bluuebunny/crossref_metadata_2025_split huggingface dataset:
Sampling‐based model order reduction for stochastic differential equations driven by fractional Brownian motion
Authors: Jamshidi Nahid , Redmann Martin 
Published: May 2023

AbstractIn this paper, we study large‐scale linear fractional stochastic systems representing, e.g., spatially discretized stochastic partial differential equations (SPDEs) driven by fractional Brownian motion (fBm) with Hurst parameter H > ½. Such equations are more realistic in modeling real‐world phenomena in comparison to frameworks not capturing memory effects. To the best of our knowledge, dimension reduction schemes for such settings have not been studied so far.In this work, we investigate empirical reduced order methods that are either based on snapshots (e.g. proper orthogonal decomposition) or on approximated Gramians. In each case, dominant subspaces are learned from data. Such model reduction techniques are introduced and analyzed for stochastic systems with fractional noise and later applied to spatially discretized SPDEs driven by fBm in order to reduce the computational cost arising from both the high dimension of the considered stochastic system and a large number of required Monte Carlo runs.We validate our proposed techniques with numerical experiments for some large‐scale stochastic differential equations driven by fBm.
Efficient model‐correction based reliability analysis of uncertain dynamical systems
Authors: Hirzinger Benjamin , Nackenhorst Udo 
Published: May 2023

AbstractIn this contribution, a model‐correction‐based strategy is applied for efficient reliability analysis of uncertain dynamical systems based on a low‐fidelity (LF) model whose outcomes are corrected in a probabilistic sense to represent the more realistic outcomes of the high‐fidelity (HF) model. In the model‐correction approach utilized, the LF model is calibrated to the HF model close to the so‐called most probable point (MPP) in standard normal space, which allows a more realistic assessment of the considered complex dynamical system. Since only few expensive limit state function evaluations of the HF model are required, an efficient reliability analysis is enabled. In an application example, the LF model describes an existing single span railway bridge modelled as simply supported Euler‐Bernoulli beam subjected to moving single forces representing the axle loads of a moving train. The HF modelling approach accounts for the bridge‐train interaction by modelling the passing train as mass‐spring‐damper (MSD) system, however increasing the computational effort of the limit state function evaluations. The failure probabilities evaluated with the model‐correction approach are contrasted and discussed with the failure probabilities of the sophisticated bridge‐train interaction model. It is shown that the model‐correction‐based approach provides reliable failure probability prediction of the HF model while leading to a significant reduction in computational effort.
Energy‐Momentum‐Entropy consistent time integration of dissipative thermomechanical systems in an extended framework of GENERIC
Authors: Valdes y Beck Vanessa , Betsch Peter 
Published: May 2023

AbstractEnergy‐Momentum‐Entropy (EME) time‐stepping schemes are distinguished by their numerical stable and robust behaviour, which stems from their ability to preserve the structure of the underlying system. In the context of closed dissipative thermomechanical systems, they are energy‐ and momentum‐preserving as well as entropy‐producing. In order to illustrate the qualification of the GENERIC framework for the design of EME integrators, a thermoviscoelastic double pendulum is chosen as discrete model problem to which the discrete gradient operator due to Gonzalez [1] is applied. The acronym GENERIC pertains to ‘General Equation for Non‐Equilibrium Reversible Irreversible Coupling’ and provides by design a thermodynamic admissible mathematical framework for the evolution equations of dissipative thermomechanic systems. This contribution enlightens the incorporation of constraints in the GENERIC formalism and the necessity of a Lyapunov function as stability criterion.
On the influence of the probabilistic microstructural characteristics of glass fiber‐reinforced composites on the wave propagation in GLARE
Authors: Rauter Natalie , Weber Wolfgang E. 
Published: May 2023

AbstractIn an attempt to reduce the crack propagation speed in structures made of fiber‐reinforced composites metal layers are added to the laminate forming a new group of materials, so‐called fiber metal laminates. GLARE, a combination of glass fiber‐reinforced polymer and aluminum, is well‐known and frequently used in the aeronautical industry. One major drawback of such materials is their susceptibility to impact damage, which is not detectable by visual inspections. Hence, an adequate structural health monitoring technique to detect interlaminar damage like delaminations is essential for components made from fiber metal laminates. One approach here is the use of guided ultrasonic waves because they travel long distances without substantial damping and cover the whole thickness of thin‐walled structures. However, the probabilistic microstructure causes a continuous mode conversion in wave guides made from fiber‐reinforced composites. This significantly influences the signal processing and as a consequence, the interpretation of captured time signals. This phenomenon is induced by the random spatial distribution of the fibers in the matrix material, leading to an ongoing excitation of new wave modes within the propagating S0 wave mode. In this research, the effect is studied for the wave propagation in GLARE 3/2‐0.4. Therefore, the spatial distribution of the transverse YOUNG's modulus for the glass fiber‐reinforced layers is represented by homogeneous second‐order GAUSSian random fields. Afterwards, the propagation of the guided ultrasonic wave is simulated numerically. The results reveal that the continuous mode conversion is not only observable within the glass fiber‐reinforced polymer layers but also at the top and bottom surface and hence, within the isotropic layers. This holds for the wave propagation both in and perpendicular to the fiber orientation of the glass fiber‐reinforced polymer layers.
Numerical relaxation limit and outgoing edges in a central scheme for networked conservation laws
Authors: Kolbe Niklas 
Published: May 2023

AbstractA recently introduced scheme for networked conservation laws is analyzed in various experiments. The scheme makes use of a novel relaxation approach that governs the coupling conditions of the network and does not require a solution of the Riemann problem at the nodes. We numerically compare the dynamics of the solution obtained by the scheme to solutions obtained using a classical coupling condition. In particular, we investigate the case of two outgoing edges in the Lighthill–Whitham–Richards model of traffic flow and in the Buckley–Leverett model of two phase flow. Moreover, we numerically study the asymptotic preserving property of the scheme by comparing it to its preliminary form before the relaxation limit in a 1‐to‐1 network.
A data‐driven solver scheme for inelastic problems
Authors: Prume Erik , Stainier Laurent , Ortiz Michael , Reese Stefanie 
Published: May 2023

AbstractWe review the data‐driven computing paradigm for inelastic problems. We extend an efficient graph search algorithm for the data search by thermodynamic constraints and a rate independent history parametrization based on the mechanical work increment. In addition, we propose a strategy how to use commercial solvers in the framework. Finally, we demonstrate the proposed method with a numerical example featuring 2‐d continuum plasticity.
Development of a FEM tool to calculate the dispersion curves of 2D phononic structures
Authors: Nies Christopher , Mellmann Marius , Ankay Benjamin , Zhang Chuanzeng 
Published: May 2023

AbstractThe control and manipulation of acoustic and elastic waves is an important research topic in engineering sciences. In acoustics, an adequate combination of different materials can contribute to an efficient and broadband sound isolation. The realization of a vibration‐free environment for high‐precision mechanical systems in laboratories and measuring environments is also desirable in many practical cases. Therefore, advanced materials and structures with outstanding acoustic and elastodynamic properties are of great importance in engineering applications. In this paper, a numerical tool based on the finite element method (FEM) is developed for computing the dispersion relations or band structures of two‐dimensional (2D) phononic crystals (PCs) composed of an elastic matrix and periodically distributed cylindrical inclusions.
A two‐dimensional analysis of the influence of delamination on the wave propagation in a fiber metal laminate
Authors: Nikiema Wendwoga Fulgence , Rauter Natalie , Lammering Rolf 
Published: May 2023

AbstractStructural Health Monitoring (SHM) of composite materials using Guided Ultrasonic Wave (GUW) represent a central research topic with a large range of application fields. One major concern in this context is the detection of hidden inter‐laminar damage such as delaminations in composites, as these cannot be detected by visual inspection [1]. Fiber Metal Laminate (FML) consist of different layers of metal (e.g. steel) and Fiber Reinforced Polymer (FRP) stacked on top of each other and belong to a new type of material system that has been insufficiently explored in the context of damage detection using GUW. Following the objective of damage detection using GUW, two dimensional numerical simulations of the wave propagation in FML composed of layers made from steel and Carbon Fiber Reinforced Polymer (CFRP) are conducted. In order to properly identify and describe the different phenomena occurring when the GUW encounter a delamination three kind of numerical models were considered: undamaged plate, damaged plate with symmetrically and off‐center placed delamination. As far as the modeling of delaminations, the present work is restricted to a zero‐thickness‐delamination generated by de‐merging nodes at the interface of the layers. Mode‐selective excitation (fundamental symmetric and anti‐symmetric mode wave) of the models was then applied and the B‐scan representations of the in‐plane and out‐of‐plane displacement fields were generated and compared. Effects such as reflection, transmission and mode conversion of the main wave are observed and analyzed. Thus, a singular phenomenon as the trapped mode wave can be clearly observed and interpreted.
On the Systematic Construction of Lyapunov Functions for Polynomial Systems
Authors: Natkowski Lars , Gerbet Daniel , Röbenack Klaus 
Published: May 2023

AbstractLyapunov functions are a widely used tool to evaluate stability properties of nonlinear dynamical systems' equilibria. In this paper quantifier elimination is used to construct Lyapunov functions for polynomial systems from a parametric ansatz. Because the existing algorithms for quantifier elimination are inherently computationally expensive, a strategy is to simplify the quantifier elimination problem beforehand. A method is presented that may help simplifying the problem of finding suitable Lyapunov functions by deriving easier to evaluate necessary conditions. Finally, the introduced method is applied to an example system to show local asymptotic stability of an equilibrium point by constructing a Lyapunov function.
DoD Stabilization of linear hyperbolic PDEs on general cut‐cell meshes
Authors: Birke Gunnar , Engwer Christian , May Sandra , Streitbürger Florian 
Published: May 2023

AbstractStandard numerical methods for hyperbolic PDEs require for stability a CFL‐condition which implies that the time step size depends on the size of the elements of the mesh. On cut‐cell meshes, elements can become arbitrarily small and thus the time step size cannot take the size of small cut‐cells into account but has to be chosen based on the background mesh elements.A remedy for this is the so called DoD (domain of dependence) stabilization for which several favorable theoretical and numerical properties have been shown in one and two space dimensions [4, 9]. Up to now the method is restricted to stabilization of cut‐cells with exactly one inflow and one outflow face, i.e. triangular cut‐cells with a no‐flow face (see [4]).We extend the DoD stabilization to cut‐cells with multiple in‐ and outflow faces by properly considering the flow distribution inside the cut‐cell. We further prove L2‐stability for the semi‐discrete formulation in space and present numerical results to validate the proposed extension.
Modeling and numerical simulation of flow processes of wood‐polymer composites
Authors: Liese Fabian , Wünsch Olaf 
Published: May 2023

AbstractThe combination of natural fibers and polymers is finding expanding application in a range of industrial branches, and knowledge of the material behavior is essential for further improving the products and the processing procedure. In this work, the material behavior of wood‐polymer composites (WPC) will be modeled and numerical simulations will be used to investigate the flow behavior. By means of rheological measurements, a shear thinning flow behavior of the composite can be determined, which is also often taken into account in the numerical simulation of WPC processing tools. Increasing shear viscosity and a formation of a yield point with increasing wood content can be observed. However, in addition to the shear‐dominant deformation states, noticeable strain deformations also occur due to cross‐sectional changes. In order to experimentally investigate and model the behavior of WPC under strain, this work involves measurements on hyperbolic dies in which a uniaxial strain state is present and extensional viscosity can be derived from this. Different boundary conditions such as noSlip, navierSlip and full slip are investigated in the simulations. In addition, during the extrusion of WPC, wall shear stresses of about 0.1 MPa and above can be observed. Measurements in a high‐pressure capillary rheometer allow the wall slip velocity to be measured as a function of the wall shear stress at different wood contents. The wall slip behavior is modeled and taken into account accordingly as a boundary condition in the numerical simulations using OpenFOAM [8].
A Reinforcement Learning Based Slope Limiter for Second‐Order Finite Volume Schemes
Authors: Schwarz Anna , Keim Jens , Chiocchetti Simone , Beck Andrea 
Published: May 2023

AbstractHyperbolic equations admit discontinuities in the solution and thus adequate and physically sound numerical schemes are necessary for their discretization. Second‐order finite volume schemes are a popular choice for the discretization of hyperbolic problems due to their simplicity. Despite the numerous advantages of higher‐order schemes in smooth regions, they fail at strong discontinuities. Crucial for the accurate and stable simulation of flow problems with discontinuities is the adequate and reliable limiting of the reconstructed slopes. Numerous limiters have been developed to handle this task. However, they are too dissipative in smooth regions or require empirical parameters which are globally defined and test case specific. Therefore, this paper aims to develop a new slope limiter based on deep learning and reinforcement learning techniques. For this, the proposed limiter is based on several admissibility constraints: positivity of the solution and a relaxed discrete maximum principle. This approach enables a slope limiter which is independent of a manually specified global parameter while providing an optimal slope with respect to the defined admissibility constraints. The new limiter is applied to several well‐known shock tube problems, which illustrates its broad applicability and the potential of reinforcement learning in numerics.
Patient‐specific simulation of brain tumour growth and regression
Authors: Suditsch Marlon , Ricken Tim , Wagner Arndt 
Published: May 2023

AbstractThe medical relevance of brain tumours is characterised by its locally invasive and destructive growth. With a high mortality rate combined with a short remaining life expectancy, brain tumours are identified as highly malignant. A continuum‐mechanical model for the description of the governing processes of growth and regression is derived in the framework of the Theory of Porous Media (TPM). The model is based on medical multi‐modal magnetic resonance imaging (MRI) scans, which represent the gold standard in diagnosis. The multi‐phase model is described mathematically via strongly coupled partial differential equations. This set of governing equations is transformed into their weak formulation and is solved with the software package FEniCS. A proof‐of‐concept simulation based on one patient geometry and tumour pathology shows the relevant processes of tumour growth and the results are discussed.
Analysis of the remote laser cutting process induced damage in carbon fibre reinforced polymers
Authors: Schmidt Benjamin , Husert Markus , Hollmer Katharina , Zimmermann Martina , Kästner Markus 
Published: May 2023

AbstractIn machining technologies for fibre reinforced polymers, remote laser cutting plays a special role as it can minimize the drawbacks of conventional laser cutting methods, in particular thermally induced damage such as charred edges and matrix evaporation. In this contribution, a thermal simulation model for the remote laser cutting process is presented. With the aim of a universally applicable model that works independently of the selected carbon fibres, matrix system, and fibre content, the effective thermal material parameters are calculated with a rule of mixture from the microscopic parameters for fibre, matrix, and process gas. The evaporation of matrix and fibre material is modelled with phase transitions. The moving laser spot is modelled with a Gaussian distribution as a heat input on the upper side. The emerging process gas is assumed to absorb a part of the laser power according to the Lambert‐Beer law.
On the numerical treatment of heat sources in laser beam welding processes
Authors: Hartwig Philipp , Scheunemann Lisa , Schröder Jörg 
Published: May 2023

AbstractLaser beam welding is a contact free fusion technique which has gained importance during the last years due to rising need for automatization in industrial processes. However, a well‐known problem is the formation of solidification cracks in the rear region of the melting pool. In order to investigate the formation of solidification cracks which is highly dependent on the chemical composition, the welding speed, weld beam intensity and the resulting temperature gradient in the material, the modeling of the laser beam as a heat source plays a prominent role. In order to investigate heat sources in laser beam welding, this contribution compares two methods, the Goldak model and a second model that mimics the region of the melt pool with the idea of an isothermal region. Suitable boundary value problems to show the differences of the methods are demonstrated.
Computational challenges in mixed‐dimensional beam/solid coupling
Authors: Firmbach Max , Steinbrecher Ivo , Popp Alexander , Mayr Matthias 
Published: May 2023

AbstractThe simulation of mixed‐dimensional couplings poses a variety of computational challenges in order to enable accurate modeling and efficient solution of problems in science, engineering and biomedicine. In this contribution, we study computational challenges and bottlenecks in the mixed‐dimensional modeling of coupled beam/solid systems and discuss possible remedies to allow large‐scale computations of applications in structural engineering. In particular, we address questions of memory consumption in geometric search operations, partitioning for computations on parallel clusters and performance of the linear solver by suitable preconditioning techniques.
Adaptive strategies based on equilibration for the Biot equations
Authors: Bertrand Fleurianne , Brodbeck Maximilian 
Published: May 2023

AbstractThe hypercircle theorem leads to a posteriori error estimates for the three‐field variational formulation of the Biot problem involving displacements, total pressure and fluid pressure. Based thereon, adaptive strategies can be constructed. In particular, the error estimator is derived on the basis of Hdiv‐conforming reconstructions of stress and flux approximations while the symmetry of the reconstructed stress is allowed to be satisfied only weakly. The reconstructions can therefore be performed locally on a set of vertex patches. The local nature of the reconstruction leads to two different possible adaptive strategies. In this paper, we review these two different adaptive strategies for the Biot problem. Numerical experiments underline the differences between the two strategies.
Consistent Euler‐Bernoulli beam theory in gradient elasticity: Two equivalent formulations of a simple constitutive law
Authors: Üngör Özer , Broese Carsten , Müller Ralf , Sideris Stergios-Alexandros , Tsakmakis Charalampos 
Published: May 2023

AbstractThe classical Euler‐Bernoulli beam theory in elastostatic is known to be inconsistent, since the equilibrium equations are not satisfied in local form. Recently, it has been shown that the theory will become consistent if one assumes elastic anisotropy subject to internal constraints. This is shown to be true even for a simple gradient elasticity law. Normally, beam bending is considered as one‐dimensional problem. We summarise in the present paper the results of a previous work concerning two well‐known one‐dimensional formulations of Euler‐Bernoulli beam and gradient elastic material behaviour. The two formulations appear to be different because the functional of internal forces includes the cross‐sectional area of the beam in one but not in the other. It is shown that the two one‐dimensional formulations can be derived as special cases of a three‐dimensional simple gradient elasticity model and that they are equivalent to each other.
Gaussian fluctuations around limit measures of generalized SQG point vortices
Authors: Geldhauser Carina , Romito Marco 
Published: May 2023

AbstractWe report on recent results on generalized surface quasi‐geostropic point vortex models. The statistical physics of these models is particularly interesting, as their mean‐field limit is a steady solution of the gSQG PDE. We present a central limit theorem‐type result for gSQG point votex models and make a comparison with results for Euler point vortex models.
Repulsion dynamics for uniform Pareto front approximation in multi‐objective optimization problems
Authors: Borghi Giacomo 
Published: May 2023

AbstractScalarization allows to solve a multi‐objective optimization problem by solving many single‐objective sub‐problems, uniquely determined by some parameters. In this work, several adaptive strategies to select such parameters are proposed in order to obtain a uniform approximation of the Pareto front. This is done by introducing a heuristic dynamics where the parameters interact through a binary repulsive potential. The approach aims to minimize the associated energy potential which is used to quantify the diversity of the computed solutions. A stochastic component is also added to overcome non‐optimal energy configurations. Numerical experiments show the validity of the proposed approach for bi‐ and tri‐objectives problems with different Pareto front geometries.