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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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Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System

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Numerical mathematics(Theory,Methods and Applications) 2023年第1期16卷 140-164页

作者： Shasha Bian Yue Cheng Boling Guo Tingchun Wang The Graduate School of China Academy of Engineering Physics Beijing 100088China School of Mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing 210044China Institute of Applied Physics and Computational Mathematics Beijing 100088China

In this paper,we derive and analyze a conservative Crank-Nicolson-type finite difference scheme for the Klein-Gordon-Dirac(KGD)*** from the derivation of the existing numerical methods given in literature where the numerical schemes are proposed by directly discretizing the KGD system,we translate the KGD equations into an equivalent system by introducing an auxiliary function,then derive a nonlinear Crank-Nicolson-type finite difference scheme for solving the equivalent *** scheme perfectly inherits the mass and energy conservative properties possessed by the KGD,while the energy preserved by the existing conservative numerical schemes expressed by two-level’s solution at each time *** using energy method together with the‘cut-off’function technique,we establish the optimal error estimate of the numerical solution,and the convergence rate is O(τ^(2)+h^(2))in l∞-norm with time stepτand mesh size *** experiments are carried out to support our theoretical conclusions.

关键词： Klein-Gordon-Dirac equation nonlinear finite difference scheme conservation error analysis

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Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations

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Applied mathematics and Mechanics(English Edition) 2022年第1期43卷 141-154页

作者： Qili TANG Yunqing HUANG Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan Province411105China

Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are *** approaches are on account of two-grid skill include two major phases:find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution,and then locally solve linearized residual subproblems by one of three iterations(Stokes-type,Newton,and Oseen-type)on subdomains with fine grid in parallel to approximate the high frequency *** error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are *** numerical examples are implemented to verify the algorithm.

关键词： local and parallel algorithm finite element(FE)method iteration stationary incompressible magnetohydrodynamics(MHD)

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A Dynamic Pyramidal Relaxation Method of AC OPF 9

A Dynamic Pyramidal Relaxation Method of AC OPF

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9th Asia Conference on Power and Electrical engineering, ACPEE 2024

作者： Tang, Yu-Yang Chen, Liang Du, Hongbo Chen, Sheng-Jie Kou, Caixia Ai, Xiaomeng Zhou, Bo Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Beijing University of Posts and Telecommunications College of Sciences Beijing China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Huazhong University of Science and Technology School of Electrical and Electronic Engineering Wuhan China University of Michigan Department of Industrial and Operations Engineering Ann Arbor United States

ISBN: (纸本)9798350309638

The Alternating Current Optimal Power Flow (AC OPF) is crucial for power system analysis, yet existing algorithms face challenges in meeting the diverse requirements of practical applications. This paper presents a Pyramidal Relaxation (PR) formulation of the Branch Flow Model (BFM) for AC OPF, where surface conical constraints are approximated through a union of tetrahedrons in a Mixed Integer Linear Programming (MILP) relaxation. To reduce problem size and to enhance computational efficiency, we proposed a Dynamic Pyramidal Relaxation (DPR) method, where the cuts (inner approximation and outer approximation) are adaptively added. In practice, the DPR method is embedded into a MILP commercial solver based on the branch-and-cut framework. Case studies in different test systems validate the effectiveness in terms of feasibility, accuracy, and efficiency of our proposed method. © 2024 IEEE.

关键词： computational efficiency

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An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions

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Communications in computational Physics 2022年第3期31卷 966-986页

作者： Jianguo Huang Haoqin Wang Tao Zhou School of Mathematical Sciences and MOE-LSCShanghai Jiao Tong UniversityShanghaiChina LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

This paper is concerned with a novel deep learning method for variational problems with essential boundary *** this end,wefirst reformulate the original problem into a minimax problem corresponding to a feasible augmented La-grangian,which can be solved by the augmented Lagrangian method in an infinite dimensional *** on this,by expressing the primal and dual variables with two individual deep neural network functions,we present an augmented Lagrangian deep learning method for which the parameters are trained by the stochastic optimiza-tion method together with a projection *** to the traditional penalty method,the new method admits two main advantages:i)the choice of the penalty parameter isflexible and robust,and ii)the numerical solution is more accurate in the same magnitude of computational *** typical applications,we apply the new ap-proach to solve elliptic problems and(nonlinear)eigenvalue problems with essential boundary conditions,and numerical experiments are presented to show the effective-ness of the new method.

关键词： The augmented Lagrangian method deep learning variational problems saddle point problems essential boundary conditions

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Strong-coupling superconductivity with Tc above 70 K in Be-decorated monolayer T-graphene

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science China(Physics,Mechanics & Astronomy) 2024年第1期67卷 99-105页

作者： Liu Yang Peng-Fei Liu Hao-Dong Liu Ya-Ping Li Na Jiao Hong-Yan Lu Bao-Tian Wang Ping Zhang School of Physics and Physical Engineering Qufu Normal UniversityQufu 273165China Institute of High Energy Physics Chinese Academy of SciencesBeijing 100049China Spallation Neutron Source Science Center Dongguan 523803China Institute of Applied Physics and Computational Mathematics Beijing 100088China

Using first-principles calculations,we predict a new type of two-dimensional(2D)beryllium(Be)-decorated T-graphene named BeC_(2),where Be atoms are inserted into C–C bonds linking the carbon tetrarings of *** band structure shows that BeC_(2)is metallic,thus,the possible phonon-mediated superconductivity is explored based on the Eliashberg *** calculated electron-phonon coupling(EPC)constantλis up to 4.07,and the corresponding superconducting critical temperature(Tc)is 72.1 K,approaching the liquid nitrogen *** reason for the high Tc is the strong *** it is proved to be an anisotropic single-gap superconductor by analyzing the superconducting gap?kof BeC_(2).The electronic susceptibility calculation shows strong nesting effect in BeC_(2).Since rare 2D superconductors show such a strong EPC constantλwhich originates from the coupling between electrons in C-pzorbital and in-plane vibrations of Be and C atoms,the predicted BeC_(2)provides a new platform for investigating strong EPC 2D superconductor.

关键词： two-dimensional carbon-based superconductor electron-phonon coupling strong coupling high superconducting critical temperature

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Design of Area Effcient Multiplier Using High Speed 15-4 Counter 9

Design of Area Effcient Multiplier Using High Speed 15-4 Cou...

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9th International Conference on Communication and Electronics Systems, ICCES 2024

作者： Vasan, J.K. Shettygari, Sudeshna Hariprasad, S. Maria Dominic Savio, M. Srm Institute of Science and Technology Department of Electronics and Communication Engineering Kattankulathur Chennai India School of Computing Srm Institute of Science and Technology Department of Computational Intelligence Kattankulathur Chennai India

ISBN: (数字)9798350377972

ISBN: (纸本)9798350377972

The high-speed counters are the building blocks to reduce the partial products, increasing the efficiency and speed of the multiplier. This paper presents an innovative approach to designing a 16 × 16 multiplier using a 15-4 counter that utilizes cross-wired 1ogic(CWL) based 3-2 counter instead of traditional full adders. A 15-4 counter is designed by employing a 5-3 counter and a CWL-based 3-2 counter to reduce circuit complexity. Using multiple 5-3 counters instead of conventional full adders reduces the computational effort, strategically integrating these 15-4 counters within specific multiplier columns, achieving greater area efficiency and speed. This method addresses the high computational demands associated with adders, optimizing both performance and area in high-speed multiplier applications. From the simulation result, it can be inferred that the proposed 15-4 counter and cross-wired logic 3-2 counter has excellent efficiency, and the power and delay product(PDP) has reduced by 3.6 % when compared to the existing 15-counter design and 30.27 % decreased in the 3-2 counter design © 2024 IEEE.

关键词： Logic design

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Image-Based Extraction of Prescription Information using OCR-Tesseract 2

Image-Based Extraction of Prescription Information using OCR...

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2nd International Conference on Machine Learning and Data engineering, ICMLDE 2023

作者： Ponnuru, Mahesh Ponmalar, Sridevi P. Likhitha, A. Sree, Tanu B. Chaitanya, Guna G. School of Computing SRM Institute of Science and Technology Potheri603203 India Department of Computational Intelligence School of Computing Faculty of Engineering and Technology SRM Institute of Science and Technology Potheri603203 India School of Computer Science Vellore Institute of Technology Amaravathi522237 India

The paper presents advancements in healthcare data capture through the application of image-based extraction techniques, which include sophisticated image processing techniques such as resizing and adaptive thresholding, for prescription information. With the increasing digitization of medical records, automating the extraction of relevant data from prescription documents has become crucial. This research explores the utilization of image processing and optical character recognition (OCR) methodologies to extract prescription information accurately. By converting prescription documents into image format and employing OCR algorithms, the text content is extracted and parsed for critical details such as medication names, dosages, and patient instructions. Notably, our methodology excels in overcoming limitations associated with handwritten documents, achieving an impressive accuracy rate of 98%. This image-based approach offers a streamlined and efficient method for capturing prescription data, reducing manual data entry efforts, and minimizing potential errors. Experimental evaluations demonstrate the effectiveness and accuracy of the proposed approach, highlighting its potential to enhance healthcare data capture and improve patient care. © 2024 Elsevier B.V.. All rights reserved.

关键词： Optical character recognition

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Semi-analytical finite element method applied for characterizing micropolar fibrous composites

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Applied mathematics and Mechanics(English Edition) 2024年第12期45卷 2147-2164页

作者： J.A.OTERO Y.ESPINOSA-ALMEYDA R.RODRIGUEZ-RAMOS J.MERODIO School of Engineering and Sciences Monterrey Institute of TechnologyEstado de Mexico 52926Mexico Institute of Engineering and Technology Autonomous University of Ciudad JuarezCiudad JuarezChihuahua 32310Mexico Postgraduate Program in Computational Modeling in Science and Technology Federal Fluminense UniversityRıo de Janeiro 27255-125Brazil Faculty of Mathematics and Computer Science University of HavanaLa Habana 10400Cuba Department of Mathematics Applied to ICT School of Informatics Systems EngineeringTechnical University of MadridMadrid 28031Spain

A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous *** framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact *** mathematical formulation of the local problems and the effective coefficients are presented by the *** local problems obtained from the AHM are solved by the FEM,which is denoted as the *** numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.

关键词： semi-analytical approach fiber-reinforced composite(FRC) effective property finite element method(FEM) asymptotic homogenization method(AHM) micropolar elasticity

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Integer multiple quantum image scaling based on NEQR and bicubic interpolation

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Chinese Physics B 2024年第4期33卷 259-273页

作者：蔡硕周日贵罗佳陈思哲 College of Information Engineering Shanghai Maritime UniversityShanghai 201306China Research Center of Intelligent Information Processing and Quantum Intelligent Computing Shanghai 201306China College of Merchant Marine Shanghai Maritime UniversityShanghai 201306China School of Mathematics and Computational Science Shangrao Normal UniversityShangrao 334001China

As a branch of quantum image processing,quantum image scaling has been widely ***,most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation,the quantum version of bicubic interpolation has not yet been *** this work,we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation(NEQR).Our scheme can realize synchronous enlargement and reduction of the image with the size of 2^(n)×2^(n) by integral ***,the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT ***,16 neighborhood pixels are obtained by quantum operation circuits,and the corresponding weights of these pixels are calculated by quantum arithmetic ***,a quantum matrix operation,instead of a classical convolution operation,is used to realize the sum of convolution of these *** simulation experiments and complexity analysis,we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm,and has better effect than the quantum version of bilinear interpolation.

关键词： quantum image processing image scaling bicubic interpolation quantum circuit

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