The other one improves the expected accuracy, compared to methods currently in use, with a comparable performance. One requires less computational effort while providing the same degree of accuracy. This new viewpoint is used to develop two new methods for solving the eigenvalue problem. These results enable us to develop a new perspective on the state-of-the-art solution approach for crystalline systems. In this work, we present new theoretical results characterizing the structure of the two forms in the language of non-standard scalar products. One form can be acquired for crystalline systems, another one is more general and can for example be used to study molecules. Additionally, certain definiteness properties typically hold. The matrix always shows a $2\times 2$ block structure. The eigenpairs of the resulting large, dense, structured matrix can be used to compute dielectric properties of the considered crystalline or molecular system. To harness the predictive power of the equation, it is mapped to an eigenvalue problem via an appropriate discretization scheme. without the need for empirical data in the model. The Bethe-Salpeter equation is the state-of-the-art approach to describe these processes from first principles (ab initio), i.e. Optical properties of materials related to light absorption and scattering are explained by the excitation of electrons. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of "morgen" and associated numerical experiments testing model reduction adapted to gas network models. This research resulted in the "morgen" (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. This many-query gas network simulation task can be accelerated by model order reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model reduction algorithms.įor this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and model reduction for nonlinear parametric systems. But, to ensure fulfillment of contracts under these new circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. Case studies were chosen from several domains such as industry, aviation and rail transport.To counter the volatile nature of renewable energy sources, gas networks take a vital role. The cases have been selected by the members of the ESReDA Project Group Dynamic Learning from Accident Investigation (PG LAI), based on their own expertise and preferences and in such a manner that they have become comparable across domains and sectors. This will be done by analysing a diversity of accidents and accident reports. The aim is to analyse what and how lessons are learned and what barriers to learning can be identified. Give an overview of how the ESReDA Cube, resulting from the analysis, may be utilized to identify possibilities to learn from accidents and assist in considering possible recommendations and change needed to prevent future accidents.Report on 5 cases analysed on dynamic learning from accidents and gives an overview of cases of accidents in the context of high risk organizations with an eye on identifying learning barriers and opportunities.This publication, Case study analysis on dynamic learning from accidents, The ESReDA Cube, a method and metaphor for exploring a learning space for safety, aims to:
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