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Network aggregation
(2020)
The simulation of fluid flows is of importance to many fields of application, especially in industry and infrastructure. The modelling equations applied describe a coupled system of non-linear, hyperbolic partial differential equations given by one-dimensional shallow water equations that enable the consistent implementation of free surface flows in open channels as well as pressurised flows in closed pipes. The numerical realisation of these equations is complicated and challenging to date due to their characteristic properties that are able to cause discontinuous solutions.
This textbook contains and explains essential mathematical formulas within an economic context. A broad range of aids and supportive examples will help readers to understand the formulas and their practical applications. This mathematical formulary is presented in a practice-oriented, clear, and understandable manner, as it is needed for meaningful and relevant application in global business, as well as in the academic setting and economic practice.
The lattice Boltzmann method (LBM) is an efficient simulation technique for computational fluid mechanics and beyond. It is based on a simple stream-and-collide algorithm on Cartesian grids, which is easily compatible with modern machine learning architectures. While it is becoming increasingly clear that deep learning can provide a decisive stimulus for classical simulation techniques, recent studies have not addressed possible connections between machine learning and LBM. Here, we introduce Lettuce, a PyTorch-based LBM code with a threefold aim. Lettuce enables GPU accelerated calculations with minimal source code, facilitates rapid prototyping of LBM models, and enables integrating LBM simulations with PyTorch's deep learning and automatic differentiation facility. As a proof of concept for combining machine learning with the LBM, a neural collision model is developed, trained on a doubly periodic shear layer and then transferred to a different flow, a decaying turbulence. We also exemplify the added benefit of PyTorch's automatic differentiation framework in flow control and optimization. To this end, the spectrum of a forced isotropic turbulence is maintained without further constraining the velocity field.
Since being introduced in the sixties and seventies, semi-implicit RosenbrockWanner (ROW) methods have become an important tool for the timeintegration of ODE and DAE problems. Over the years, these methods have been further developed in order to save computational effort by regarding approximations with respect to the given Jacobian [5], reduce effects of order reduction by introducing additional conditions [2, 4] or use advantages of partial explicit integration by considering underlying Runge-Kutta formulations [1]. As a consequence, there is a large number of different ROW-type schemes with characteristic properties for solving various problem formulations given in literature today.
Ein mathematisches Modell zur schiffahrtsbezogenen Wasserstandsvorhersage am Beispiel des Rheins
(1996)
Das Cutting sticks-Problem ist in seiner allgemeinen Formulierung ein NP-vollständiges Problem mit Anwendungspotenzialen im Bereich der Logistik. Unter der Annahme, dass P ungleich NP (P != NP) ist, existieren keine effizienten, d.h. polynomiellen Algorithmen zur Lösung des allgemeinen Problems.
In diesem Papier werden für eine Reihe von Instanzen effiziente Lösungen angegeben.
An Universitäten und Fachhochschulen ist die Mathematik-Ausbildung eines der Nadelöhre für angehende Ingenieurinnen und Ingenieure. Viele Studierende der Ingenieurwissenschaften scheitern in den ersten Studiensemestern an den Anforderungen der Mathematik. Lehrende, Fach- und Hochschuldidaktiker/innen und zunehmend auch Fachvertretungen und Verbände stellen sich die Frage, was an den Fakultäten und Fachbereichen getan werden kann, damit Studierende ihre mathematischen Fähigkeiten vergrößern und den anspruchsvollen Studienweg zur Ingenieurin oder zum Ingenieur meistern können.