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Previous work on multilevel techniques for compression and reduction of scientific data is extended to the case of data given on unstructured meshes in two and three dimensions. The centerpiece of ...

Although many compression algorithms are focused on preserving pointwise values of the data, application scientists are generally more concerned with derived quantities. Equally well, the user may ...

We develop a technique for multigrid adaptive reduction of data (MGARD). Special attention is given to the case of tensor product grids, where our approach permits the use of nonuniformly spaced gr...

We present a multilevel technique for the compression and reduction of univariate data and give an optimal complexity algorithm for its implementation. A hierarchical scheme offers the flexibility to produce multiple levels of partial decompression of the data so that each user can work with a reduced representation that requires minimal storage whilst achieving the required level of tolerance. The algorithm is applied to the case of turbulence modelling in which the datasets are traditionally not only extremely large but inherently non-smooth and, as such, rather resistant to compression. We decompress the data for a range of relative errors, carry out the usual analysis procedures for turbulent data, and compare the results of the analysis on the reduced datasets to the results that would be obtained on the full dataset. The results obtained demonstrate the promise of multilevel compression techniques for the reduction of data arising from large scale simulations of complex phenomena such as turbulence modelling.

A crude but commonly used technique for compressing ordered scientific data consists of simply retaining every $s$th datum (with a value of $s=10$ generally the default) and discarding the remainder. Should the value of a discarded datum be required afterwards, an approximation is generated by linear interpolation of the two nearest retained values. Despite the widespread use of this and similar techniques, there is little by way of theoretical analysis of their expected performance. First, we quantify the accuracy achieved by linear interpolation when approximating values discarded by decimation, obtaining both deterministic bounds in terms of appropriate smoothness measures of the data and probabilistic bounds in terms of statistics of the data. Second, we investigate the efficiency of the lossless compression scheme consisting of decimation coupled with encoding of the interpolation errors. In particular, we bound the expected compression ratio in terms of the appropriate measures of the data. Finally,...

With the growing computational complexity of science and the complexity of new and emerging hardware, it is time to re-evaluate the traditional monolithic design of computational codes. One new paradigm is constructing larger scientific computational experiments from the coupling of multiple individual scientific applications, each targeting their own physics, characteristic lengths, and/or scales. We present a framework constructed by leveraging capabilities such as in-memory communications, workflow scheduling on HPC resources, and continuous performance monitoring. This code coupling capability is demonstrated by a fusion science scenario, where differences between the plasma at the edges and at the core of a device have different physical descriptions. This infrastructure not only enables the coupling of the physics components, but it also connects in situ or online analysis, compression, and visualization that accelerate the time between a run and the analysis of the science content. Results from runs on Titan and Cori are presented as a demonstration.

We use a polyhedral criterion for the existence of diagonal splittings to investigate which toric varieties X are diagonally split. Our results are stated in terms of the vector configuration given by primitive generators of the 1-dimensional cones in the fan defining X. We show, in particular, that X is diagonally split at all q if and only if this configuration is unimodular, and X is not diagonally split at any q if this configuration is not 2-regular. We also study implications for the possibilities for the set of q at which a toric variety X is diagonally split., Comment: 11 pages v2: minor revisions, to appear in Proc. Amer. Math. Soc