires scalable data partitioning approaches to compute MFA representations in amenable wall clock times. We introduce a fully parallel scheme to reduce the total work per task in combination with an overlapping additive Schwarz-based iterative scheme to compute MFA with a tensor expansion of B-spline bases, while preserving full degree continuity across subdomain boundaries. While previous work on MFA has been successfully proven to be effective, the computational complexity of encoding large datasets on a single process can be severely prohibitive. Parallel algorithms for generating reconstructions from the MFA have had to rely on post-processing techniques to blend discontinuities across subdomain boundaries. In contrast, a robust constrained minimization infrastructure to impose higher-order continuity directly on the MFA representation is presented here. We demonstrate the effectiveness of the parallel approach with domain decomposition solvers, to minimize the subdomain error residuals of the decoded MFA, and more specifically to recover continuity across non-matching boundaries at scale. The analysis of the presented scheme for analytical and scientific datasets in 1-, 2- and 3-dimensions are presented. Extensive strong and weak scalability performances are also demonstrated for large-scale datasets to evaluate the parallel speedup of the MPI-based algorithm implementation on leadership computing machines.
翻译:通过多变量功能组合(MFA)对大型数据集进行压缩表达,对于分析和可视化推动科学发现至关重要。解决这些问题要求采用可缩放的数据分割法,在可调整的墙钟钟时段内计算MFA的表示。我们引入了一个完全平行的计划,以减少每项任务的总工作,同时采用一个重叠的添加式Schwarz基的迭代计划,将MFA与B-Sprine基础的扩展相匹配,同时保持子体外边界之间的充分连续性。虽然以往关于MFA的工作已经成功地证明是有效的,但将大型数据集编码成大数据集的计算复杂性可能非常高。从MFA重建的平行算法方法不得不依靠后处理技术来混合分界外的不连续性。与此形成对照的是,此处展示了一个严格的限制最小化基础设施,以直接对MFA代表处进行更高阶梯级的扩展。我们展示了与域解剖解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解析的解决方案的平行方法的有效性,并尽可能减少误差错残存的剩余,更严重减少解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解的逻辑,更的逻辑的逻辑的逻辑的逻辑的逻辑,更的逻辑的逻辑,更是无法解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解解析的逻辑性,更精确性的逻辑性的逻辑性,更具体的算,更具体,更难,更难,更难,更难,以及更具体地在1级的大规模解后,更具体而言,更是,更是,在1级性分析1级的系统化分析1级的大规模解解解解解解解解后,在1级的大规模解解解解后,在1级的大规模分析中,在1级分析中,在1级的大规模分析中,在1级的大规模分析中,在1级的大规模分析中,更深入解析分析中,在1级