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arXiv 2024年

作者： Bartuska, Arved Carlon, André Gustavo Espath, Luis Krumscheid, Sebastian Tempone, Raúl Department of Mathematics RWTH Aachen University Gebäude-1953 1.OG Pontdriesch 14-16 161 Aachen52062 Germany Thuwal23955-6900 Saudi Arabia School of Mathematical Sciences University of Nottingham NottinghamNG7 2RD United Kingdom RWTH Aachen University Germany Scientific Computing Center Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Germany

Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form R f (R g(y, x) dx) dy, for nonlinear f, making them computationally challenging, particularly in high-dimensional settings. Although widely used for single integrals, traditional Monte Carlo (MC) methods can be inefficient when encountering complexities of nested integration. This work introduces a novel multilevel estimator, combining deterministic and randomized quasi-MC (rQMC) methods to handle nested integration problems efficiently. In this context, the inner number of samples and the discretization accuracy of the inner integrand evaluation constitute the level. We provide a comprehensive theoretical analysis of the estimator, deriving error bounds demonstrating significant reductions in bias and variance compared with standard methods. The proposed estimator is particularly effective in scenarios where the integrand is evaluated approximately, as it adapts to different levels of resolution without compromising precision. We verify the performance of our method via numerical experiments, focusing on estimating the expected information gain of experiments. When applied to Gaussian noise in the experiment, a truncation scheme ensures finite error bounds at the same computational complexity as in the bounded noise case up to multiplicative logarithmic terms. The results reveal that the proposed multilevel rQMC estimator outperforms existing MC and rQMC approaches, offering a substantial reduction in computational costs and offering a powerful tool for practitioners dealing with complex, nested integration problems across various *** Codes 62F15, 65C05, 65D30, 65D32 © 2024, CC0.

关键词： Risk assessment

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Tunka-Rex Virtual Observatory 37

Tunka-Rex Virtual Observatory

引用

37th International Cosmic Ray Conference, ICRC 2021

作者： Lenok, V. Wochele, D. Polgart, F. Golovachev, S. Sotnikov, V. Sotnikov, E. Bezyazeekov, P. Budnev, N. Fedorov, O. Gress, O. Grishin, O. Haungs, A. Huege, T. Kazarina, Y. Kleifges, M. Korosteleva, E. Kostunin, D. Kuzmichev, L. Lubsandorzhiev, N. Malakhov, S. Marshalkina, T. Monkhoev, R. Osipova, E. Pakhorukov, A. Pankov, L. Prosin, V. Schröder, F.G. Shipilov, D. Zagorodnikov, A. Applied Physics Institute ISU Irkutsk664020 Russia Karlsruhe Institute of Technology Institute for Astroparticle Physics KarlsruheD-76021 Germany Astrophysical Institute Vrije Universiteit Brussel Pleinlaan 2 Brussels1050 Belgium Karlsruhe76021 Germany Skobeltsyn Institute of Nuclear Physics MSU Moscow119991 Russia DESY Zeuthen15738 Germany Bartol Research Institute Department of Physics and Astronomy University of Delaware NewarkDE19716 United States X5 Retail Group Moscow119049 Russia JetBrains Research St. Petersburg194100 Russia Sobolev Institute of Mathematics Novosibirsk630090 Russia

Tunka-Rex (Tunka Radio Extension) was a detector for ultra-high energy cosmic rays measuring radio emission for air showers in the frequency band of 30-80 MHz, operating in 2010s. It provided an experimental proof that sparse radio arrays can be a cost-effective technique to measure the depth of shower maximum with resolutions competitive to optical detectors. After the decommissioning of Tunka-Rex, as last phase of its lifecycle and following the FAIR (Findability - Accessibility - Interoperability - Reuse) principles, we publish the data and software under free licenses in the frame of the TRVO (Tunka-Rex Virtual Observatory), which is hosted at KIT under the partnership with the KCDC and GRADLCI projects. We present the main features of TRVO, its interface and give an overview of projects, which benefit from its open software and data. © 2021 Copyright owned by the author(s) under the terms of the Creative Commons.

关键词： Cost effectiveness

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ON THE EXTINCTION OF MULTIPLE SHOCKS IN SCALAR VISCOUS CONSERVATION LAWS

arXiv

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arXiv 2024年

作者： Lin, Jeanne Pelinovsky, Dmitry E. de Rijk, Björn Department of Mathematics and Statistics McMaster University HamiltonONL8S 4K1 Canada Department of Applied Mathematics Nizhny Novgorod State Technical University 24 Minin street Nizhny Novgorod603950 Russia Department of Mathematics Karlsruhe Institute for Technology Englerstraße 2 Karlsruhe76131 Germany

We are interested in the dynamics of interfaces, or zeros, of shock waves in general scalar viscous conservation laws with a locally Lipschitz continuous flux function, such as the modular Burgers’ equation. We prove that all interfaces coalesce within finite time, leaving behind either a single interface or no interface at all. Our proof relies on mass and energy estimates, regularization of the flux function, and an application of the Sturm theorems on the number of zeros of solutions of parabolic problems. Our analysis yields an explicit upper bound on the time of extinction in terms of the initial condition and the flux function. Moreover, in the case of a smooth flux function, we characterize the generic bifurcations arising at a coalescence event with and without the presence of odd symmetry. We identify associated scaling laws describing the local interface dynamics near collision. Finally, we present an extension of these results to the case of anti-shock waves converging to asymptotic limits of opposite signs. Our analysis is corroborated by numerical simulations in the modular Burgers’ equation and its regularizations. © 2024, CC BY.

关键词： Shock waves

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SIMD vectorization for simultaneous solution of locally varying linear systems with multiple right hand sides

Research Square

引用

Research Square 2022年

作者： Kühn, Martin J. Holke, Johannes Lutz, Annette Thies, Jonas Röhrig-Zöllner, Melven Bleh, Alexander Backhaus, Jan Basermann, Achim Institute for Software Technology Department for High-Performance Computing Cologne Germany Technische Universität Darmstadt Department of Mathematics Germany Delft University of Technology Institute of Applied Mathematics Netherlands Institute of Propulsion Technology Department of Numerical Methods Cologne Germany

Developments in numerical simulation of flows and high performance computing influence one another. More detailed simulation methods create a permanent need for more computational power, while new hardware developments often require changes to the software to exploit new hardware features. This dependency is very pronounced in the case of vector-units which are featured by all modern processors to increase their numerical throughput but require vectorization of the software to be used efficiently. We study the vectorization of a simulation method that exhibits an inherent level of vector-parallelism. This is of particular interest as SIMD operations will hopefully be available with std::simd in a future C++ standard. The simulation method considered here results in the simultaneous solution of multiple sparse linear systems of equations which only differ by their main diagonal and right hand sides. Such structure arises in the simulation of unsteady flow in turbomachinery by means of a frequency domain approach called harmonic balance. © 2022, CC BY.

关键词： Computational fluid dynamics

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Parametric Dynamic Mode Decomposition for nonlinear parametric dynamical systems

arXiv

引用

arXiv 2023年

作者： Sun, Shuwen Feng, Lihong Chan, Hoon Seng Miličić, Tamara Vidaković-Koch, Tanja Röder, Fridolin Benner, Peter Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39016 Germany Karlsruhe Institute of Technology Institute for Applied Materials - Electrochemical Technologies Karlsruhe76131 Germany University of Bayreuth Bayreuth95447 Germany Faculty of Mathematics Otto von Guericke University Magdeburg39016 Germany

A non-intrusive model order reduction (MOR) method that combines features of the dynamic mode decomposition (DMD) and the radial basis function (RBF) network is proposed to predict the dynamics of parametric nonlinear systems. In many applications, we have limited access to the information of the whole system, which motivates non-intrusive model reduction. One bottleneck is capturing the dynamics of the solution without knowing the physics inside the "black-box" system. DMD is a powerful tool to mimic the dynamics of the system and to give a reliable approximation of the solution in the time domain using only the dominant DMD modes. However, DMD in general cannot reproduce the parametric behavior of the dynamics. Our contribution focuses on extending DMD to parametric DMD by RBF interpolation. Specifically, a RBF network is first trained using snapshot matrices at a limited number of parameter samples. The snapshot matrix at any new parameter sample can be quickly learned from the RBF network. DMD then uses the newly generated snapshot matrix at the online stage to predict the time patterns of the dynamics corresponding to the new parameter sample. The proposed framework and algorithm are tested and validated by numerical examples including models with parametrized and time-varying inputs. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamic mode decomposition

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Multi-Scale Electromagnetic Simulation Through Parallel Adaptive Mesh Refinement FDTD Method with Symmetric Positive Semi-Definite Subgridding Scheme

Multi-Scale Electromagnetic Simulation Through Parallel Adap...

引用

International applied Computational Electromagnetics Society Symposium (ACES)

作者： Hanyu Li Haijing Zhou Xianfeng Bao Xiaojie Chen School of Physical Science and Technology Southwest Jiaotong University Chengdu China Institute of Applied Physics and Computational Mathematics Beijing China Software Center for High Performance Numerical Simulation CAEP Beijing China

FDTD method is a common approach for electromagnetic propagation, scattering and coupling simulation. Conventional FDTD with universal mesh requires numerous computations to represent solve problems with multi-scale structures. In this paper, adaptive mesh refinement (AMR) strategy is performed to reduce the calculations along with symmetric positive semi-definite subgridding scheme to guarantee stability. numerical example of a missile seeker coupling simulation shows that the computation time decrease down to 2% while preserving excellent precision.

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Large-Eddy Simulation of Dual-Fuel Spray Ignition at Varying Levels of Methane Diluted Ambient Oxidizer Using FGM

SSRN

引用

SSRN 2023年

作者： Bao, Hesheng Han, Jinlin Zhang, Yan Matteo, Andrea Di Roekaerts, Dirk van Oijen, Jeroen Somers, Bart Department of Mechanical Engineering Eindhoven University of Technology Netherlands CAEP Software Center for High Performance Numerical Simulation China Institute of Applied Physics and Computational Mathematics China Department of Process & Energy Delft University of Technology Netherlands

In the current work, the Flamelet Generated Manifold (FGM) method is applied with large-eddy simulation (LES) to investigate the effect of methane on dualfuel (DF) spray ignition. The diesel surrogate n-dodecane is injected as the socalled pilot fuel into selected lean methane-air mixtures, ranging from CH4 = 0 to CH4 = 0.75, at engine relevant conditions. The operating conditions are those of the completely characterized Engine Combustion Network (ECN) Spray A configuration, for which the modeling approach adopted in the present study was extensively validated. The specific purpose of this study is to extend and validate the FGM approach for dual-fuel combustion. In order to understand the interplay of chemistry and mixing, the ignition behavior of selected cases is investigated. It is found that both low and high temperature combustion (LTC and HTC, respectively) are increasingly retarded by higher values of CH4, while the induction time between LTC and HTC is relatively insensitive compared to the ignition delay time (IDT). Analysis reveals a more prominent role of mixing for increased CH4. The development of LTC and HTC are quantitatively analyzed for different cases. The transition from LTC to HTC is found to be highly correlated with the evolution of lift-off length (LOL), which on its turn is seriously affected by CH4. The local flame behavior is analyzed via chemical explosive mode analysis (CEMA), suggesting a clear flame propagation due to diffusion towards lean mixtures after the ignition of the pilot fuel. Besides, it is found that diffusion helps to stabilize the flame in leaner mixtures, which is more important in DF combustion. The results show FGM to be a promising tool in modeling the DF sprays. © 2023, The Authors. All rights reserved.

关键词： Large eddy simulation

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Bound States in Bent Soft Waveguides

arXiv

引用

arXiv 2023年

作者： Exner, Pavel Vugalter, Semjon Doppler Institute for Mathematical Physics and Applied Mathematics Czech Technical University Břehová 7 Prague11519 Czech Republic Department of Theoretical Physics NPI Academy of Sciences Řež Prague25068 Czech Republic Institute for Analysis Karlsruhe Institute of Technology Englerstrasse 2 Karlsruhe76131 Germany

The aim of this paper is to show that a two-dimensional Schrödinger operator with the potential in the form of a ‘ditch’ of a fixed profile can have a geometrically induced discrete spectrum;this happens if such a potential channel has a single or multiple bends being straight outside a compact. Moreover, under stronger geometric restrictions the claim remains true in the presence of a potential bias at one of the channel ‘banks’.MSC Codes Primary 81Q37;Secondary 35J10, 35P15 © 2023, CC BY.

关键词： Waveguides

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Reconstruction of sub-threshold events of cosmic-ray radio detectors using an autoencoder 37

Reconstruction of sub-threshold events of cosmic-ray radio d...

引用

37th International Cosmic Ray Conference, ICRC 2021

作者： Bezyazeekov, P. Shipilov, D. Kostunin, D. Plokhikh, I. Mikhaylenko, A. Turishcheva, P. Golovachev, S. Sotnikov, V. Sotnikova, E. Bezyazeekov, P. Budnev, N. Fedorov, O. Gress, O. Grishin, O. Haungs, A. Huege, T. Kazarina, Y. Kleifges, M. Korosteleva, E. Kostunin, D. Kuzmichev, L. Lenok, V. Lubsandorzhiev, N. Malakhov, S. Marshalkina, T. Monkhoev, R. Osipova, E. Pakhorukov, A. Pankov, L. Prosin, V. Schröder, F.G. Shipilov, D. Zagorodnikov, A. Applied Physics Institute Irkutsk State University Irkutsk664020 Russia DESY Zeuthen15738 Germany Novosibirsk State University Novosibirsk630090 Russia Innopolis University Innopolis420500 Russia JetBrains Research St. Petersburg194100 Russia Sobolev Institute of Mathematics Novosibirsk630090 Russia Applied Physics Institute ISU Irkutsk664020 Russia Karlsruhe Institute of Technology Institute for Astroparticle Physics KarlsruheD-76021 Germany Astrophysical Institute Vrije Universiteit Brussel Pleinlaan 2 Brussels1050 Belgium Karlsruhe76021 Germany Skobeltsyn Institute of Nuclear Physics MSU Moscow119991 Russia DESY Zeuthen15738 Germany Bartol Research Institute Department of Physics and Astronomy University of Delaware NewarkDE19716 United States X5 Retail Group Moscow119049 Russia

Radio detection of air showers produced by ultra-high energy cosmic rays is a cost-effective technique for the next generation of sparse arrays. The performance of this technique strongly depends on the environmental background, which has different constituents, namely anthropogenic radio frequency interference, synchrotron galactic radiation and others. These components have recognizable features, which can help for background suppression. A powerful method for handling this is the application of convolution neural networks with a specific architecture called autoencoder. By suppressing unwanted signatures, the autoencoder keeps the signal-like ones. We have successfully developed and trained an autoencoder, which is now applied to the data from Tunka-Rex. We show the procedures of the training and optimization of the network including benchmarks of different architectures. Using the autoencoder, we improved the standard analysis of Tunka-Rex in order to lower the threshold of the detection. This enables the reconstructing of sub-threshold events with energies lower than 0.1 EeV with satisfactory angular and energy resolutions. © Copyright owned by the author(s).

关键词： Cosmic rays

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Elliptical Silicon Nanowire Covered by the SEI in a 2D Chemo-Mechanical Simulation

arXiv

引用

arXiv 2024年

作者： Schoof, Raphael Köbbing, Lukas Latz, Arnulf Horstmann, Birger Dörfler, Willy Institute for Applied and Numerical Mathematics Englerstraße 2 Karlsruhe76131 Germany Wilhelm-Runge-Straße 10 Ulm89081 Germany Helmholtzstraße 11 Ulm89081 Germany Faculty of Natural Sciences Ulm University Albert-Einstein-Allee 47 Ulm89081 Germany

Understanding the mechanical interplay between silicon anodes and their surrounding solid-electrolyte interphase (SEI) is essential to improve the next generation of lithium-ion batteries. We model and simulate a 2D elliptical silicon nanowire with SEI via a thermodynamically consistent chemo-mechanical continuum ansatz using a higher order finite element method in combination with a variable-step, variable-order time integration scheme. Considering a soft viscoplastic SEI for three half cycles, we see at the minor half-axis the largest stress magnitude at the silicon nanowire surface, leading to a concentration anomaly. This anomaly is caused by the shape of the nanowire itself and not by the SEI. Also for the tangential stress of the SEI, the largest stress magnitudes are at this point, which can lead to SEI fracture. However, for a stiff SEI, the largest stress magnitude inside the nanowire occurs at the major half-axis, causing a reduced concentration distribution in this area. The largest tangential stress of the SEI is still at the minor half-axis. In total, we demonstrate the importance of considering the mechanics of the anode and SEI in silicon anode simulations and encourage further numerical and model improvements. © 2024, CC BY-NC-SA.

关键词： Nanowires

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