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On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics

应用数学与计算数学学报 2025年第1期7卷 3-39页

作者： Hendrik Ranocha Andrew R.Winters Hugo Guillermo Castro Lisandro Dalcin Michael Schlottke-Lakemper Gregor J.Gassner Matteo Parsani Applied Mathematics University of HamburgBundesstr.5520146 HamburgGermany Department of Mathematics Applied Mathematics Linköping UniversityLinköpingSweden Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Applied and Computational Mathematics RWTH Aachen UniversityAachenGermany High-Performance Computing Center Stuttgart University of StuttgartStuttgartGermany Department of Mathematics and Computer Science University of CologneCologneGermany Center for Data and Simulation Science University of CologneCologneGermany Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Physical Science and Engineering Division(PSE) King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia

We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fluid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler *** demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy(CFL)*** numerical examples show that the error-based step size control is easy to use,robust,and efficient,e.g.,for(initial)transient periods,complex geometries,nonlinear shock captur-ing approaches,and schemes that use nonlinear entropy *** demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases,the open source Julia pack-ages *** with *** and the C/Fortran code SSDC based on PETSc.

关键词： Explicit Runge-Kutta(RK)methods Step size control Compressible fluid dynamics Adaptivity in space and time Shock capturing

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Adaptive Input Sampling: A Novel Approach for Efficient Object Detection in High Resolution Traffic Monitoring Images

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IEEE Access 2025年 13卷 73003-73021页

作者： Gebre, Tewodros Syum Wasehun, Eden Tsehaye Dorbu, Freda Elikem Agboola, Gazali Oluwasegun Hashemi-Beni, Leila Karimoddini, Ali NC AandT State University Applied Science and Technology Program GreensboroNC United States NC AandT State University Department of Computational Data Science and Engineering GreensboroNC United States NC AandT State University Geomatics Program Department of Built Environment GreensboroNC United States NC AandT State University Department of Electrical and Computer Engineering GreensboroNC United States

Real-time traffic monitoring is crucial for efficient transportation management, but it poses significant computational challenges, particularly when dealing with high-resolution videos. Most modern traffic monitoring systems employ object detection models followed by object tracking models, which require processing every frame of the video footage to detect and track vehicles. However, even efficient object detection models are computationally expensive, making it difficult to process high-resolution videos in real-time. To address this challenge, we introduce an Adaptive Input Sampler (AIS) as a preprocessing module that selectively activates the object detector only when vehicles are present in the scene. The AIS targets the area of the frame where vehicles are detected and samples that area without compressing the sample, thereby reducing the computational load on the object detector. By doing so, the AIS enables significant computational savings, especially when fewor no vehicles are present in the monitored scene. Our experiments demonstrate that the AIS achieves 96.40% traffic counting accuracy and 95.60% classification accuracy, while reducing the data size for analysis by up to 79.00%. AIS presents a promising solution to optimize the volume of input data in traffic monitoring applications, improve computational efficiency, and speed up inference results. © 2013 IEEE.

关键词： Footage counters

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Synergetic effects of multiple junction and surface hydroxyl in Cu/CuO/Cu2O/TiO2 heterostructures towards highly efficient photocatalysts for hydrogen generation

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Materials Science for Energy Technologies 2025年 8卷 131-142页

作者： Subagyo, Riki Anindika, Garcelina Rizky Aufkani, Afif Akmal Zhang, Lei Ardhyananta, Hosta Burhan, R.Y. Perry Nugraheni, Zjahra Vianita Akhlus, Syafsir Bahruji, Hasliza Prasetyoko, Didik Wellia, Diana Vanda Ivansyah, Atthar Luqman Arramel Kusumawati, Yuly Department of Chemistry Faculty of Science and Analytic Data Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Center of Excellence Applied Physics and Chemistry Nano Center Indonesia Jl PUSPIPTEK South Tangerang Banten15314 Indonesia Department of Physics National University of Singapore Singapore117551 Singapore Department of Materials and Metallurgical Engineering Faculty of Industrial Technology and Systems Engineering Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Centre of Advanced Material and Energy Science Universiti Brunei Darussalam Jalan Tungku Link BE 1410 Brunei Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Andalas Padang25163 Indonesia Master Program in Computational Science Faculty of Mathematics and Natural Science Institut Teknologi Bandung Jalan Ganesha No. 10 Bandung40132 Indonesia Instrumentation and Computational Physics Research Group Department of Physics Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jalan Ganesha No.10 West Java Bandung40132 Indonesia

The implementation of titanium dioxide (TiO2) as a photocatalyst material in hydrogen (H2) evolution reaction (HER) has embarked renewed interest in the past decade. Rapid electron-hole pairs recombination and wide band gap of a photo-sensitive material of TiO2 are detrimental toward the targeted catalytical reaction. In this study, we present the rational design, fabrication, photocatalytic performance of TiO2-Cu/CuO/Cu2O heterostructures (CuTi) using viable chemical reduction method. The Z-scheme and S-scheme are succesfully generated across the TiO2/CuO/Cu2O interfaces, while the Schottky junction arises on the Cu perimeters. This is evidenced from the blue shifted about 0.3 eV of Cu 2p core level determined by using X-ray photoemission spectroscopy (XPS), in combination with the formation of inverse V-shape of the Mott-Schottky plots. In addition, we find that Cu/CuO/Cu2O facilitates photon absorption range up to the visible region. The multiple heterojunction and the large number of OHsurface enhanced charge carrier transfer are associated to the suppression of photoluminescence (PL) intensity, high surface hydroxyl (OHsurface) density in CuTi probed by XPS, and fast electron transfer based on the electrochemical measurements. The presence of OHsurface inhibits the recombination of electron. A significant H2 photogeneration rate enhancement is achieved when an optimized 5 wt% Cu/CuO/Cu2O concentration is used on TiO2 to achieve 7,157.19 μmol·g−1 (1,789.30 μmol·g−1·h−1). Based on this finding, zero emission energy innitiative could be materialized under multiple heterojunctions in photocatalytic process is beneficial for enhancing the H2 production. © 2025 The Authors

关键词： Titanium dioxide

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Revealing Actual Viscoelastic Relaxation Times in Capillary Breakup

arXiv

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arXiv 2025年

作者： Hu, Nan Hwang, Jonghyun Ruangkriengsin, Tachin Stone, Howard A. Department of Mechanical and Aerospace Engineering Princeton University NJ08544 United States Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We use experiments and theory to elucidate the size effect in capillary breakup rheometry, where pre-stretching in the visco-capillary stage causes the apparent relaxation time to be consistently smaller than the actual value. We propose a method accounting for both the experimental size and the finite extensibility of polymers to extract the actual relaxation time. A phase diagram characterizes the expected measurement variability and delineates scaling law conditions. The results refine capillary breakup rheometry for viscoelastic fluids and advance the understanding of breakup dynamics across scales. Copyright © 2025, The Authors. All rights reserved.

关键词： Relaxation time

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Enhancing the Swanepoel method: precise envelope detection of thin-film transmission spectra

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Optics Express 2025年第6期33卷 13376-13400页

作者： Ballester, Manuel Marquez, Almudena P. Lopez-Tapia, Santiago Fernandez, Susana Bass, John Minkov, Dorian Wuersch, Christoph Willomitzer, Florian Marquez, Emilio Katsaggelos, Aggelos K. Computer Science Department Northwestern University EvanstonIL60208 United States Department of Mathematics Faculty of Science University of Cadiz Puerto Real11510 Spain Department of Electrical and Computer Engineering Northwestern University EvanstonIL60208 United States CIEMAT Avenida Complutense 40 Madrid28040 Spain Wyant College of Optical Sciences University of Arizona TucsonAZ85721 United States Sofia1000 Bulgaria Institute for Computational Engineering ICE OST Eastern Switzerland University of Applied Sciences Switzerland Department of Condensed-matter Physics Faculty of Science University of Cadiz Puerto Real11510 Spain

The Swanepoel method is a widely used optical technique for characterizing thin films through normal-incidence transmission measurements. A critical step in this approach involves extracting the upper and lower envelopes of the measured oscillatory spectrum. By analyzing the transmission spectrum and its corresponding envelopes, the Swanepoel procedure enables precise determination of the film refractive index and extinction coefficient. However, even minor inaccuracies in envelope construction can propagate significant errors into the final characterization results. To address this challenge, we present what we believe to be a novel physics-informed optimization algorithm for envelope detection. Our mathematical model reformulates the envelope detection problem as a global optimization task that enforces the physical properties of the Swanepoel envelopes. Extensive validation on fifty randomly generated transmission spectra demonstrates unprecedented accuracy: the method achieves root-mean-square errors (RMSE) below 0.10% for the upper envelope and 0.06% for the lower envelope (more than doubling the accuracy of current state-of-the-art approaches). Furthermore, the proposed model has been assessed with two experimental transmission spectra, demonstrating its robustness and accuracy with real noisy data. We have developed an open-source Python software package (see text below). This software includes not only our innovative envelope construction algorithm but also additional envelope drawing algorithms for comparison and an efficient implementation of the Swanepoel method, enabling complete optical characterization of thin films. © 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement.

关键词： Mean square error

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CONVERGENCE OF DISCONTINUOUS GALERKIN METHODS FOR QUASICONVEX AND RELAXED VARIATIONAL PROBLEMS

arXiv

引用

arXiv 2025年

作者： Grekas, Georgios Koumatos, Konstantinos Makridakis, Charalambo Vikelis, Andreas Computer Electrical Mathematical Sciences and Engineering Division KAUST Saudi Arabia Department of Mathematics University of Sussex United Kingdom Institute of Applied & Computational Mathematics Foundation for Research & Technology-Hellas Greece Department of Mathematics and Applied Mathematics University of Crete Greece Faculty of Civil Engineering Czech Technical University of Prague Czech Republic

In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular, we demonstrate that these schemes provide essential flexibility by removing inter-element continuity while also guaranteeing convergent approximations in the quasiconvex case. Notably, quasiconvexity is the weakest form of convexity pertinent to elasticity. Furthermore, we show that in the non-convex case discrete minimisers converge to minimisers of the relaxed problem. In this case, the minimisation problem corresponds to the energy defined by the quasiconvex envelope of the original energy. Our approach covers all discontinuous Galerkin formulations known to converge for convex energies. This work addresses an open challenge in the vectorial calculus of variations: developing and rigorously justifying numerical schemes capable of reliably approximating nonlinear energy minimization problems with potentially singular solutions, which are frequently encountered in materials science. © 2025, CC BY.

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Unbiased Parameter Estimation for Bayesian Inverse Problems

arXiv

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arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

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Inferring System and Optimal Control Parameters of Closed-Loop Systems from Partial Observations

arXiv

引用

arXiv 2025年

作者： Geadah, Victor Arbelaiz, Juncal Ritz, Harrison Daw, Nathaniel D. Cohen, Jonathan D. Pillow, Jonathan W. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ United States Princeton Neuroscience Institute Princeton University PrincetonNJ United States

We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting, where the state is observed noisily. To recover closed-loop system parameters, we develop inference methods based on probabilistic state-space model (SSM) techniques. First, we show that the system parameters exhibit non-identifiability in the infinite-horizon from closed-loop measurements, and we provide exact and numerical methods to disentangle the parameters. Second, to improve parameter identifiability, we show that we can further enhance recovery by either (1) incorporating additional partial measurements of the control signals or (2) moving to the finite-horizon setting. We further illustrate the performance of our methodology through numerical examples. © 2025, CC BY.

关键词： Stochastic systems

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Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets

arXiv

引用

arXiv 2025年

作者： Zhu, Guorui Bierman, Joel Lu, Jianfeng Li, Yingzhou School of Mathematical Sciences Fudan University China Electrical and Computer Engineering North Carolina State University United States Department of Mathematics Department of Physics Department of Chemistry Duke University United States School of Mathematical Sciences Shanghai Key Laboratory for Contemporary Applied Mathematics Fudan University Key Laboratory of Computational Physical Sciences Ministry of Education China

This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition (SVD) into the process, the method achieves an operational depth of O(n) with about n ancilla qubits, enhancing the computational capabilities for analyzing fermionic systems. The non-unitarity of the transformation allows us to transform a wave function from one basis to another, which can span different spaces. By this trick, we can calculate the overlap of two wavefunctions that live in different (but non-distinct Hilbert subspaces) with different basis representations. This provides the opportunity to use state specific ansatzes to calculate different energy eigenstates under orbital-optimized settings and may improve the accuracy when computing the energies of multiple eigenstates simultaneously in VQE or other framework. It allows for a deeper exploration of complex quantum states and phenomena, expanding the practical applications of quantum computing in physics and chemistry. © 2025, CC BY.

关键词： Wave functions

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Multiphysics simulations of microstructure influence on hysteresis and eddy current losses of electrical steel

arXiv

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arXiv 2025年

作者： Kühn, Patrick Yang, Yangyiwei Chen, Guanyu Foster, Shanelle N. Egger, Herbert Xu, Bai-Xiang Mechanics of Functional Materials Division Institute of Materials Science Technische Universität Darmstadt Darmstadt64287 Germany Department of Electrical and Computer Engineering Michigan State University MI48824 United States Johann Radon Institute for Computational and Applied Mathematics Linz Austria Institute for Numerical Mathematics Johannes Kepler University Linz Austria

Improving efficiency of electrical machines requires fundamental knowledge on the mechanisms behind magnetic and eddy current losses of the magnetic core materials, with Fe-Si alloy as a prototype. These losses are intrinsically influenced by the microstructure of the materials. This necessitates physics-based, microstructure-informed multiscale simulations. In the present paper, we utilised micromagnetic simulations and computational homogenization methods to calculate the effective hysteresis and effective conductivities of Fe-Si electrical steels. To demonstrate the methodology, binder-jet printed electrical steel material samples with different microstructure were investigated. The microstructure samples were digitized based on both the descriptor-based synthetic reconstruction and SEM-image-based digitization. More samples were generated with varying microstructure features such as grain size and grain boundary phases. The micromagnetic simulations were then performed to investigate the magnetic hysteresis and hysteresis loss. The eddy current loss was also evaluated by using the effective conductivity through computational homogenization. By performing parameter research on a series of synthetic microstructures, effects of average grain size and grain boundary (GB) phase thickness on the hysteresis loss and eddy current loss were unveiled. An average grain size around 120 µm has the lowest hysteresis loss, although the eddy current loss increases with the grain size. Increasing GB-phase thickness helps reduce both losses. Results indicate the potential to decrease loss of magnetic core materials by microstructure optimization. © 2025, CC BY.

关键词： Silicon alloys

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