08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction(2021) Benacchio, Tommaso; Bonaventura, Luca; Altenbernd, Mirco; Cantwell, Chris D.; Düben, Peter D.; Gillard, Mike; Giraud, Luc; Göddeke, Dominik; Raffin, Erwan; Teranishi, Keita; Wedi, NilsProgress in numerical weather and climate prediction accuracy greatly depends on the growth of the available computing power. As the number of cores in top computing facilities pushes into the millions, increased average frequency of hardware and software failures forces users to review their algorithms and systems in order to protect simulations from breakdown. This report surveys hardware, application-level and algorithm-level resilience approaches of particular relevance to time-critical numerical weather and climate prediction systems. A selection of applicable existing strategies is analysed, featuring interpolation-restart and compressed checkpointing for the numerical schemes, in-memory checkpointing, user-level failure mitigation and backup-based methods for the systems. Numerical examples showcase the performance of the techniques in addressing faults, with particular emphasis on iterative solvers for linear systems, a staple of atmospheric fluid flow solvers. The potential impact of these strategies is discussed in relation to current development of numerical weather prediction algorithms and systems towards the exascale. Trade-offs between performance, efficiency and effectiveness of resiliency strategies are analysed and some recommendations outlined for future developments.Item Open Access Ordinal patterns in clusters of subsequent extremes of regularly varying time series(2020) Oesting, Marco; Schnurr, AlexanderIn this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and the ordinal patterns giving the relative positions of the data points within a cluster. Since these patterns take only the ordinal structure of consecutive data points into account, the method is robust under monotone transformations and measurement errors. We verify the existence of the corresponding limit distributions in the framework of regularly varying time series, develop non-parametric estimators and show their asymptotic normality under appropriate mixing conditions. The performance of the estimators is demonstrated in a simulated example and a real data application to discharge data of the river Rhine.Item Open Access Water structuring induces nonuniversal hydration repulsion between polar surfaces : quantitative comparison between molecular simulations, theory, and experiments(2024) Schlaich, Alexander; Daldrop, Jan O.; Kowalik, Bartosz; Kanduč, Matej; Schneck, Emanuel; Netz, Roland R.Polar surfaces in water typically repel each other at close separations, even if they are charge-neutral. This so-called hydration repulsion balances the van der Waals attraction and gives rise to a stable nanometric water layer between the polar surfaces. The resulting hydration water layer is crucial for the properties of concentrated suspensions of lipid membranes and hydrophilic particles in biology and technology, but its origin is unclear. It has been suggested that surface-induced molecular water structuring is responsible for the hydration repulsion, but a quantitative proof of this water-structuring hypothesis is missing. To gain an understanding of the mechanism causing hydration repulsion, we perform molecular simulations of different planar polar surfaces in water. Our simulated hydration forces between phospholipid bilayers agree perfectly with experiments, validating the simulation model and methods. For the comparison with theory, it is important to split the simulated total surface interaction force into a direct contribution from surface-surface molecular interactions and an indirect water-mediated contribution. We find the indirect hydration force and the structural water-ordering profiles from the simulations to be in perfect agreement with the predictions from theoretical models that account for the surface-induced water ordering, which strongly supports the water-structuring hypothesis for the hydration force. However, the comparison between the simulations for polar surfaces with different headgroup architectures reveals significantly different decay lengths of the indirect water-mediated hydration-force, which for laterally homogeneous water structuring would imply different bulk-water properties. We conclude that laterally inhomogeneous water ordering, induced by laterally inhomogeneous surface structures, shapes the hydration repulsion between polar surfaces in a decisive manner. Thus, the indirect water-mediated part of the hydration repulsion is caused by surface-induced water structuring but is surface-specific and thus nonuniversal.Item Open Access Implications of modeling seasonal differences in the extremal dependence of rainfall maxima(2022) Jurado, Oscar E.; Oesting, Marco; Rust, Henning W.For modeling extreme rainfall, the widely used Brown-Resnick max-stable model extends the concept of the variogram to suit block maxima, allowing the explicit modeling of the extremal dependence shown by the spatial data. This extremal dependence stems from the geometrical characteristics of the observed rainfall, which is associated with different meteorological processes and is usually considered to be constant when designing the model for a study. However, depending on the region, this dependence can change throughout the year, as the prevailing meteorological conditions that drive the rainfall generation process change with the season. Therefore, this study analyzes the impact of the seasonal change in extremal dependence for the modeling of annual block maxima in the Berlin-Brandenburg region. For this study, two seasons were considered as proxies for different dominant meteorological conditions: summer for convective rainfall and winter for frontal/stratiform rainfall. Using maxima from both seasons, we compared the skill of a linear model with spatial covariates (that assumed spatial independence) with the skill of a Brown-Resnick max-stable model. This comparison showed a considerable difference between seasons, with the isotropic Brown-Resnick model showing considerable loss of skill for the winter maxima. We conclude that the assumptions commonly made when using the Brown-Resnick model are appropriate for modeling summer (i.e., convective) events, but further work should be done for modeling other types of precipitation regimes.Item Open Access Bright source of Purcell‐enhanced, triggered, single photons in the telecom C‐band(2023) Nawrath, Cornelius; Joos, Raphael; Kolatschek, Sascha; Bauer, Stephanie; Pruy, Pascal; Hornung, Florian; Fischer, Julius; Huang, Jiasheng; Vijayan, Ponraj; Sittig, Robert; Jetter, Michael; Portalupi, Simone Luca; Michler, PeterSeveral emission features mark semiconductor quantum dots as promising non-classical light sources for prospective quantum implementations. For long-distance transmission and Si-based on-chip processing, the possibility to match the telecom C-band is decisive, while source brightness and high single-photon purity are key features in virtually any quantum implementation. An InAs/InGaAs/GaAs quantum dot emitting in the telecom C-band coupled to a circular Bragg grating is presented here. This cavity structure stands out due to its high broadband collection efficiency and high attainable Purcell factors. Here, simultaneously high brightness with a fiber-coupled single-photon count rate of 13.9 MHz for an excitation repetition rate of 228 MHz (first-lens single-photon collection efficiency ≈17% for NA = 0.6), while maintaining a low multi-photon contribution of g(2)(0) = 0.0052 is demonstrated. Moreover, the compatibility with temperatures of up to 40 K attainable with compact cryo coolers, further underlines the suitability for out-of-the-lab implementations.Item Open Access Irradiation-dependent topology optimization of metallization grid patterns and variation of contact layer thickness used for latitude-based yield gain of thin-film solar modules(2022) Zinßer, Mario; Braun, Benedikt; Helder, Tim; Magorian Friedlmeier, Theresa; Pieters, Bart; Heinlein, Alexander; Denk, Martin; Göddeke, Dominik; Powalla, MichaelWe show that the concept of topology optimization for metallization grid patterns of thin-film solar devices can be applied to monolithically integrated solar cells. Different irradiation intensities favor different topological grid designs as well as a different thickness of the transparent conductive oxide (TCO) layer. For standard laboratory efficiency determination, an irradiation power of 1000W/m2is generally applied. However, this power rarely occurs for real-world solar modules operating at mid-latitude locations. Therefore, contact layer thicknesses and also lateral grid patterns should be optimized for lower irradiation intensities. This results in material production savings for the grid and TCO layer of up to 50 % and simultaneously a significant gain in yield of over 1%for regions with a low annual mean irradiation.Item Open Access Renormalized charge and dielectric effects in colloidal interactions : a numerical solution of the nonlinear Poisson-Boltzmann equation for unknown boundary conditions(2023) Schlaich, Alexander; Tyagi, Sandeep; Kesselheim, Stefan; Sega, Marcello; Holm, ChristianThe Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, introduced more than 70 years ago, is a hallmark of colloidal particle modeling. For highly charged particles in the dilute regime, it is often supplemented by Alexander’s prescription (Alexander et al. in J Chem Phys 80:5776, 1984) for using a renormalized charge. Here, we solve the problem of the interaction between two charged colloids at finite ionic strength, including dielectric mismatch effects, using an efficient numerical scheme to solve the nonlinear Poisson-Boltzmann (NPB) equation with unknown boundary conditions. Our results perfectly match the analytical predictions for the renormalized charge by Trizac and coworkers (Aubouy et al. in J Phys A 36:5835, 2003). Moreover, they allow us to reinterpret previous molecular dynamics (MD) simulation results by Kreer et al. (Phys Rev E 74:021401, 2006), rendering them now in agreement with the expected behavior. We furthermore find that the influence of polarization becomes important only when the Debye layers overlap significantly.Item Open Access Multilevel Monte Carlo estimators for elliptic PDEs with Lévy-type diffusion coefficient(2022) Merkle, Robin; Barth, AndreaGeneral elliptic equations with spatially discontinuous diffusion coefficients may be used as a simplified model for subsurface flow in heterogeneous or fractured porous media. In such a model, data sparsity and measurement errors are often taken into account by a randomization of the diffusion coefficient of the elliptic equation which reveals the necessity of the construction of flexible, spatially discontinuous random fields. Subordinated Gaussian random fields are random functions on higher dimensional parameter domains with discontinuous sample paths and great distributional flexibility. In the present work, we consider a random elliptic partial differential equation (PDE) where the discontinuous subordinated Gaussian random fields occur in the diffusion coefficient. Problem specific multilevel Monte Carlo (MLMC) Finite Element methods are constructed to approximate the mean of the solution to the random elliptic PDE. We prove a-priori convergence of a standard MLMC estimator and a modified MLMC-control variate estimator and validate our results in various numerical examples.Item Open Access Knowledge-based modeling of simulation behavior for Bayesian optimization(2024) Huber, Felix; Bürkner, Paul-Christian; Göddeke, Dominik; Schulte, MiriamNumerical simulations consist of many components that affect the simulation accuracy and the required computational resources. However, finding an optimal combination of components and their parameters under constraints can be a difficult, time-consuming and often manual process. Classical adaptivity does not fully solve the problem, as it comes with significant implementation cost and is difficult to expand to multi-dimensional parameter spaces. Also, many existing data-based optimization approaches treat the optimization problem as a black-box, thus requiring a large amount of data. We present a constrained, model-based Bayesian optimization approach that avoids black-box models by leveraging existing knowledge about the simulation components and properties of the simulation behavior. The main focus of this paper is on the stochastic modeling ansatz for simulation error and run time as optimization objective and constraint, respectively. To account for data covering multiple orders of magnitude, our approach operates on a logarithmic scale. The models use a priori knowledge of the simulation components such as convergence orders and run time estimates. Together with suitable priors for the model parameters, the model is able to make accurate predictions of the simulation behavior. Reliably modeling the simulation behavior yields a fast optimization procedure because it enables the optimizer to quickly indicate promising parameter values. We test our approach experimentally using the multi-scale muscle simulation framework OpenDiHu and show that we successfully optimize the time step widths in a time splitting approach in terms of minimizing the overall error under run time constraints.