Smoothness-increasing accuracy-conserving (SIAC) line filtering: effective rotation for multidimensional fields

Docampo-Sanchez, Julia (2016) Smoothness-increasing accuracy-conserving (SIAC) line filtering: effective rotation for multidimensional fields. Doctoral thesis, University of East Anglia.

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Abstract

Over the past few decades there has been a strong effort towards the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters for Discontinuous Galerkin (DG) methods, designed to increase the smoothness and improve the convergence rate
of the DG solution through this post-processor. The applications of these filters in
multidimension have traditionally employed a tensor product kernel, allowing a natural
extension of the theory developed for one-dimensional problems. In addition, the
tensor product has always been done along the Cartesian axis, resulting in a filter
whose support has fixed shape and orientation. This thesis has challenged these assumptions,
leading to the investigation of rotated�filters: tensor product filters with variable orientation. Combining this approach with previous experiments on lower-dimension
filtering, a new and computationally efficient subfamily for post-processing multidimensional data has been developed: SIAC Line filters. These filters transform
the integral of the convolution into a line integral. Hence, the computational advantages are immediate: the simulation times become significantly shorter and the complexity of the algorithm design reduces to a one-dimensional problem.
In the thesis, a solid theoretical background for SIAC Line �filters has been established.
Theoretical error estimates have been developed, showing how Line filtering
preserves the properties of traditional tensor product �filtering, including smoothness
recovery and improvement in the convergence rate. Furthermore, different numerical
experiments were performed, exhibiting how these filters achieve the same accuracy
at significantly lower computational costs. This affords great advantages towards the
applications of these filters during
flow visualization; one important limiting factor of
a tensor product structure is that the filter grows in support as the field dimension increases,
becoming computationally expensive. SIAC Line filters have proven effi�ciency
in computational performance, thus overcoming the limitations presented by the tensor
product filter. The experiments carried out on streamline visualization suggest that
these filters are a promising tool in scientific visualisation.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Katie Miller
Date Deposited: 13 Jun 2017 14:11
Last Modified: 13 Jun 2017 14:11
URI: https://ueaeprints.uea.ac.uk/id/eprint/63740
DOI:

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