Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

Please note that all times are shown in the time zone of the conference. The current conference time is: 29th Nov 2022, 06:08:34am CET

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Session Overview
MS 11b: recent developments in high-order methods for time-dependent problems
Tuesday, 13/July/2021:
12:00pm - 2:00pm

Session Chair: Reza Abedi
Session Chair: Tamas Horvath
Virtual location: Zoom 1

Session Abstract

Both hyperbolic and parabolic time-dependent problems have been of great interest in the

applied mathematics and engineering communities as they cover a wide range of applications.

To improve the accuracy both in space and time, several high order methods have been

developed in the recent years.

However, with today's exascale computing architectures we also aim to solve these prob-

lems eectively, not just accurately. Many methods have achieved great success in paral-

lelization, such as parallel-in-time and space-time methods, among many others.

In this minisymposium we aim to present the state-of-the-art theoretical and application

based results, and bring the members of this community closer to each other. Methods

of interest include, but are not limited to, space-time discontinuous Galerkin, space-time

nite element, implicit-explicit methods, asynchronous, parallel-in-time and adaptive mesh


Presentations regarding exascale or highly parallel implementations (such as application

of GPU platforms) are also welcomed.

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12:00pm - 12:30pm

A p-adaptive discontinuous Galerkin method with hp-shock capturing

Pascal Mossier1, Andrea Beck2, Claus-Dieter Munz1

1University of Stuttgart, Germany; 2Otto von Guericke University Magdeburg

In this talk, we present a novel hybrid Discontinuous Galerkin scheme with hp-adaptive capabilities for the compressible Euler equations. In smooth regions, an efficient and accurate discretization is achieved via local p-adaptation. At strong discontinuities and shocks, a finite volume scheme on an h-refined element-local subgrid gives robustness. Thus, we obtain a hp-adaptive scheme that exploits both the high convergence rate and efficiency of a p-adaptive high order scheme as well as the stable and accurate shock capturing abilities of a low order finite volume scheme, but avoids the inherent resolution loss through h-refinement. A single a priori indicator, based on the modal decay of the local polynomial solution representation, is used to distinguish between discontinuous and smooth regions and control the p-refinement. Our method is implemented as an extension to the open source software FLEXI. Hence, the efficient implementation of the method for high performance computers was an important criterion during the development. The efficiency of our adaptive scheme is demonstrated for a variety of test cases, where results are compared against non adaptive simulations. Our findings suggest that the proposed adaptive method produces comparable or even better results with significantly less computational costs.

12:30pm - 1:00pm

An arbitrary order variational discretization for Maxwell's equations in nonlinear media

Herbert Egger, Vsevolod Shashkov

TU Darmstadt, Germany

We consider the propagation of electromagnetic waves in nonlinear media. A particular formulation based on magnetic vector potential and electric displacement is used which reveals an underlying gradient flow structure. This geometric form can be preserved exactly under Galerkin projection in space and Petrov-Galerkin discretization in time. The resulting implicit time-integration schemes can be constructed for any desired order of approximation and they exactly preserve the energy-dissipation identity of the system. This leads to an excellent long-time behavour which is demonstrated by numerical tests.

1:00pm - 1:30pm

Space-time Galerkin method for cross-diffusion systems

Marcel Braukhoff1, Ilaria Perugia2, Paul Stocker2

1Heinrich-Heine-Universität Düsseldorf; 2University of Vienna

Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are most commonly used to describe dynamical processes in chemical concentrations and cell biology. We present a space-time approach to the proof of existence of bounded weak solutions of cross-diffusion systems, making use of the system's entropy to examine long-term behavior and show that the solution is nonnegative, when the maximum principle is not available. This approach naturally gives rise to a novel space-time Galerkin method that conserves the structure of the problem. We present numerical results for porous medium, Maxwell-Stefan, and Fisher-KPP equation.

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