Smoothness-increasing accuracy-conserving filters (SIAC) for discontinuous Galerkin solutions

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Publication Type dissertation
School or College College of Engineering
Department Computing
Author Mirzaee, Hanieh
Title Smoothness-increasing accuracy-conserving filters (SIAC) for discontinuous Galerkin solutions
Date 2013-05
Description Smoothness-increasing accuracy-conserving (SIAC) filters were introduced as a class of postprocessing techniques to ameliorate the quality of numerical solutions of discontinuous Galerkin (DG) simulations. SIAC filtering works to eliminate the oscillations in the error by introducing smoothness back to the DG field and raises the accuracy in the L2-n o rm up to its natural superconvergent accuracy in the negative-order norm. The increased smoothness in the filtered DG solutions can then be exploited by simulation postprocessing tools such as streamline integrators where the absence of continuity in the data can lead to erroneous visualizations. However, lack of extension of this filtering technique, both theoretically and computationally, to nontrivial mesh structures along with the expensive core operators have been a hindrance towards the application of the SIAC filters to more realistic simulations. In this dissertation, we focus on the numerical solutions of linear hyperbolic equations solved with the discontinuous Galerkin scheme and provide a thorough analysis of SIAC filtering applied to such solution data. In particular, we investigate how the use of different quadrature techniques could mitigate the extensive processing required when filtering over the whole computational field. Moreover, we provide detailed and efficient algorithms that a numerical practitioner requires to know in order to implement this filtering technique effectively. In our first attempt to expand the application scope of this filtering technique, we demonstrate both mathematically and through numerical examples that it is indeed possible to observe SIAC filtering characteristics when applied to numerical solutions obtained over structured triangular meshes. We further provide a thorough investigation of the interplay between mesh geometry and filtering. Building upon these promising results, we present how SIAC filtering could be applied to gain higher accuracy and smoothness when dealing with totally unstructured triangular meshes. Lastly, we provide the extension of our filtering scheme to structured tetrahedral meshes. Guidelines and future work regarding the application of the SIAC filter in the visualization domain are also presented. We further note that throughout this document, the terms postprocessing and filtering will be used interchangeably.
Type Text
Publisher University of Utah
Subject Discontinous Galerkin; Oscillation; Partial differential euqation; Postprocessing; SIAC; Smoothness
Dissertation Institution University of Utah
Dissertation Name Doctor of Philosophy
Language eng
Rights Management Copyright © Hanieh Mirzaee 2013
Format Medium application/pdf
Format Extent 4,253,285 bytes
Identifier etd3/id/2118
ARK ark:/87278/s6765w5n
Setname ir_etd
ID 195803
Reference URL https://collections.lib.utah.edu/ark:/87278/s6765w5n