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Efficient Sparse-Grid Implementation of a Fifth-Order Multi-resolution WENO Scheme for Hyperbolic Equations

Communications on applied mathematics and Computation 2023年第4期5卷 1339-1364页

作者： Ernie Tsybulnik Xiaozhi Zhu Yong-Tao Zhang Department of Applied and Computational Mathematics and Statistics University of Notre DameNotre DameIN46556USA

High-order accurate weighted essentially non-oscillatory(WENO)schemes are a class of broadly applied numerical methods for solving hyperbolic partial differential equations(PDEs).Due to highly nonlinear property of the WENO algorithm,large amount of computational costs are required for solving multidimensional *** our previous work(Lu et *** Pure Appl Math Q 14:57–86,2018;Zhu and Zhang in J Sci Comput 87:44,2021),sparse-grid techniques were applied to the classical finite difference WENO schemes in solving multidimensional hyperbolic equations,and it was shown that significant CPU times were saved,while both accuracy and stability of the classical WENO schemes were maintained for computations on sparse *** this technical note,we apply the approach to recently developed finite difference multi-resolution WENO scheme specifically the fifth-order scheme,which has very interesting properties such as its simplicity in linear weights’construction over a classical WENO *** experiments on solving high dimensional hyperbolic equations including Vlasov based kinetic problems are performed to demonstrate that the sparse-grid computations achieve large savings of CPU times,and at the same time preserve comparable accuracy and resolution with those on corresponding regular single grids.

关键词： Weighted essentially non-oscillatory(WENO)schemes Multi-resolution WENO schemes Sparse grids High spatial dimensions Hyperbolic partial differential equations(PDEs)

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Finite Volume computational Analysis of the Heat Transfer Characteristic in a Double-Cylinder Counter-Flow Heat Exchanger with Viscoelastic Fluids

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Defect and Diffusion Forum 2023年 424卷 19-43页

作者： Mavi, Anele Chinyoka, Tiri Department of Mathematics and Applied Mathematics University of Cape Town Rondebosch7701 South Africa Centre for Research in Computational & Applied Mechanics University of Cape Town Rondebosch7701 South Africa

This work presents a computational analysis of the heat-exchange characteristics in a doublecylinder (also known as a double-pipe) geometrical arrangement. The heat-exchange is from a hotter viscoelastic fluid flowing in the core (inner) cylinder to a cooler Newtonian fluid flowing in the shell (outer) annulus. For optimal heat-exchange characteristics, the core and shell fluid flow in opposite directions, the so-called counter-flow arrangement. The mathematical modelling of the given problem reduces to a system of nonlinear coupled Partial Differential Equations (PDEs). Specifically, the rheological behaviour of the core fluid is governed by the Giesekus viscoelastic constitutive model. The governing system of coupled nonlinear PDEs is intractable to analytic treatment and hence is solved numerically using Finite Volume Methods (FVM). The FVM numerical methodology is implemented via the open-source software package OpenFOAM. The numerical methods are stabilized, specifically to address numerical instabilities arising from the High Weissenberg Number Problem (HWNP), via a combination of the Discrete Elastic Viscous Stress Splitting (DEVSS) technique and the Log-Conformation Reformulation (LCR) methodology. The DEVSS and LCR stabilization techniques are integrated into the relevant viscoelastic fluid solvers. The novelties of the study center around the simulation and analysis of the optimal heat-exchange characteristics between the heated Giesekus fluid and the coolant Newtonian fluid within a double-pipe counter-flow arrangement. Existing studies in the literature have either focused exclusively on Newtonian fluids and/or on rectangular geometries. The existing OpenFOAM solvers have also largely focused on non-isothermal viscoelastic flows. The relevant OpenFOAM solvers are modified for the present purposes by incorporating the energy equation for viscoelastic fluid flow. The flow characteristics are presented qualitatively (graphically) via the fluid pressure, tem

关键词： Finite volume method

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COVID-19 Pandemic is an Eye-Opener for Academicians to Use the Technology in the Teaching–Learning Process

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International Journal of Educational Reform 2023年第1期32卷 3-18页

作者： Senthil Kumaran, Velayutham Periakaruppan, Ramanathan M. Department of Applied Mathematics and Computational Sciences PSG College of Technology Coimbatore India

Few things exist in life from the beginning but you don't realize until they become a habit. Education is also one of those things which cannot be exempted from this. The lockdown forced most of the academicians to take some determining decisions and new interests to revamp the teaching–learning process. The objective of this study is to analyze the impact of technology in teaching–learning process before and after a pandemic. This analysis is done by statistical tests using paired t-test and z-test by collecting data from students and teachers. Results show that this pandemic is an eye-opener for academicians to use the technology in teaching–learning process. © The Author(s) 2022.

关键词： COVID-19 eye-opener for academicians online education technology-enabled learning

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Batched Nonparametric Contextual Bandits

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IEEE Transactions on Information Theory 2025年第6期71卷 4537-4555页

作者： Jiang, Rong Ma, Cong The University of Chicago Committee on Computational and Applied Mathematics ChicagoIL60637 United States The University of Chicago Department of Statistics ChicagoIL60637 United States

We study nonparametric contextual bandits under batch constraints, where the expected reward for each action is modeled as a smooth function of covariates, and the policy updates are made at the end of each batch of observations. We establish a minimax regret lower bound for this setting and propose a novel batch learning algorithm that achieves the optimal regret (up to logarithmic factors). In essence, our procedure dynamically splits the covariate space into smaller bins, carefully aligning their widths with the batch size. Our theoretical results suggest that for mathematical framework of contextual bandit, a nearly constant number of policy updates can attain optimal regret in the fully online setting. © 1963-2012 IEEE.

关键词： Lower bound Switches Costs Heuristic algorithms Standards Hands Games Decision making Training Polynomials

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Optimizations and applications in large-scale scenes of Monte Carlo geometry conversion code CMGC

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Nuclear Science and Techniques 2025年第4期36卷 220-232页

作者： Xin Wang Ling-Yu Zhang Xue-Ming Shi Zhen Wu Jun-Li Li Gui-Ming Qin Yuan-Guang Fu CAEP Software Center for High Performance Numerical Simulation Beijing 100088China Institute of Applied Physics and Computational Mathematics Beijing 100088China Department of Engineering Physics Tsinghua UniversityBeijing 100084China

In response to the demand for rapid geometric modeling in Monte Carlo radiation transportation calculations for large-scale and complex geometric scenes,functional improvements,and algorithm optimizations were performed using CAD-to-Monte Carlo geometry conversion(CMGC)*** representation(BRep)to constructive solid geometry(CSG)conversion and visual CSG modeling were combined to address the problem of non-convertible geometries such as spline *** splitting surface assessment method in BRep-to-CSG conversion was optimized to reduce the number of Boolean operations using an Open ***,in turn,reduced the probability of CMGC conversion *** auxiliary surface generation algorithm was optimized to prevent the generation of redundant auxiliary surfaces that cause an excessive decomposition of CAD geometry *** optimizations enhanced the usability and stability of the CMGC model *** was applied successfully to the JMCT transportation calculations for the conceptual designs of five China Fusion Engineering Test Reactor(CFETR)*** rapid replacement of different blanket schemes was achieved based on the baseline CFETR *** geometric solid number of blankets ranged from hundreds to tens of *** correctness of the converted CFETR models using CMGC was verified through comparisons with the MCNP calculation *** CMGC supported radiation field evaluations for a large urban scene and detailed ship *** enabled the rapid conversion of CAD models with thousands of geometric solids into Monte Carlo CSG *** analysis of the JMCT transportation simulation results further demonstrated the accuracy and effectiveness of the CMGC.

关键词： Monte Carlo CAD BRep to CSG CMGC

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Computer-Aided Diagnostic System for Brain Tumor Classification using Explainable AI 2

Computer-Aided Diagnostic System for Brain Tumor Classificat...

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2nd IEEE International Conference on Interdisciplinary Approaches in Technology and Management for Social Innovation, IATMSI 2024

作者： Padmapriya, S.T. Devi, M.S. Gayathri Department of Applied Mathematics and Computational Science Thiagarajar College of Engineering TamilNadu Madurai India

ISBN: (纸本)9798350360523

The field of computer-aided diagnosis (CAD) of brain tumors has been transformed by developments in medical imaging and artificial intelligence. The accuracy and interpretability of brain tumor classification are improved in this research using Explainable AI (XAI) techniques. A timely and correct diagnosis of brain tumors is essential for the best possible care and treatment of the patient. In contrast, traditional machine learning models often lack transparency and interpretability, making it difficult for clinicians to rely on their judgment. This study uses a Grad-Cam algorithm to create an understandable and interpretable CAD system for classifying brain tumors. Our approach not only achieves high classification accuracy, but also provides physicians with insights into the decision-making process, improving their understanding and confidence in the system's recommendations. We evaluate our model using a large and diverse dataset and compare it to modern deep learning models and traditional CAD systems. The results show that our CAD system with XAI extensions not only achieves improved accuracy but also provides useful insights into the decision-making process. Using this method, doctors may be able to diagnose patients more accurately. © 2024 IEEE.

关键词： Deep learning

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Dynamic mode decomposition of nonequilibrium electron-phonon dynamics:accelerating the firstprinciples real-time Boltzmann equation

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npj computational Materials 2024年第1期10卷 1970-1977页

作者： Ivan Maliyov Jia Yin Jia Yao Chao Yang Marco Bernardi Department of Applied Physics and Materials Science California Institute of TechnologyPasadenaCA 91125USA Applied Mathematics and Computational Research Division Lawrence Berkeley National LaboratoryBerkeleyCA 94720USA Department of Physics California Institute of TechnologyPasadenaCA 91125USA

Nonequilibrium dynamics governed by electron–phonon(e-ph)interactions plays a key role in electronic devices and spectroscopies and is central to understanding electronic excitations in *** real-time Boltzmann transport equation(rt-BTE)with collision processes computed from first principles can describe the coupled dynamics of electrons and atomic vibrations(phonons).Yet,a bottleneck of these simulations is the calculation of e–ph scattering integrals on dense momentum grids at each time *** we show a data-driven approach based on dynamic mode decomposition(DMD)that can accelerate the time propagation of the rt-BTE and identify dominant electronic *** apply this approach to two case studies,high-field charge transport and ultrafast excited electron *** both cases,simulating only a short time window of~10%of the dynamics suffices to predict the dynamics from initial excitation to steady state using DMD *** of the momentum-space modes extracted from DMD sheds light on the microscopic mechanisms governing electron relaxation to a steady state or *** combination of accuracy and efficiency makes our DMD-based method a valuable tool for investigating ultrafast dynamics in a wide range of materials.

关键词： materials dynamics phonon

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Machine Learning: Driven Strategies for Enhancing Student Academic Performance

Machine Learning: Driven Strategies for Enhancing Student Ac...

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2024 IEEE International Conference on Intelligent Computing and Emerging Communication Technologies, ICEC 2024

作者： Sakthipriya, D. Chandrakumar, T. Johnson, B. Thiagaraiar College of Engineering Department of Applied Mathematics and Computational Science Tamilnadu Madurai India

ISBN: (数字)9798331508432

ISBN: (纸本)9798331508432

In order to improve learning outcomes and reduce dropouts, educational institutions must anticipate students' academic performance. This study focuses on identifying effective prediction models and employing a wrapper feature selection method to estimate students' performance in final examinations. Utilizing a well-established dataset from diverse engineering departments, comprising 3560 data samples, the research aims to select the optimal algorithm and feature selection technique for predicting the number of course arrears for each student. Regression predictive modeling, specifically for numerical value prediction, is employed along with relevant metrics to assess model performance. The study employs various machine learning approaches to forecast students' academic performance based on acquired data, including ongoing assessments and examinations. A comparative evaluation of ML techniques using different metrics is presented. This information empowers students to monitor their academic progress and adapt their study strategies for improved performance. Additionally, five feature selection strategies are applied to identify the most accurate predictor. The study incorporates regression algorithms and wrapper feature selection methods to enhance student performance outcomes. Experimental results highlight the effectiveness of the Variance Inflation Factor (VIF) with adaptive Decision Tree regression as the superior approach. © 2024 IEEE.

关键词： Prediction models

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STABLE BOUNDARY CONDITIONS AND DISCRETIZATION FOR P_(N) EQUATIONS

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Journal of computational mathematics 2022年第6期40卷 977-1003页

作者： Jonas Bunger Neeraj Sarna Manuel Torrilhon Applied and Computational Mathematics(ACoM) Department of MathematicsRWTH Aachen UniversitySchinkelstr 252062 AachenGermany

A solution to the linear Boltzmann equation satisfies an energy bound,which reflects a natural fact:The energy of particles in a finite volume is bounded in time by the energy of particles initially occupying the volume augmented by the energy transported into the volume by particles entering the volume over *** this paper,we present boundary conditions(BCs)for the spherical harmonic(P_(N))approximation,which ensure that this fundamental energy bound is satisfied by the P_(N) *** BCs are compatible with the characteristic waves of P_(N) equations and determine the incoming waves ***,energy bound and compatibility,are shown on abstract formulations of P_(N) equations and BCs to isolate the necessary structures and *** BCs are derived from a Marshak type formulation of BC and base on a non-classical even/odd-classification of spherical harmonic functions and a stabilization step,which is similar to the truncation of the series expansion in the P_(N) *** show that summation by parts(SBP)finite differences on staggered grids in space and the method of simultaneous approximation terms(SAT)allows to maintain the energy bound also on the semi-discrete level.

关键词： Boundary conditions Energy stability Spherical harmonic(P_(N))approximation Kinetic theory Moment method Boltzmann Linear transport

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A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting:Convergence and Rate Analyses

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Journal of the Operations Research Society of China 2024年第2期12卷 298-340页

作者： Peng-Jie Liu Jin-Bao Jian Hu Shao Xiao-Quan Wang Jia-Wei Xu Xiao-Yu Wu School of Mathematics Jiangsu Center for Applied MathematicsChina University of Mining and TechnologyXuzhou 221116JiangsuChina School of Mathematics and Physics Center for Applied Mathematics of GuangxiGuangxi Minzu UniversityNanning 530006GuangxiChina Department of Civil and Environmental Engineering The Hong Kong Polytechnic UniversityHong KongChina School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105HunanChina

This work explores a family of two-block nonconvex optimization problems subject to linear *** first introduce a simple but universal Bregman-style improved alternating direction method of multipliers(ADMM)based on the iteration framework of ADMM and the Bregman ***,we utilize the smooth performance of one of the components to develop a linearized version of *** to the traditional ADMM,both proposed methods integrate a convex combination strategy into the multiplier update *** each proposed method,we demonstrate the convergence of the entire iteration sequence to a unique critical point of the augmented Lagrangian function utilizing the powerful Kurdyka–Łojasiewicz property,and we also derive convergence rates for both the sequence of merit function values and the iteration ***,some numerical results show that the proposed methods are effective and encouraging for the Lasso model.

关键词： Nonconvex optimization Alternating direction method of multipliers Kurdyka-Lojasiewicz property Convergence rate

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