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Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering and Its Application

Banff International Research Station for Mathematical Innovation and Discovery

Since the introduction of Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for DG approximation of univariate hyperbolic equations by Cockburn et al., many generalizations of SIAC filtering have been proposed. Recently, new advancements in connecting the spline theory and SIAC filtering have paved the way for a more geometric view of this filtering technique. Based on which, various generalizations of the SIAC kernel have been proposed to make the filtering viable for more realistic applications. Examples include the introduction of SIAC line integral with applications for streamlining and flow visualization, hexagonal SIAC using nonseparable splines, and position dependent SIAC with nonuniform knot sequences. In this talk, I will introduce the basic concept of the SIAC filtering, its connection with well-established concepts from approximation theory, and discuss the recent advances in SIAC filtering.

Mathematics; Numerical analysis; Mechanics of deformable solids; Applied computer science

video/mp4

Author affiliation: University of Miami

2018-03-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64941

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/