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arXiv 2025年

作者： Huang, Xueling Goubet, Olivier Shen, Jie School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian Xiamen361005 China Laboratoire Paul Painlevé CNRS UMR 8524 et équipe projet INRIA PARADYSE Université de Lille Lille59000 France School of Mathematical Science Eastern Institute of Technology Zhejiang Ningbo315200 China

We study the properties of a semi-implicit Euler scheme that is widely used in time discretization of Keller-Segel equations both in the parabolic-elliptic form and the parabolic-parabolic form. We prove that this linear, decoupled, first-order scheme preserves unconditionally the important properties of Keller-Segel equations at the semi-discrete level, including the mass conservation and positivity preserving of the cell density, and the energy dissipation. We also establish optimal error estimates in Lp-norm (1 Copyright © 2025, The Authors. All rights reserved.

关键词： Euler equations

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LOCAL SUPERCONVERGENCE OF CONTINUOUS GALERKIN SOLUTIONS FOR DELAY DIFFERENTIAL EQUATIONS OF PANTOGRAPH TYPE

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Journal of Computational Mathematics 2016年第2期34卷 186-199页

作者： Xiuxiu Xu Qiumei Huang Hongtao Chen Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Xiamen 361005 China

This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution U and the interpolation Hhu of the exact solution u. The theoretical results are illustrated by numerical examples.

关键词： Pantograph delay differential equations Uniform mesh Continuous Galerkinmethods Supercloseness Superconvergence.

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An oscillation-free Hermite WENO scheme for hyperbolic conservation laws

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Science China Mathematics 2024年第2期67卷 431-454页

作者： Zhuang Zhao Jianxian Qiu School of Mathematical Sciences and Institute of Natural Sciences Shanghai Jiao Tong UniversityShanghai 200240China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, the sixth-order oscillation-free Hermite weighted essentially non-oscillatory (OFHWENO) scheme is proposed for hyperbolic conservation laws on structured meshes, where the zeroth- andfirst-order moments are the variables for the governing equations. The main difference from other HWENOschemes existing in the literature is that we add high-order numerical damping terms in the first-order momentequations to control spurious oscillations for the OF-HWENO scheme. The OF-HWENO scheme not only canachieve the designed optimal numerical order, but also can be easily implemented as we use only one set ofstencils in the reconstruction procedure and the same reconstructed polynomials are applied for the zeroth- andfirst-order moment equations. In order to obtain the adaptive order resolution when facing discontinuities, atransition polynomial is added in the reconstruction, where the associated linear weights can also be any positivenumbers as long as their summation equals one. In addition, the OF-HWENO scheme still keeps compactnessas only immediate neighbor values are needed in the space discretization. Some benchmark numerical tests areperformed to illustrate the high-order accuracy, high resolution and robustness of the proposed scheme.

关键词： Hermite WENO scheme hyperbolic conservation laws oscillation-free adaptive order discontinuous Galerkin method

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Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions

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Applied Mathematics and Mechanics(English Edition) 2023年第7期44卷 1069-1084页

作者： Zhiping MAO Xuhui MENG School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamen 361005Fujian ProvinceChina Institute of Interdisciplinary Research for Mathematics and Applied Science School of Mathematics and StatisticsHuazhong University of Science and TechnologyWuhan 430074China

We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this *** particular,to better capture the sharpness of the solution,we propose the adaptive sampling methods(ASMs)based on the residual and the gradient of the *** first present a residual only-based ASM denoted by ASMⅠ.In this approach,we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains,then we add new residual points in the sub-domain which has the largest mean absolute value of the residual,and those points which have the largest absolute values of the residual in this sub-domain as new residual *** further develop a second type of ASM(denoted by ASMⅡ)based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the *** procedure of ASMⅡis almost the same as that of ASMⅠ,and we add new residual points which have not only large residuals but also large *** demonstrate the effectiveness of the present methods,we use both ASMⅠand ASMⅡto solve a number of PDEs,including the Burger equation,the compressible Euler equation,the Poisson equation over an Lshape domain as well as the high-dimensional Poisson *** has been shown from the numerical results that the sharp solutions can be well approximated by using either ASMⅠor ASMⅡ,and both methods deliver much more accurate solutions than the original PINNs with the same number of residual ***,the ASMⅡalgorithm has better performance in terms of accuracy,efficiency,and stability compared with the ASMⅠ*** means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the ***,we also employ the similar adaptive sampling technique fo

关键词： physics-informed neural network(PINN) adaptive sampling high-dimension L-shape Poisson equation accuracy

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Asymptotic stability of explicit infinite energy blowup solutions of the 3D incompressible Navier-Stokes equations

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Science China Mathematics 2023年第11期66卷 2523-2544页

作者： Fangyu Han Zhong Tan School of Mathematical Sciences Xiamen UniversityXiamen 361005China Fujian Provincial Key Laboratory on Mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamen UniversityXiamen 361005China Shenzhen Research Institute of Xiamen University Shenzhen 518057China

In this paper,we study the dynamical stability of a family of explicit blowup solutions of the threedimensional(3D)incompressible Navier-Stokes(NS)equations with smooth initial values,which is constructed in Guo et al.(2008).This family of solutions has finite energy in any bounded domain of R3,but unbounded energy in *** on similarity coordinates,energy estimates and the Nash-Moser-H?rmander iteration scheme,we show that these solutions are asymptotically stable in the backward light-cone of the ***,the result shows the existence of local energy blowup solutions to the 3D incompressible NS equations with growing ***,the result also shows that in the absence of physical boundaries,the viscous vanishing limit of the solutions does not satisfy the 3D incompressible Euler equations.

关键词： Navier-Stokes equations asymptotic stability blowup solution infinite energy Nash-Moser-Hormander iteration scheme zero-viscosity limit

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Scattering Phase Correction for Semiclassical Quantization Rules in Multi-Dimensional Quantum Systems

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Communications in Theoretical Physics 2010年第2期53卷 250-256页

作者： HUANG Wen-Min MOU Chung-Yu CHANG Cheng-Hung Department of Physics National Tsing-Hua University Hsinchu Taiwan physics Division National Center for Theoretical Sciences Hsinchu Taiwan Institute of Physics National Chiao Tung University Hsinchu Taiwan Institute of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu Taiwan

While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny＇s transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semielassical Landauer Buttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.

关键词： Bogomolny's transfer operator semiclassical quantization rules quantum chaos

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The Immersed Boundary Method for Two-Dimensional Foam with Topological Changes

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Communications in Computational Physics 2012年第7期12卷 479-493页

作者： Yongsam Kim Yunchang Seol Ming-Chih Lai Charles S.Peskin Department of Mathematics Chung-Ang UniversityDongjakgu HeukseokdongSeoul 156-756Korea Department of Applied Mathematics Center of Mathematical Modeling and Scientific ComputingNational Chiao Tung University1001Ta Hsueh RoadHsinchu 300Taiwan Courant Institute of Mathematical Sciences New York University251 Mercer StreetNew YorkNY 10012 USA

We extend the immersed boundary(IB)method to simulate the dynamics of a 2D dry foam by including the topological changes of the bubble *** the article[***,M.-***,and ***,***.229:5194-5207,2010],we implemented an IB method for the foam problem in the two-dimensional case,and tested it by verifying the von Neumann relation which governs the coarsening of a two-dimensional dry ***,the method implemented in that article had an important limitation;we did not allow for the resolution of quadruple or higher order junctions into triple junctions.A total shrinkage of a bubble with more than four edges generates a quadruple or higher order *** reality,a higher order junction is unstable and resolves itself into triple *** here extend the methodology previously introduced by allowing topological changes,and we illustrate the significance of such topological changes by comparing the behaviors of foams in which topological changes are allowed to those in which they are not.

关键词： Foam permeability capillary-driven motion immersed boundary method coarsening topological changes T1 and T2 processes

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Kinetic modeling of ace operon genetic regulation Escherichia coli

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Journal of Bioinformatics and Computational Biology 2008年第5期6卷 933-959页

作者： Peskov, Kirill Goryanin, Igor Prank, Klaus Tobin, Frank Demin, Oleg Institute of Theoretical and Experimental Biophysics RAS 142290 Pushchino Institutskaya St. 3 Russian Federation Institute for Systems Biology SPb Sankt-Peterburg Russian Federation Edinburgh University Edinburgh United Kingdom Scientific Computing and Mathematical Modeling Group GlaxoSmithKline Stevenage Hertfordshire SG1 2NY Gunnels Wood Road United Kingdom Scientific Computing and Mathematical Modeling Group GlaxoSmithKline King of Prussia PA 19406 709 Swedeland Road United States A. N. Belozersky Institute of Physico-Chemical Biology Moscow Russian Federation

A family of kinetic models has been developed that takes into account available experimental information on the regulation of ace operon expression in Escherichia coli. This has allowed us to study and analyze possible versions of regulation of the ace operon and to test their possibilities. Based on literature analysis, we found that there is an ambiguity of properties of IclR (main repressor of ace operon). The main aspect of this ambiguity are two different forms of IclR purified from E. coli K strain and different coeffector sets for IclR purified from E. coli K and B strains. It has been shown that the full-length form of IclR is physiologically relevant and that IclR truncation is a result of purification of the protein from E. coli K strains. We also found that the IclR protein purified from E. coli B strain carries two coeffector binding sites. Using model-developed levels of steady state aceBAK expression against physiological ranges of coeffectors, concentration has been predicted. © 2008 Imperial College Press.

关键词： Acetate (ace) operon FruR Glyoxylate bypass IclR Kinetic modeling Regulation of gene expression

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High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

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Advances in Aerodynamics 2020年第1期2卷 555-578页

作者： Yanqun Jiang Xun Chen Xu Zhang Tao Xiong Shuguang Zhou Department of Mathematics Southwest University of Science and Technology621010 MianyangChina School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen University361005 XiamenChina Computational Aerodynamics Institute China Aerodynamics Research and Development Center621000 MianyangChina

The computation of compressible flows at all Mach numbers is a very challenging *** efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime,while it can deal with stiffness and accuracy in the low Mach number *** paper designs a high order semi-implicit weighted compact nonlinear scheme(WCNS)for the all-Mach isentropic Euler system of compressible gas *** avoid severe Courant-Friedrichs-Levy(CFL)restrictions for low Mach flows,the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components.A third-order implicit-explicit(IMEX)method is used for the time discretization of the split components and a fifth-order WCNS is used for the spatial discretization of flux *** high order IMEX method is asymptotic preserving and asymptotically accurate in the zero Mach number ***-and two-dimensional numerical examples in both compressible and incompressible regimes are given to demonstrate the advantages of the designed IMEX WCNS.

关键词： High order scheme IMEX time discretization WCNS Asymptotic-preserving property Low Mach number Isentropic Euler equations

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Improved analysis of rectangular dielectric waveguides based on a legendre pseudospectral penalty scheme

Improved analysis of rectangular dielectric waveguides based...

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Integrated Photonics Research, Silicon and Nanophotonics, IPRSN 2010

作者： Chiang, Shun-Fan Lin, Bang-Yan Teng, Chun-Hao Chang, Hung-Chun Department of Electrical Engineering Graduate Institute of Photonics and Optoelectronics Graduate Institute of Communication Engineering National Taiwan University Taipei 10617 Taiwan Department of Applied Mathematics and Center of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu 30010 Taiwan

A Legendre pseudospectral method with penalty scheme is established in frequency domain for high-accuracy waveguide mode analysis. For a square dielectric waveguide, the calculated modal index is seen to converge to t... 详细信息

ISBN: (纸本)9781557528957

关键词： Frequency domain analysis

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