Automated parameters for troubled-cell indicators using outlier detection

Vuik, Mathea and Ryan, Jennifer (2016) Automated parameters for troubled-cell indicators using outlier detection. SIAM Journal on Scientific Computing, 38 (1). A84–A104. ISSN 1064-8275

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Abstract

In Vuik and Ryan (2014) we studied the use of troubled-cell indicators for discontinuity detection in nonlinear hyperbolic partial differential equations and introduced a new multiwavelet technique to detect troubled cells. We found that these methods perform well as long as a suitable, problem-dependent parameter is chosen. This parameter is used in a threshold which decides whether or not to detect an element as a troubled cell. Until now, these parameters could not be chosen automatically. The choice of the parameter has impact on the approximation: it determines the strictness of the troubled-cell indicator. An inappropriate choice of the parameter will result in detection (and limiting) of too few or too many elements. The optimal parameter is chosen such that the minimal number of troubled cells is detected and the resulting approximation is free of spurious oscillations. In this paper we will see that for each troubled-cell indicator the sudden increase or decrease of the indicator value with respect to the neighboring values is important for detection. Indication basically reduces to detecting the outliers of a vector (one dimension) or matrix (two dimensions). This is done using Tukey's boxplot approach to detect which coefficients in a vector are straying far beyond others (Tukey, 1977). We provide an algorithm that can be applied to various troubled-cell indication variables. Using this technique the problem-dependent parameter that the original indicator requires is no longer necessary as the parameter will be chosen automatically.

Item Type:	Article
Uncontrolled Keywords:	troubled cells,shock detection,discontinuous galerkin,high-order methods,wavelets,limiters
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Fluid and Solid Mechanics
Depositing User:	Pure Connector
Date Deposited:	02 Feb 2016 13:08
Last Modified:	22 Oct 2022 00:32
URI:	https://ueaeprints.uea.ac.uk/id/eprint/56915
DOI:	10.1137/15M1018393

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