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NVERSE CONDUCTIVITY PROBLEM WITH INTERNAL DATA

Journal of computational mathematics 2023年第3期41卷 482-500页

作者： Faouzi Triki Tao Yin Laboratoire Jean Kuntzmann UMR CNRS 5224Université Grenoble-Alpes700 Avenue Centrale38401 Saint-Martin-d’HèresFrance Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of ScienceBeijing 100190China

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal *** problem finds applications in multi-wave imaging,greedy methods to approximate parameter-dependent elliptic problems,and image treatment with partial differential *** first show that the inverse problem for smooth coefficients can be rewritten as a linear transport *** that the coefficient is known near the boundary,we study the well-posedness of associated transport equation as well as its numerical resolution using discontinuous Galerkin *** propose a regularized transport equation that allow us to derive rigorous convergence rates of the numerical method in terms of the order of the polynomial approximation as well as the regularization *** finally provide numerical examples for the inversion assuming a lower regularity of the coefficient,and using synthetic data.

关键词： Inverse problems Multi-wave imaging Static transport equation Internal data Diffusion coeffcient Stability estimates Regularization

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Rigorous biaxial limit of a molecular-theory-based two-tensor hydrodynamics

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Journal of Differential Equations 2023年第1期366卷 862-911页

作者： Li, Sirui Xu, Jie School of Mathematics and Statistics Guizhou University Guiyang 550025 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC) Academy of Mathematics and Systems Science (AMSS) Chinese Academy of Sciences Beijing China

We consider a two-tensor hydrodynamics derived from the molecular model, where high-order tensors are determined by closure approximation through the maximum entropy state or the quasi-entropy. We prove the existence and uniqueness of local in time smooth solutions to the two-tensor system. Then, we rigorously justify the connection between the molecular-theory-based two-tensor hydrodynamics and the biaxial frame hydrodynamics. More specifically, in the framework of Hilbert expansion, we show the convergence of the solution to the two-tensor hydrodynamics to the solution to the frame hydrodynamics. © 2023 Elsevier Inc.

关键词： Biaxial limit Frame hydrodynamics Liquid crystals Two-tensor hydrydynamics

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Efficient Real-Time Obstacle Avoidance Using Multi-Objective Nonlinear Model Predictive Control and Semi-Smooth Newton Method 10

Efficient Real-Time Obstacle Avoidance Using Multi-Objective...

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10th International Conference on Vehicle Technology and Intelligent Transport Systems, VEHITS 2024

作者： Emam, Mostafa Rottmann, Thomas Gerdts, Matthias Department of Aerospace Engineering Institute of Applied Mathematics and Scientific Computing University of the Bundeswehr Munich Neubiberg85579 Germany

ISBN: (纸本)9789897587030

This work discusses the theory and methodology of applying Nonlinear Model Predictive Control (NMPC) in an efficient manner to achieve real-time path planning and obstacle avoidance for autonomous vehicles. First, we explain the optimization problem formulation and the numerical solution approach using a semi-smooth Newton method adapted for nonlinear problems. Then, an MPC path planning problem is described in terms of the vehicle model, the controller design, and the mathematical representation of obstacles as proper system constraints. Afterwards, the developed controller is numerically evaluated for different vehicle models in a simulated environment to dynamically assess its flexibility and real-time performance, which serves as a prerequisite to deferred real-life testing. Copyright © 2024 by SCITEPRESS - Science and Technology Publications, Lda.

关键词： Motion planning

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Nonlinear Extrapolation Estimates of π

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 91-108页

作者： Wen-qing Xu Sha-sha Wang Da-chuan Xu Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing100124China Department of Mathematics and Statistics California State UniversityLong BeachCalifornia90840USA Department of Mathematics and Physics Shijiazhuang Tiedao UniversityShijiazhuang050043China

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R~2 and it is well-known that by using linear combinations of these basic estimates,modern extrapolation techniques can greatly speed up the approximation ***,when n vertices are randomly selected on the circle,the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to π almost surely as n→∞,and by further applying extrapolation processes,faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random *** this paper,we further develop nonlinear extrapolation methods for approximating π through certain nonlinear functions of the semiperimeter and area of such *** focus on two types of extrapolation estimates of the forms χ_n=S_n~αA_n~β and Y_n(p)=(αS_n~p+βA_n~p)~(1/p) where α+β=1,p≠0,and Sn and An respectively represents the semiperimeter and area of a random n-gon inscribed in the unit circle in R~2,and Xn may be viewed as the limit of Y_n(p) when p→*** deriving probabilistic asymptotic expansions with carefully controlled error estimates for Xn and Y_n(p),we show that the choice α=4/3,β=-1/3 minimizes the approximation error in both cases,and their distributions are also asymptotically normal.

关键词： Archimedean polygons random polygons approximations ofπ extrapolation processes asymptotic convergence

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SOLVING OPTIMIZATION PROBLEMS OVER THE STIEFEL MANIFOLD BY SMOOTH EXACT PENALTY FUNCTIONS

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Journal of computational mathematics 2024年第5期42卷 1246-1276页

作者： Nachuan Xiao Xin Liu The Institute of Operations Research and Analytics National University of SingaporeSingapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of Sciencesand University of Chinese Academy of SciencesChina

In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel *** from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function without using any first-order derivative of the objective *** show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible,namely,are the first-order stationary points of the original optimization problem,or far from the Stiefel ***,the original problem and ExPen share the same second-order stationary ***,the exact gradient and Hessian of ExPen are easy to *** a consequence,abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.

关键词： Orthogonality constraint Stiefel manifold Penalty function

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Bicriteria Algorithms for Approximately Submodular Cover Under Streaming Model

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Tsinghua Science and Technology 2023年第6期28卷 1030-1040页

作者： Yijing Wang Xiaoguang Yang Hongyang Zhang Yapu Zhang Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematics and Statistics Ningbo UniversityNingbo 315211China Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China

In this paper,we mainly investigate the optimization model that minimizes the cost function such that the cover function exceeds a required threshold in the set cover problem,where the cost function is additive linear,and the cover function is non-monotone approximately *** study the problem under streaming model and propose three bicriteria approximation ***,we provide an intuitive streaming algorithm under the assumption of known optimal objective *** intuitive streaming algorithm returns a solution such that its cover function value is no less thanα(1−ϵ)times threshold,and the cost function is no more than(2+ϵ)^(2)/(ϵ^(2)ω^(2))⋅κ,whereκis a value that we suppose for the optimal solution andαis the approximation ratio of an algorithm for unconstrained maximization problem that we can call *** we present a bicriteria streaming algorithm scanning the ground set multi-pass to weak the assumption that we guess the optimal objective value in advance,and maintain the same bicriteria approximation *** we modify the multi-pass streaming algorithm to a single-pass one without compromising the performance ***,we also propose some numerical experiments to test our algorithm’s performance comparing with some existing methods.

关键词： approximately submodular linear additive streaming model bicriteria algorithm

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LINEAR QUADRATURE METHOD OF MOMENTS FOR SOLVING THE PDF MODEL EQUATION FOR TURBULENT REACTIVE FLOWS

LINEAR QUADRATURE METHOD OF MOMENTS FOR SOLVING THE PDF MODE...

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ASME 2024 International Mechanical engineering Congress and Exposition, IMECE 2024

作者： Wang, Yunchu Wang, Yize Yuan, Li NCMIS 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

ISBN: (纸本)9780791888667

Quadrature-based moment methods (QBMMs) are an alternative approach for the numerical solution of the probability density function (PDF) model equation for turbulent combustion. In this work, we propose a new QBMM called Linear Quadrature Method Of Moments (LQMOM) for the univariate PDF case. We use a set of predefined quadrature nodes and weights in the sample space to establish linear equations for the PDF values at the nodes in the moment inversion. The LQMOM is more economic than the original QMOM which needs to solve nonlinear equations in the moment inversion. However, the LQMOM may return negative PDF values for a non-smooth PDF. So we construct the LQMOM-QMOM hybrid algorithm. Further, we develop the linear Conditional Quadrature Method Of Moments (LCQMOM) and a simplified version (LCQMOM-S) for the multivariate PDF case by referring to the main idea of the original CQMOM. The LQMOM-QMOM hybrid algorithm is tested in a plug-flow reactor example, and the LQMOM(-S)-CQMOM hybrid algorithms in conjunction with a LES method are tested in two compressible turbulent reactive flow examples. The numerical results show that the hybrid algorithms can reduce 20-35% computational cost compared with the respective QMOM and CQMOM. Copyright © 2024 by ASME.

关键词： Probability density function

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A two-dimensional double layer-averaged model of hyperconcentrated turbidity currents with non-Newtonian rheology

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International Journal of Sediment Research 2023年第6期38卷 794-810页

作者： Yining Sun Ji Li Zhixian Cao Alistair George Liam Borthwick State Key Laboratory of Water Resources Engineering and Management Wuhan University Zienkiewicz Centre for Computational Engineering Faculty of Science and EngineeringSwansea University Institute for Infrastructure and Environment University of Edinburgh School of Engineering Computing and MathematicsUniversity of Plymouth

Hyperconcentrated turbidity currents typically display non-Newtonian characteristics that influence sediment transport and morphological evolution in alluvial ***,hydro-sedimentmorphological processes involving hyperconcentrated turbidity currents are poorly understood,with little known about the effect of the non-Newtonian *** current paper extends a recent twodimensional double layer-averaged model to incorporate non-Newtonian constitutive *** extended model is benchmarked against experimental and numerical data for cases including subaerial mud flow,subaqueous debris flow,and reservoir turbidity *** computational results agree well with observations for the subaerial mud flow and independent numerical simulations of subaqueous debris *** between the non-Newtonian and Newtonian model results become more pronounced in terms of propagation distance and sediment transport rate as sediment concentration *** model is then applied to turbidity currents in the Guxian Reservoir planned for middle Yellow River,China,which connects to a tributary featuring hyperconcentrated sediment-laden *** non-Newtonian model predicts slower propagation of turbidity currents and more significant bed aggradation at the confluence between the tributary Wuding River and the Yellow River in the reservoir than its Newtonian *** difference in model performance could be of considerable importance when optimizing reservoir operation schemes.

关键词： Double layer-averaged model Non-Newtonian rheology Mud flow Reservoir turbidity current Yellow River

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DISCRETE ENERGY ANALYSIS OF THE THIRD-ORDER VARIABLE-STEP BDF TIME-STEPPING FOR DIFFUSION EQUATIONS

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Journal of computational mathematics 2023年第2期41卷 325-344页

作者： Hong-lin Liao Tao Tang Tao Zhou Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China

This is one of our series works on discrete energy analysis of the variable-step BDF *** this part,we present stability and convergence analysis of the third-order BDF(BDF3)schemes with variable steps for linear diffusion equations,see,e.g.,[SIAM ***.,58:2294-2314]and[***.,90:1207-1226]for our previous works on the BDF2 *** this aim,we first build up a discrete gradient structure of the variable-step BDF3 formula under the condition that the adjacent step ratios are less than 1.4877,by which we can establish a discrete energy dissipation ***-robust stability and convergence analysis in the L^(2) norm are then *** the mesh robustness means that the solution errors are well controlled by the maximum time-step size but independent of the adjacent time-step *** also present numerical tests to support our theoretical results.

关键词： Diffusion equations Variable-step third-order BDF scheme Discrete gradient structure Discrete orthogonal convolution kernels Stability and convergence

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Human-Machine Pilot Navigation Method Using Nonlinear Model Predictive Control, Simulation and Inflight Testing 43

Human-Machine Pilot Navigation Method Using Nonlinear Model ...

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43rd AIAA DATC/IEEE Digital Avionics Systems Conference, DASC 2024

作者： Bertoncini, Jeremy Dudek, Adrian Ostler, Johannes Russ, Martin Gerdts, Matthias Institute of Applied Mathematics and Scientific Computing Institute of Flight Systems University of the Bundeswehr Munich Department of Aerospace Engineering Neubiberg85577 Germany

ISBN: (纸本)9798350349610

In military or civil aviation, depending on the mission to be accomplished, an aircraft may need to avoid prohibited or dangerous areas that are not always within line of sight. However, these areas can be identified by external information and communicated from a ground station. The aim of this work is to provide an optimal control method that generates trajectories and assists the pilot in navigating. Using a human-machine interface, the pilot has access to a digital twin of the actual airspace, where the route is modeled using a tunnel-in-the-sky method. The research can be applied to airborne mission management, airport maneuver management or military operations. The path planning task is formulated as an optimal control problem and solved on a fixed time horizon using a nonlinear model predictive controller (NMPC) [5]. © 2024 IEEE.

关键词： Motion planning

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