Location: 4100, Room J302
Abstract: The advent of exascale computer systems poses new challenges, motivating methods to cope with vastly increased amounts of simulation data. Enter data compression and reduction. Of particular interest are multilevel and hierarchical reduction methods, which split input data into a sequence of components tailored to the heterogeneous storage media of modern machines. Such methods are especially appropriate when the applications for which the data are to be used require varying levels of resolution. For instance, one user might require that the reduced dataset meet a prescribed error tolerance for the calculation of some derived quantity, while another might need it to fit in the available RAM for a responsive visualization. The first topic of this talk will be the analysis of a simple lossless compression method based on decimation. Bounds on the expected compression ratio will be derived and numerical illustrations of the performance of the technique will be presented. The remainder will be devoted to a suite of multilevel adaptive techniques inspired by the orthogonal and hierarchical decompositions. First, univariate algorithms for the two use cases of constrained loss and constrained storage will be discussed. Next, the technique will be extended to the multivariate setting, and a loss estimator permitting the control of pointwise errors will be introduced. A related loss estimator for Sobolev norms will be used to perform reduction while limiting distortion in quantities of interest, and finally ongoing work on extending the method to the setting of unstructured meshes will be presented.
Biography: Ben Whitney studied pure math at Harvard University before switching to applied math during graduate school at Brown University. There he studied abstract and numerical analysis before writing his dissertation on multilevel compression methods under the supervision of Mark Ainsworth. Ben graduated last spring.