arXiv subjects

Michael Fleck

Publications and source records attributed to Michael Fleck.

6 recordsLinked to original sources

arXiv2023

An Application Driven Method for Assembling Numerical Schemes for the Solution of Complex Multiphysics Problems

Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely remains the status quo for scientists and engineers focusing on applying simulation tools to specific problems in practice. We attribute this growing technical gap to the increasing complexity and knowledge required to pick and assemble state-of-the-art methods. Thus, with this work, we initiate an effort to build a common taxonomy for the most popular grid-based approximation schemes to draw comparisons regarding accuracy and computational efficiency. We then build upon this foundation and introduce a method to systematically guide an application expert through classifying a given PDE problem setting and identifying a suitable numerical scheme. Great care is taken to ensure that making a choice this way is unambiguous, i.e. the goal is to obtain a clear and reproducible recommendation. Our method not only helps to identify and assemble suitable schemes but enables the unique combination of multiple methods on a per-field basis. We demonstrate this process and its effectiveness using different model problems, each comparing the resulting numerical scheme from our method with the next best choice. For both the Allen Cahn and advection equations, we show that substantial computational gains can be attained for the recommended numerical methods regarding accuracy and efficiency. Lastly, we outline how one can systematically analyze and classify a coupled multiphysics problem of considerable complexity with 6 different unknown quantities, yielding an efficient, mixed discretization that in configuration compares well to high-performance implementations from the literature.

math.NA↗

arXiv2023

wav2vec and its current potential to Automatic Speech Recognition in German for the usage in Digital History: A comparative assessment of available ASR-technologies for the use in cultural heritage contexts

In this case study we trained and published a state-of-the-art open-source model for Automatic Speech Recognition (ASR) for German to evaluate the current potential of this technology for the use in the larger context of Digital Humanities and cultural heritage indexation. Along with this paper we publish our wav2vec2 based speech to text model while we evaluate its performance on a corpus of historical recordings we assembled compared against commercial cloud-based and proprietary services. While our model achieves moderate results, we see that proprietary cloud services fare significantly better. As our results show, recognition rates over 90 percent can currently be achieved, however, these numbers drop quickly once the recordings feature limited audio quality or use of non-every day or outworn language. A big issue is the high variety of different dialects and accents in the German language. Nevertheless, this paper highlights that the currently available quality of recognition is high enough to address various use cases in the Digital Humanities. We argue that ASR will become a key technology for the documentation and analysis of audio-visual sources and identify an array of important questions that the DH community and cultural heritage stakeholders will have to address in the near future.

eess.AS↗

arXiv2022

Sharp phase-field modeling of isotropic solidification with a super efficient spatial resolution

The numerical resolution efficiency of phase-field models is limited by grid friction, grid anisotropy and pinning. The 1D sharp phase-field model eliminates grid friction and pinning by a global restoration of Translational Invariance (TI) in the discretized phase-field equation (Phys. Rev. Lett. 121, 025501, 2018). In 3D global TI restricts the beneficial modeling properties to a finite number of fixed interface orientations. We propose an accurate scheme to restore TI locally in the local interface normal direction. At one-grid-point interface resolutions, the new model captures the formation of isotropic seaweed structures without spurious dendritic selection by grid anisotropy.

cond-mat.mtrl-sci↗

arXiv2020

Phase-field modeling of $\gamma/\gamma''$ microstructure formation in Ni-based superalloys with high $\gamma''$ volume fraction

The excellent mechanical properties of the Ni-based superalloy IN718 mainly result from coherent $\gamma''$ precipitates. Due to a strongly anisotropic lattice misfit between the matrix and the precipitate phase, the particles exhibit pronounced plate-shaped morphologies. Using a phase-field model, we investigate various influencing factors that determine the equilibrium shapes of $\gamma"$ precipitates, minimizing the sum of the total elastic and interfacial energy. Upon increasing precipitate phase fractions, the model predicts increasingly stronger particle-particle interactions, leading to shapes with significantly increased aspect ratios. Matching the a priori unknown interfacial energy density to fit experimental $\gamma"$ shapes is sensitive to the phase content imposed in the underlying model. Considering vanishing phase content leads to 30% lower estimates of the interfacial energy density, as compared to estimates based on realistic phase fractions of 12%. We consider the periodic arrangement of precipitates in different hexagonal and rectangular superstructures, which result from distinct choices of point-symmetric and periodic boundary conditions. Further, non-volume conserving boundary conditions are implemented to compensate for strains due to an anisotropic lattice mismatch between the $\gamma$ matrix and the $\gamma''$ precipitate. As compared to conventional boundary conditions, this specifically tailored simulation configuration does not conflict with the systems periodicity and provides substantially more realistic total elastic energies at high precipitate volume fractions. The energetically most favorable superstructure is found to be a hexagonal precipitate arrangement.

cond-mat.mtrl-sci↗

arXiv2019

Frictionless motion of diffuse interfaces by sharp phase-field modeling

Diffuse interface descriptions offer many advantages for the modeling of microstructure evolution. However, the numerical representation of moving diffuse interfaces on discrete numerical grids involves spurious grid friction, which limits the overall performance of the model in many respects. Interestingly, this intricate and detrimental effect can be overcome in Finite Difference (FD) and Fast Fourier Transformation (FFT) based implementations by employing the so-called Sharp Phase-Field Method (SPFM). The key idea is to restore the discretization induced broken Translational Invariance (TI) in the discrete phase-field equation by using analytic properties of the equilibrium interface profile. We proof that this method can indeed eliminate spurious grid friction in the three dimensional space. Focussing on homogeneous driving forces, we quantitatively evaluate the impact of spurious grid friction on the overall operational performance of different phase-field models. We show that the SPFM provides superior degrees of interface isotropy with respect to energy and kinetics. The latter property enables the frictionless motion of arbitrarily oriented diffuse interfaces on a fixed 3D grid.

cond-mat.mtrl-sci↗

arXiv2018

Phase-field modeling of Li-insertion kinetics in single LiFePO\textsubscript{4}-nano-particles for rechargeable Li-ion battery application

We develop a continuum phase-field model for the simulation of diffusion limited solid-solid phase transformations during lithium insertion in LiFePO4-nano-particles. The solid-solid phase boundary between the LiFePO4 (LFP)-phase and the FePO4 (FP)-phase is modeled as a diffuse interface of finite width. The model-description explicitly resolves a single LiFePO4-particle, which is embedded in an elastically soft electrolyte-phase. Furthermore, we explicitly include anisotropic (orthorhombic) and inhomogeneous elastic effects, resulting from the coherency strain, as well as anisotropic (1D) Li-diffusion inside the nano-particle. The effect of the nano-particle's size on the kinetics of FP to LFP phase transformations is investigated by means of both model. Both models predict a substantial increase in the steady state transformation velocity as the particle-size decreases down to dimensions that are comparable with the width of the interface between the FP and the LFP-phase. However, the extra kinetic parameter of the Allen-Cahn-type description may be used to reduce the strength of the velocity-increase with the decreasing particle size. Further, we consider the influence of anisotropic and inhomogeneous elasticity on the lithiation-kinetics within a rectangularly shaped LiFePO4-particle embedded in an elastically soft electrolyte. Finally, the simulation of equilibrium shapes of LiFePO4-particles is discussed. Within a respective feasibility study, we demonstrate that also the simulation of strongly anisotropic particles with aspect ratios up to 1/5 is possible.

cond-mat.mtrl-sci↗