Abstract

High performance computing simulations often produce datasets defined over unstructured grids. Those grids allow for the local refinement of the resolution and can accommodate arbitrary boundary geometry. From a visualization standpoint, however, such grids have a high storage cost, require special spatial data structures, and make the computation of high-quality derivatives challenging. Rectilinear grids, in contrast, have a negligible memory footprint and readily support smooth data reconstruction, though with reduced geometric flexibility. The present work is concerned with the creation of an accurate reconstruction of large unstructured datasets on rectilinear grids. We present an efficient method to automatically determine the geometry of a rectilinear grid upon which a low-error data reconstruction can be achieved with a given reconstruction kernel. Using this rectilinear grid, we address the potential ill-posedness of the data fitting problem, as well as the necessary balance between smoothness and accuracy, through a bi-level smoothness regularization. To tackle the computational challenge posed by very large input datasets and high-resolution reconstructions, we propose a block-based approach that allows us to obtain a seamless global approximation solution from a set of independently computed sparse least-squares problems. Results are presented for several 3D datasets that demonstrate the quality of the visualization results that our reconstruction enables, at a greatly reduced computational and memory cost.

Graphical Abstract

中文翻译：

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直线网格上非结构化数据集的精确并行重建

摘要

高性能计算仿真通常会生成在非结构化网格上定义的数据集。这些网格允许局部改善分辨率，并可以容纳任意边界几何形状。但是，从可视化的角度来看，这样的网格具有很高的存储成本，需要特殊的空间数据结构，并使高质量导数的计算具有挑战性。相比之下，直线网格的内存占用量可忽略不计，并且尽管几何灵活性降低了，但很容易支持平滑的数据重建。当前的工作是关于在直线网格上创建大型非结构化数据集的精确重建。我们提出一种有效的方法来自动确定直线网格的几何形状，在该网格上可以使用给定的重构内核实现低误差数据重构。使用此直线网格，我们通过双层平滑正则化解决了数据拟合问题的潜在不适性，以及平滑性和准确性之间的必要平衡。为了解决非常大的输入数据集和高分辨率重构带来的计算难题，我们提出了一种基于块的方法，该方法允许我们从一组独立计算的稀疏最小二乘问题中获得无缝的全局逼近解。呈现了几个3D数据集的结果，这些数据集展示了我们的重构可实现的可视化结果的质量，

图形概要