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首页> 外文期刊>Journal of visualization >Accurate parallel reconstruction of unstructured datasets on rectilinear grids
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Accurate parallel reconstruction of unstructured datasets on rectilinear grids

机译：直线栅格上的非结构化数据集准确并行重建

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摘要

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.
机译：高性能计算模拟通常会产生在非结构化网格上定义的数据集。这些网格允许局部改进分辨率，可以适应任意边界几何形状。然而，从可视化角度来看，这种网格具有高存储费用，需要特殊的空间数据结构，并使高质量衍生物的计算具有挑战性。相比之下，直线电网具有可忽略不计的内存占用空间，并且易于支持平滑的数据重建，但随着几何灵活性的降低。本工作涉及在直线网格上创建对大型非结构化数据集的准确重建。我们介绍了一种有效的方法来自动确定直线栅格的几何形状，在给定的重建内核可以实现低误差数据重建。使用这种直线网格，我们通过双级平滑正规化来解决数据拟合问题的潜在不良态度，以及平稳性和准确性之间的必要平衡。为了解决由非常大的输入数据集和高分辨率重建构成的计算挑战，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获得无缝的全局近似解。结果显示了几个3D数据集，其展示了我们的重建能够实现的可视化结果的质量，以大大降低计算和内存成本。

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