Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems

We propose a new geometrically unfitted finite element method based on discontinuous Trefftz ansatz spaces. Trefftz methods allow for a reduction in the number of degrees of freedom in discontinuous Galerkin methods, thereby, the costs for solving arising linear systems significantly. This work shows that they are also an excellent way to reduce the number of degrees of freedom in an unfitted setting. We present a unified analysis of a class of geometrically unfitted discontinuous Galerkin methods with different stabilisation mechanisms to deal with small cuts between the geometry and the mesh. We cover stability and derive a-priori error bounds, including errors arising from geometry approximation for the class of discretisations for a model Poisson problem in a unified manner. The analysis covers Trefftz and full polynomial ansatz spaces, alike. Numerical examples validate the theoretical findings and demonstrate the potential of the approach

When Robots Write the News: A Guideline Based Interview Study on Opportunities and Risks of Using Artificial Intelligence in Political Reporting in Germany and the U.S.

Artificial Intelligence (AI) is increasingly being implemented in journalism, possibly leading to various fundamental changes within the field. Especially the forerunner countries U.S. and Germany make use of the technologies in several sub-sectors of reporting. While pioneer-studies exploring said implementation have focused on audience, as well as practitioners’ perceptions of AI, a focus on the democratically crucial political journalism is lacking. Therefore, the given paper investigates how those working in the journalistic field in Germany and the U.S. evaluate AI-usage in political reporting. Scopes, contexts, and opportunities, as well as risks of the technologies are considered. Eleven interviews with experts from leading news organizations were conducted and analyzed using a qualitative content analysis, focusing on comparisons between the two countries. Results show varying strategies of AI implementation within the two countries, with election coverage being the predominant political topic reported on with the help of AI. Furthermore, the findings show that AI could possibly free journalists from routine tasks, and allows for more in-depth and large-scale research, which in turn could lead to an increase in the qualitative standard of political journalism. However, journalists also point towards ethical and economic concerns. Considering the results, directions for future research and the practice of journalism are discussed

Multiple Scenario Generation of Subsurface Models:Consistent Integration of Information from Geophysical and Geological Data throuh Combination of Probabilistic Inverse Problem Theory and Geostatistics

Neutrinos with energies above 1017 eV are detectable with the Surface Detector Array of the Pierre Auger Observatory. The identification is efficiently performed for neutrinos of all flavors interacting in the atmosphere at large zenith angles, as well as for Earth-skimming \u3c4 neutrinos with nearly tangential trajectories relative to the Earth. No neutrino candidates were found in 3c 14.7 years of data taken up to 31 August 2018. This leads to restrictive upper bounds on their flux. The 90% C.L. single-flavor limit to the diffuse flux of ultra-high-energy neutrinos with an E\u3bd-2 spectrum in the energy range 1.0 7 1017 eV -2.5 7 1019 eV is E2 dN\u3bd/dE\u3bd < 4.4 7 10-9 GeV cm-2 s-1 sr-1, placing strong constraints on several models of neutrino production at EeV energies and on the properties of the sources of ultra-high-energy cosmic rays

Geometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains

In this paper, we propose new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space and time. As a model problem, the convection-diffusion problem on a moving domain is studied. For geometrically higher order accuracy, we apply a parametric mapping on a background space-time tensor-product mesh. Concerning discretisation in time, we consider discontinuous Galerkin, as well as related continuous (Petrov-)Galerkin and Galerkin collocation methods. For stabilisation with respect to bad cut configurations and as an extension mechanism that is required for the latter two schemes, a ghost penalty stabilisation is employed. The article puts an emphasis on the techniques that allow to achieve a robust but higher order geometry handling for smooth domains. We investigate the computational properties of the respective methods in a series of numerical experiments. These include studies in different dimensions for different polynomial degrees in space and time, validating the higher order accuracy in both variables

Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems

We propose a new geometrically unfitted finite element method based on discontinuous Trefftz ansatz spaces. Trefftz methods allow for a reduction in the number of degrees of freedom in discontinuous Galerkin methods, thereby, the costs for solving arising linear systems significantly. This work shows that they are also an excellent way to reduce the number of degrees of freedom in an unfitted setting. We present a unified analysis of a class of geometrically unfitted discontinuous Galerkin methods with different stabilisation mechanisms to deal with small cuts between the geometry and the mesh. We cover stability and derive a-priori error bounds, including errors arising from geometry approximation for the class of discretisations for a model Poisson problem in a unified manner. The analysis covers Trefftz and full polynomial ansatz spaces, alike. Numerical examples validate the theoretical findings and demonstrate the potential of the approach