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arXiv 2023年

作者： Wichitrnithed, Chayanon Valseth, Eirik Kubatko, Ethan J. Kang, Younghun Hudson, Mackenzie Dawson, Clint The Oden Institute for Computational Engineering and Sciences The University of Texas at Austin 201 E. 24th St. Stop C0200 AustinTX78712 United States The Department of Data Science The Norwegian University of Life Science Drobakveien 31 As1433 Norway Department of Scientific Computing and Numerical Analysis Simula Research Laboratory Kristian Augusts gate 23 Oslo0164 Norway The Department of Civil Environmental and Geodetic Engineering The Ohio State University 2070 Neil Ave ColumbusOH43210 United States

Many tropical cyclones, e.g., Hurricane Harvey (2017), have lead to significant rainfall and resulting runoff. When the runoff interacts with storm surge, the resulting floods can be greatly amplified and lead to effects that cannot be correctly modeled by simple superposition of its distinctive sources. In an effort to develop accurate numerical simulations of runoff, surge, and compounding floods, we develop a local discontinuous Galerkin method for modified shallow water equations. In this modification, nonzero sources to the continuity equation are included to incorporate rainfall into the model using parametric rainfall models from literature as well as hindcast data. The discontinuous Galerkin spatial discretization is accompanied with a strong stability preserving explicit Runge Kutta time integrator. Hence, temporal stability is ensured through the Courant-Friedrichs-Lewy (CFL) condition and we exploit the embarrassingly parallel nature of the developed method using MPI parallelization. We demonstrate the capabilities of the developed method though a sequence of physically relevant numerical tests, including small scale test cases based on laboratory measurements and large scale experiments with Hurricane Harvey in the Gulf of Mexico. The results highlight the conservation properties and robustness of the developed method and show the potential of compound flood modeling using our approach. Copyright © 2023, The Authors. All rights reserved.

关键词： Runoff

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Development and illustration of a framework for computational thinking practices in introductory physics

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Physical Review Physics Education Research 2022年第2期18卷 020106-020106页

作者： Daniel P. Weller Theodore E. Bott Marcos D. Caballero Paul W. Irving Department of Physics and Astronomy Michigan State University East Lansing Michigan 48824 USA School of Mathematical and Physical Sciences University of New England Biddeford Maine 04005 USA Department of Computational Mathematics Science and Engineering and CREATE for STEM Institute Michigan State University East Lansing Michigan 48824 USA Department of Physics and Center for Computing in Science Education University of Oslo Oslo 0316 Norway

Physics classes with computation integrated into the curriculum are a fitting setting for investigating computational thinking. In this paper, we present a framework for exploring this topic in introductory physics courses. The framework, which was developed by reviewing relevant literature and acquiring video data from high school classrooms, comprises 14 practices that students could engage in when working with Glowscript VPython activities. For every practice, we provide in-class video data to exemplify the practice. In doing this work, we hope to provide ways for teachers to assess their students’ development of computational thinking and give physics education researchers a foundation to study the topic in greater depth.

关键词： Technology K-12 students K-12 teachers

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Pseudo complementary measurement for traditional single-pixel cameras

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Chinese Physics B 2020年第11期29卷 315-322页

作者： Qian Dong Xu-Ri Yao Xin Liu Bing Liu Guang-Jie Zhai State Key Laboratory of Computer Science Institute of SoftwareChinese Academy of SciencesBeijing 100190China Key Laboratory of Electronics and Information Technology for Space Systems National Space Science CenterChinese Academy of SciencesBeijing 100190China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

A traditional single-pixel camera needs a large number of measurements to reconstruct the object with compressive sensing *** with the 1/0 matrices in classical measurement,the 1/-1 matrices in the complementary measurement has better property for reconstruction computation and returns better reconstruction ***,each row of the 1/-1 matrices needs two measurements with the traditional single-pixel camera which results into double measurements compared with the 1/0 *** this paper,we consider the pseudo complementary measurement which only takes the same amount of measurements with the row number of some properly designed 1/0 matrix to compute the total luminous flux of the objective and derives the measurement data of the corresponding 1/-1 matrix in a mathematical *** numerical simulation and experimental result show that the pseudo complementary measurement is an efficient tool for the traditional single-pixel camera imaging under low measurement rate,which can combine the advantages of the classical and complementary measurements and significantly improve the peak signal-to-noise ratio.

关键词： computational imaging single-pixel camera

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Efficient multiscale algorithms for simulating nonlocal optical response of metallic nanostructure arrays

arXiv

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arXiv 2020年

作者： Zhang, Yongwei Ma, Chupeng Cao, Liqun Shi, Dongyang School of Mathematics and Statistics Zhengzhou University Zhengzhou450001 China Institute for Applied Mathematics Interdisciplinary Center for Scientific Computing Heidelberg University Im Neuenheimer Feld 205 Heidelberg69120 Germany LSEC NCMIS University of Chinese Academy of Sciences Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, we consider numerical simulations of the nonlocal optical response of metallic nanostructure arrays inside a dielectric host, which is of particular interest to the nanoplasmonics community due to many unusual properties and potential applications. Mathematically, it is described by Maxwell’s equations with discontinuous coefficients coupled with a set of Helmholtz-type equations defined only on the domains of metallic nanostructures. To solve this challenging problem, we develop an efficient multiscale method consisting of three steps. First, we extend the system into the domain occupied by the dielectric medium in a novel way and result in a coupled system with rapidly oscillating coefficients. A rigorous analysis of the error between the solutions of the original system and the extended system is given. Second, we derive the homogenized system and define the multiscale approximate solution for the extended system by using the multiscale asymptotic method. Third, to fix the inaccuracy of the multiscale asymptotic method inside the metallic nanostructures, we solve the original system in each metallic nanostructure separately with boundary conditions given by the multiscale approximate solution. A fast algorithm based on the LU decomposition is proposed for solving the resulting linear systems. By applying the multiscale method, we obtain the results that are in good agreement with those obtained by solving the original system directly at a much lower computational cost. Numerical examples are provided to validate the efficiency and accuracy of the proposed method. Copyright © 2020, The Authors. All rights reserved.

关键词： Finite element method

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Stabilization of nonautonomous parabolic equations by a single moving actuator

arXiv

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arXiv 2020年

作者： Azmi, Behzad Kunisch, Karl Rodrigues, Sérgio S. Johann Radon Institute for Computational and Applied Mathematics Altenbergerstr. 69 Linz4040 Austria Institute for Mathematics and Scientific Computing University of Graz Heinrichstr. 36 Graz8010 Austria

It is shown that an internal control based on a moving indicator function is able to stabilize the state of parabolic equations evolving in rectangular domains. For proving the stabilizability result, we start with a control obtained from an oblique projection feedback based on a finite number of static actuators, then we used the continuity of the state when the control varies in relaxation metric to construct a switching control where at each given instant of time only one of the static actuators is active, finally we construct the moving control by traveling between the static actuators. Numerical computations are performed by a concatenation procedure following a receding horizon control approach. They confirm the stabilizing performance of the moving *** Codes 93C05, 93C10, 93C20, 93D20 Copyright © 2020, The Authors. All rights reserved.

关键词： Feedback

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Single Relaxation Time and Multiple Revised Matrix Lattice Boltzmann Simulations of Forced Isotropic Turbulence

arXiv

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arXiv 2022年

作者： Kareem, Waleed Abdel Asinari, Pietro Succi, Sauro Izawa, Seiichiro Fukunishi, Yu Department of Mathematics Faculty of Science Suez University Egypt Academy of Scientific Research & Technology Egypt Politecnico di Torino Department of Energy Corso Duca degli Abruzzi 24 Torino10129 Italy Instituto Applicazioni Calcolo CNR Italy Department of Mechanical Engineering and Sciences University of Toyama Japan Institute of Computational Fluid Dynamics Japan

The single relaxation time (SRT) and the revised matrix (RM) lattice Boltzmann models are compared for simulations of three dimensional forced isotropic turbulence with resolutions of 1283 and 2563, respectively. The forcing technique by Guo et al. (2002) is applied with the two models using the same parameters and conditions. Some new aspects and results have been confirmed such as the superiority of the MRT model to simulate forced turbulence and using the Courant-Friedichs-Lewy condition (CFL) (Courant et al., 1967) by multiplying the velocity input with the coefficient CFL −4 for all cases. The single relaxation time is set to τ = 0.503 in all SRT simulations. Results show that the obtained turbulent velocity fields yield universal characteristics as proven in previous theoretical, experimental and numerical studies. The Taylor Reynolds number for the simulations are found as SRT: Rλ = 62 and MRT: Rλ = 65 for 1283 and SRT: Rλ = 107 and MRT: Rλ = 82 for the case of 2563, respectively. To test the weak incompressibility for the SRT model in comparison to the MRT model, the density probability distribution function (PDF) is depicted and it is found that ρ is almost unity at all timesteps for the MRT case, while a clear disturbance about unity is observed for the SRT case. Time variation's statistics such as the Taylor Reynolds number Rλ, the Taylor microscale λ, the Kolmogrov microscale η and energy spectra are calculated and depicted for all cases. One of the disadvantages of the MRT case is the simulations time which is found about twice the SRT simulations time, where about 80 hours are needed for simulating 12000 timesteps in the 2563 case in comparison to 42 hours for the SRT model using the same hardware resources. © 2022, CC BY.

关键词： Velocity

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Efficient multi-level hp-finite elements in arbitrary dimensions

arXiv

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arXiv 2021年

作者： Kopp, Philipp Rank, Ernst Calo, Victor M. Kollmannsberger, Stefan Computational Modeling and Simulation Technical University of Munich Germany Computation in Engineering Technical University of Munich Germany Institute for Advanced Study Technical University of Munich Germany Applied Mathematics School of Electrical Engineering Computing & Mathematical Science Faculty of Science and Engineering Curtin University Australia

We present an efficient algorithmic framework for constructing multi-level hp-bases that uses a data-oriented approach that easily extends to any number of dimensions and provides a natural framework for performance-optimized implementations. We only operate on the bounding faces of finite elements without considering their lower-dimensional topological features and demonstrate the potential of the presented methods using a newly written open-source library. First, we analyze a Fichera corner and show that the framework does not increase runtime and memory consumption when compared against the classical p-version of the finite element method. Then, we compute a transient example with dynamic refinement and derefinement, where we also obtain the expected convergence rates and excellent performance in computing time and memory usage. ©2022TheAuthor(s).*** (http://***/licenses/by/4.0/). © 2021, CC BY.

关键词： Finite element method

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A novel randomized XR-based preconditioned CholeskyQR algorithm

arXiv

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arXiv 2021年

作者： Fan, Yuwei Guo, Yixiao Lin, Ting Theory Lab Huawei Hong Kong Research Center Sha Tin Hong Kong Lsec Institute of Computational Mathematics and Scientific/Engineering Computing Amss Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China School of Mathematical Sciences Peking University Beijing100871 China

CholeskyQR is a simple and fast QR decomposition via Cholesky decomposition, while it has been considered highly sensitive to the condition number. In this paper, we provide a randomized preconditioner framework for CholeskyQR algorithm. Under this framework, two methods (randomized LU-CholeskyQR and randomized QR-CholeskyQR) are proposed and discussed. We prove the proposed preconditioners can effectively reduce the condition number, which is also demonstrated by numerical tests. Abundant numerical tests indicate our methods are more stable and faster than all the existing algorithms and have good *** Codes 65F25, 65Y05 Copyright © 2021, The Authors. All rights reserved.

关键词： Number theory

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PRACTICAL NEWTON METHODS FOR ELECTRONIC STRUCTURE CALCULATIONS ∗

arXiv

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arXiv 2020年

作者： Dai, Xiaoying Zhang, Liwei Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper, we propose and analyze some practical Newton methods for electronic structure calculations. We show the convergence and the local quadratic convergence rate for the Newton method when the Newton search directions are well-obtained. In particular, we investigate some basic implementation issues in determining the search directions and step sizes which ensures the convergence of the subproblem at each iteration and accelerates the algorithm, respectively. It is shown by our numerical experiments that our Newton methods perform better than the existing conjugate gradient method, and the Newton method with the adaptive step size strategy is even more efficient. Copyright © 2020, The Authors. All rights reserved.

关键词： Newton-Raphson method

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The role of isotropic and anisotropic Hubbard corrections for the magnetic ordering and absolute band alignment of hematite α-Fe2O3（0001）surfaces

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Progress in Natural Science:Materials International 2019年第3期29卷 349-355页

作者： Sateesh Bandaru Ivan Scivetti Chi-Yung Yam Gilberto Teobaldi School of Chemical and Bioprocess Engineering University College Dublin Beijing Computational Science Research Center Stephenson Institute for Renewable Energy Department of ChemistryThe University of Liverpool Scientific Computing Department Science and Technology Facilities CouncilDaresbury Laboratory

An isotropic （+U） and anisotropic [+（U-J）] corrected Density Functional Theory study for bulk hematite （α-Fe2O3） was carried out,and several competing terminations of its （0001） surface modeled via slabs of increasing thickness from twelve to thirty-six *** spite of small quantitative differences,the use of either U or （U-J）corrections showed not to qualitatively affect the results of the simulations both for bulkα-Fe2O3and the lowestenergyα-Fe2O3（0001） surface studied,regardless of the thickness of the slab *** energy favored antiferromagnetic ordering of bulkα-Fe2O3was preserved in the relaxed slabs,with the largest surface-induced effects limited to the outermost three Fe-layers in the *** O-and Fe-terminations were found to be energetically favored and ***,fully O-or Fe-terminated surfaces were calculated to be energetically disfavored and ***,the role of Fe-or O-termination for the semiconducting or metallic nature as well as absolute band alignment ofα-Fe2O3（0001） surfaces was analyzed and discussed with respect to the challenges in enhancing the activity ofα-Fe2O3samples as photo-electrode for water splitting.

关键词： Hematite α-Fe2O3 Surfaces Photo-electrodes Density functional theory Electronic properties Magnetic properties

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