Fraunhofer Institute for Industrial Mathematics

Abstract Large linear systems are ubiquitous in modern computational science and engineering. Their efficient solution is frequently challenging, especially in conjunction with problems described by parametric PDEs, where many such systems have to be solved. The primary approach for solving large linear systems is the use of Krylov subspace iterative methods with well-designed preconditioners. Recently, graph neural networks (GNNs) have been used in conjunction with solving parametric PDEs, and have been shown to be promising tool for designing preconditioners. Nevertheless, the GNN-based preconditioners reported in the literature have worse effect on system’s spectrum than analogous preconditioners from classical linear algebra. Here we employ well-established preconditioners from linear algebra as starting point for training GNN to obtain preconditioners that yield a more substantial reduction in the condition number of the systems when compared to classical preconditioners. Numerical experiments demonstrate the efficiency of our approach in comparison to classical and known neural network-based methods for parametric PDEs. In addition, a heuristic justification for the loss function employed in this study is provided, and we demonstrate that preconditioners obtained by learning with this loss function reduce the condition number in a way that is more desirable for the conjugate gradient iterative method.

Abstract Understanding the vaporisation of cutting fluids in machining processes is essential for improving cooling effectiveness and tool life. In order to gain basic knowledge regarding vapour formation, this study presents a combined experimental and numerical investigation of submerged turning of C45 and Inconel 718. High-speed imaging is employed to qualitatively visualise vapour phenomena, while simulations using the Finite Pointset Method (FPM) extend existing models to incorporate a physically realistic vapour phase and fluid–structure interaction. Jet cooling simulations capture the intermittent nature of vapour formation, with shorter time intervals and larger affected areas at higher wall temperatures. Increasing surface velocity shifts vaporisation farther from the stagnation point. Machining simulations indicate that cutting fluids tend to vaporise at a certain distance from the chip root rather than directly at it, while submerged machining experiments reveal a stable vapour region on the chip surface. These results advance the understanding of cooling performance and heat transfer in metal cutting and contribute to the development of more accurate simulation tools for process and tool optimization.

Abstract The conversion of processes controlled by human expertise and know-how into automated operations is the goal of a wide range of modern research. This study reports on a blind test in which twelve unknown samples were analyzed by human experts and an AI system developed to check the genera of hardwoods used in paper production. Trained to detect hardwood cells in microscopic images of maceration slides, it assigns them to the nine most commonly used hardwood species. Softwoods were also added to the samples, to make the test as realistic as possible. Human experts achieved an accuracy of 0.96 for recognizing a genus contained in a sample. The two-stage machine recognition system achieved an accuracy of 0.79 at the defined threshold values of 0.7 for object recognition and 0.75 for genus probability. Human experts failed to recognize some genera contained in the samples, whereas the AI models did not miss any genus at these thresholds. A comparison of the results revealed the strengths and weaknesses of the independent methods. This study is an important step towards optimizing the automated image recognition system developed to support the implementation of the European Union Deforestation Regulation (EUDR) with regard to deforestation-free products/supply chains.

Increasing demands for resource efficiency as well as cost and time reduction require new innovative approaches in terms of an accelerated and reliable provision of fatigue data. A promising approach is given by the combination of non-destructive testing methods such as IR thermography or electrical resistance with conventional destructive testing (constant amplitude tests and load increase tests). This synergy enables a material-response related evaluation of the material degradation based on a reduced number of specimens. Because of the decreased number of fatigue specimens, a reliable assessment of different failure probabilities becomes challenging, creating a gap between accelerated lifetime prediction and sufficient statistical validation, which must be closed by the integration of mathematical methods. This paper addresses two key research objectives. First, a mathematical and material-independent algorithm is presented which enables an accelerated and automated estimation of the fatigue strength of materials. Besides that, the main focus is on the statistical provision of S-N curve parameters based on existing lifetime prediction methods. Therefore, the quality of virtually determined numbers of cycles to failure is compared with conventionally performed constant amplitude tests. Furthermore, the newly introduced Splitted Parameter Approach enables a quantitative statement to be made regarding the reliability of the parameters of the virtual S-N curve. The presented methods are developed on a 20MnMoNi5-5 steel with a ferritic-bainitic microstructure. • Short-time S-N curve prediction based on one load increase test. • Development of a novel 3-step algorithm for automated estimation of fatigue strength. • NDT-monitored fatigue tests combined with mathematics for reliable fatigue assessment. • Reliable parameter prediction based on an innovative Splitted Parameter Approach.

Abstract This paper presents an overview about the state of the art in the development of structured packings for distillation applications. The focus is on highlighting different approaches, including heuristic development cycles, the development of new packing structures, 3D printing as a tool for manufacturing, and computational fluid dynamics to determine the packings’ performance through use of simulations. Special attention is given to the recently upcoming application of shape optimization algorithms to improve structured packings. It is evaluated how this approach fits into the conventional development process, what the limitations of current shape optimization approaches are, and how they can impact the performance of structured packings. Finally, an opinion about the next steps in the development of shape optimization algorithms for packing development is given.

The next generation of wireless mobile networks will be driven by software and infrastructure virtualization. At the same time, the underlying hardware will become more diverse. Edge, intermediate and central network nodes will allow distributed deployments of never seen before scale. Non-terrestrial networks, nomadic networks and networks in networks promise more dynamicity, changing their topologies over time in predictable and unpredictable ways. To handle the complexity and dynamicity, a highly flexible and adaptable network is required. The key enablers of this complex digital communication system will be programmable infrastructures. From programmable access and flexible backhauls to zero-touch, adaptable and resilient control planes, we conducted research into advanced programmability at different layers of the network, within the Open6GHub project. In this article, we present innovative solutions for advanced programmable network infrastructure and show why they are essential for our vision of the programmable infrastructure of future wireless mobile networks.

ABSTRACT We apply the discrete mechanics approach to the discretisation of geometrically exact Cosserat rods. We consider discrete Cosserat rods defined on a vertex (or nodal) grid, as well as on a staggered grid, and provide a review and update of the results already obtained in Part I for the nodal model variant and, for the first time, present a detailed version for the staggered variant. Several numerical examples underline the validity of the presented theory.

Techniques like speckle holography and shearography are rarely applied due to the complexity of instrument setup and lack of automated result analysis, despite their potential. By simulating speckle interferometric outcomes, we seek to address these challenges, enabling more efficient measurement processes and paving the way for automated defect recognition. This research focuses on developing a simulation code for speckle interferometric results derived from finite element analyses. The aim is to improve the parameter settings of speckle interferometry measurements and create specific datasets, which will be used to develop machine learning-based methods for automation in series production.