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16.01.2019 Prof. Dr. Siegfried Müller "Multiwavelet-Based Grid Adaptation with Discontinuous-Galerkin schemes for Conservation Laws"

Vortrag im Oberseminar Numerik und Optimierung am 16. Januar 2019

Im Rahmen des Oberseminares "Numerik und Optimierung" hält

Herr Prof. Dr. Siegfried Müller (RWTH Aachen)

am Mittwoch, 16. Januar 2019, einen Vortrag mit dem Titel

Multiwavelet-Based Grid Adaptation with Discontinuous-Galerkin schemes for Conservation Laws

Beginn: 16:30 Uhr, Raum

Alle Interessierten sind herzlich willkommen!

We present an adaptive strategy for solving unsteady compressible flows by a discontinuous Galerkin method. The underlying idea of our adaptive strategy is to perform a multiresolution analysis using multiwavelets on a hierarchy of nested grids. This provides information on the difference between successive refinement levels that may become negligibly small in regions where the solution is smooth. Applying thresholding, the data is compressed thereby triggering local grid adaptation.
Furthermore, this information is used as an additional indicator for limiting. We will give a heuristic strategy how to choose the threshold value such that the accuracy of a reference solution on a uniform discretization is maintained asymptotically. Although there is no rigorous proof available we will verify the reliability of the strategy by numerous computations and parameter studies for different conservations laws, e.g., Burgers equation [1], Euler equations [2], shallow water equations [3], in one and two space dimensions.

[1] N. Gerhard, S. Müller, Adaptive Multiresolution Discontinuous Galerkin Schemes for Conservation Laws: Multi-Dimensional Case,
     Computational and Applied Mathematics, 35(2), 321-349, 2016.

[2] N. Gerhard, F. Iacono, G. May, S. Müller, R. Schäfer. A High-Order Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows, Journal of Scientific Computing, 62(1), 25-52, 2015.

[3] N. Gerhard, D. Caviedes-Voullième, S Müller, G. Kesserwani, Multiwavelet-Based Grid Adaptation with Discontinuous Galerkin Schemes for Shallow Water Equations,     Journal of Computational Physics, 301, 265-288, 2015.