Print Email Facebook Twitter Multiwavelets and outlier detection for troubled-cell indication in discontinuous Galerkin methods Title Multiwavelets and outlier detection for troubled-cell indication in discontinuous Galerkin methods Author Vuik, M.J. (TU Delft Mathematical Physics) Contributor Heemink, A.W. (promotor) Ryan, J.K. (copromotor) Degree granting institution Delft University of Technology Date 2017-01-24 Abstract This dissertation addresses practical use of multiwavelets and outlier detection for troubled-cell indication for discontinuous Galerkin (DG) methods. For smooth solutions, the DG approximation converges to the exact solution with a high order of accuracy. However, problems may arise when shock waves or discontinuities appear: non-physical spurious oscillations are formed close to these discontinuous regions. These oscillations can be prevented by applying a limiter near these regions. One of the difficulties in using a limiter is identifying the difference between a true discontinuity and a local extremum of the approximation. Troubled-cell indicators can help to detect this difference and identify the discontinuous regions (so-called ’troubled cells’) where a limiter should be applied.In this dissertation, a multiwavelet formulation is used to decompose the DG approximation. The multiwavelet coefficients act as a troubled-cell indicator since they suddenly increase in the neighborhood of a discontinuity. This leads to the definition of a new multiwavelet indicator that detects elements as troubled if the coefficient is large enough in absolute value. Here, a problem-dependent parameter is needed to define the strictness of the indicator. To forgo the reliance on a parameter, a new outlier-detection algorithm is defined that uses boxplot theory. This method can also be applied to different troubled-cell indicators.Results are shown for regular one-dimensional and tensor-product two-dimensional meshes, as well as for irregular meshes in one dimension and triangular meshes in two dimensions. Subject Runge-Kutta discontinuous Galerkin methodhigh-order methodslimitersshock detectionmultiresolution analysiswaveletsmultiwaveletstroubled cellsoutlier detectionboxplots To reference this document use: https://doi.org/10.4233/uuid:a01a0a14-798f-44f7-9b5e-88b56b7a4a84 ISBN 978-94-92516-24-4 Part of collection Institutional Repository Document type doctoral thesis Rights © 2017 M.J. Vuik Files PDF dissertation_MJVuik.pdf 16.44 MB Close viewer /islandora/object/uuid:a01a0a14-798f-44f7-9b5e-88b56b7a4a84/datastream/OBJ/view