作者： Li, Jianliang*

期刊： Applicable Analysis,2022年101(1):48-62 ISSN：0003-6811

通讯作者： Li, Jianliang

作者机构： [Li, Jianliang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.

通讯机构： [Li, Jianliang] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.

关键词： Inverse acoustic scattering;generalized impedance boundary condition;reverse time migration method;35J05;65N21;65R32;78A46

摘要： We consider the inverse scattering problem of determining the shape of an impenetrable two-dimensional obstacle with a generalized impedance boundary condition from near-field measurements. We propose the reverse time migration method where the imaging functional is defined as the imaginary part of the cross-correlation. Our analysis shows that, on the one hand, the imaging functional has contrast at the boundary of the scatterer and decays outside the scatterer; On the other hand, the imaging functional is always positive thus may have better stability properties. These imply that the approach has powerful imaging quality which is confirmed in our numerical experiments. © 2020 Informa UK Limited, trading as Taylor & Francis Group.

语种： 英文

作者： Xie, Yongqin;Li, Jun*;Zhu, Kaixuan

期刊： Advances in Difference Equations,2021年2021(1):1-17 ISSN：1687-1839

通讯作者： Li, Jun

作者机构： [Li, Jun; Xie, Yongqin] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.;[Zhu, Kaixuan] Hunan Univ Arts & Sci, Coll Math & Phys Sci, Changde, Peoples R China.

通讯机构： [Li, Jun] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.

关键词： Nonclassical diffusion equation;Global attractor;Regularity;Upper semicontinuity;Arbitrary polynomial growth

摘要： <jats:title>Abstract</jats:title><jats:p>In this paper, we mainly investigate upper semicontinuity and regularity of attractors for nonclassical diffusion equations with perturbed parameters<jats:italic>ν</jats:italic>and the nonlinear term<jats:italic>f</jats:italic>satisfying the polynomial growth of arbitrary order<jats:inline-formula><jats:alternatives><jats:tex-math>$p-1$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:math></jats:alternatives></jats:inline-formula>(<jats:inline-formula><jats:alternatives><jats:tex-math>$p \geq 2$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math></jats:alternatives></jats:inline-formula>). We extend the asymptotic a priori estimate method (see (Wang et al. in Appl. Math. Comput. 240:51–61, 2014)) to verify asymptotic compactness and upper semicontinuity of a family of semigroups for autonomous dynamical systems (see Theorems 2.2 and 2.3). By using the new operator decomposition method, we construct asymptotic contractive function and obtain the upper semicontinuity for our problem, which generalizes the results obtained in (Wang et al. in Appl. Math. Comput. 240:51–61, 2014). In particular, the regularity of global attractors is obtained, which extends and improves some results in (Xie et al. in J. Funct. Spaces 2016:5340489, 2016; Xie et al. in Nonlinear Anal. 31:23–37, 2016).</jats:p>

语种： 英文

作者： Ying, Jinyong;Fan, Ronghong*;Li, Jiao;Lu, Benzhuo

期刊： Journal of Computational Physics,2021年430:110098 ISSN：0021-9991

通讯作者： Fan, Ronghong

作者机构： [Ying, Jinyong] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.;[Fan, Ronghong; Lu, Benzhuo] Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, State Key Lab Sci Engn Comp, Beijing 100190, Peoples R China.;[Li, Jiao] Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.

通讯机构： [Fan, Ronghong] C;Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, State Key Lab Sci Engn Comp, Beijing 100190, Peoples R China.

关键词： Continuum mechanics;Eigenvalues and eigenfunctions;Finite element method;Linear systems;Mesh generation;Newton-Raphson method;Software packages;Software testing;Acceleration technique;Block preconditioner;Continuum Modeling;Finite element solver;Molecular biosciences;Poisson-Nernst-Planck equations;Preconditioned linear system;Solution decomposition;Poisson equation

摘要： The Poisson-Nernst-Planck (PNP) equation is one important continuum model for studying charge transport in ion channels, which is a common phenomenon and plays a key role in molecular biosciences. In this paper, to improve the current PNP solvers, according to the equation structure, a new block preconditioner was proposed and proved that the preconditioned linear system has bounded eigenvalues independent of mesh sizes under some conditions, thus guaranteeing that the convergence rate of the preconditioned linear solver is independent of mesh sizes. Meanwhile, the commonly-used solution decomposition schemes in classic continuum models for isolating the singularities were presented and then one was chosen for solving PNP when zero initial guess was used for the Newton method. Furthermore, an efficient and improved finite element PNP solver was proposed by further combining the two-grid method as an acceleration technique. Then the new program package was fulfilled based on the state-of-the-art finite element library FEniCS and the efficient scientific library PETSc. Finally, numerical simulations on a test model with analytical solution as well as some tests on protein cases were carried out to validate the new program package and our theoretical results. © 2020 Elsevier Inc.

语种： 英文

作者： 李景

期刊： 文渊(高中版),2020年(6):509 ISSN：2096-6288

作者机构： 长沙理工大学数学与统计学院 湖南 长沙 410000;[李景] 长沙理工大学

关键词： 数学学科;研究生;培养现状;改革方案

摘要： 本文结合工作经验,通过分析当前数学学科硕士研究生培养的现状,探索并发现当前数学学科硕士研究生培养质量现存在的问题,并提出解决问题相应的改革方案,望起到抛砖引玉的作用.

语种： 中文

作者： Chang, Wanru;Chen, C. S.;Liu, Xiao-Yan*;Li, J.

期刊： Mathematics and Computers in Simulation,2020年177:487-499 ISSN：0378-4754

通讯作者： Liu, Xiao-Yan

作者机构： [Chang, Wanru] Zhejiang Univ, Sch Math Sci, Hangzhou, Zhejiang, Peoples R China.;[Chen, C. S.] Univ Southern Mississippi, Dept Math, Hattiesburg, MS 39406 USA.;[Liu, Xiao-Yan] Taiyuan Univ Technol, Coll Data Sci, Taiyuan, Peoples R China.;[Li, J.] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.

通讯机构： [Liu, Xiao-Yan] T;Taiyuan Univ Technol, Coll Data Sci, Taiyuan, Peoples R China.

关键词： Functions;Numerical methods;Axisymmetric equations;Axisymmetric problems;Chebyshev polynomials;Low-order polynomials;Method of particular solution;Particular solution;Polynomial basis functions;Preconditioning treatment;Polynomials

摘要： In this paper, two localized meshless methods based on polynomial basis functions are utilized to solve axisymmetric problems. In the first approach, we applied the localized method of particular solutions (LMPS) and the closed-form particular solution to simplify the two-stage approach using Chebyshev polynomial as the basis functions for solving axisymmetric problems. We also propose the modified local Pascal polynomial method (MLPM) to compare the results with LMPS. Since only the low order polynomial basis functions are used, no preconditioning treatment is required and the solution is quite stable. Four numerical examples are given to demonstrate the effectiveness of the proposed methods. © 2020 International Association for Mathematics and Computers in Simulation (IMACS)

语种： 英文

作者： Li, J.;Ying, J.*

期刊： JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,2020年16(1):325-356 ISSN：1547-5816

通讯作者： Ying, J.

作者机构： School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114, China;School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, China

通讯机构： School of Mathematics and Statistics, Central South University, Changsha, Hunan, China

关键词： Biomolecular electrostatics;Block iteration method;Finite element method;Implicit continuum model;Nonlocal model

摘要： The nonlocal mofied Poisson-Boltzmann equation (NMPBE) is one important variant of a commonly-used dielectric continuum model, Poisson-Boltzmann equation (PBE). In this paper, we use a nonlinear block relaxation method to develop a new nonlinear solver for the nonlinear equation of Φ and thus a new NMPBE solver, which is then programmed as a software package in C\C++, Fortran and Python for computing the electrostatics of a protein in a symmetric 1:1 ionic solvent. Numerical tests validate the new package and show that the new solver can improve the efficiency by at least 40% than the finite element NMPBE solver without compromising solution accuracy. © 2020, American Institute of Mathematical Sciences.

语种： 英文

作者： Gong, Hongfang*;Li, Junyi;Li, Renfa

期刊： IEEE ACCESS,2020年8:174516-174529 ISSN：2169-3536

通讯作者： Gong, Hongfang

作者机构： [Gong, Hongfang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.;[Li, Junyi; Li, Renfa] Hunan Univ, Coll Comp Sci & Elect Engn, Changsha 410082, Hunan, Peoples R China.

通讯机构： [Gong, Hongfang] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.

关键词： Petri nets;Fault detection;Test pattern generators;Boolean functions;Software;Licenses;Automatic test cases generation;fault-based testing;general Boolean expression test;ordered binary label-driven Petri net;path-oriented test criteria

摘要： Boolean expression testing requires certain types of tests for each Boolean expression in program specification or implementation. Fault-based testing essentially uses a subset of the exhaustive test set to detect certain special types of faults. A fault-based Boolean expression testing strategy called constraint true and false test point (CTFTP) is proposed. The test consists of two test case generation strategies, namely a unique constraint true point (UCTP) strategy and a near constraint false point (NCFP) strategy. An ordered binary label-driven Petri net model is presented to analyze the interaction between Boolean transitions and Boolean literals and yield the test paths of a singular term for the irredundant disjunctive normal forms (IDNFs). On the basis of the test paths, we develop a configuration-based IDNF test generation algorithm, which is employed to obtain the UCTP, NCFP, and CTFTP test sets for the IDNFs. The proposed test generation algorithm based on literal substitution is applied to extend the CTFTP strategy and generate a test suite for general Boolean expressions, which are evaluated using TCAS II specifications. Experimental results show that the CTFTP strategy can detect the same seven types of faults similar to the MUMCUT strategy when testing IDNFs, but only a subset of the MUMCUT test set is required. Five types of faults of general Boolean expressions can also be detected using CTFTP strategies.

语种： 英文

作者： 李景;王芳

期刊： 科教导刊：电子版,2020年(18):195-195 ISSN：1674-6813

作者机构： 长沙理工大学数学与统计学院 湖南·长沙 410114;[李景; 王芳] 长沙理工大学

关键词： 课程教学;多元化教学模式;大学数学

摘要： 本文首先梳理大学数学课程教学的现状,再针对现有的问题提出教学模式的改革,综合多元化教学理念提出实际的改革方式,探索大学数学课程教学的多元化模式.

语种： 中文

作者： Chen, C. S.;Shen, Shu-Hui;Dou, Fangfang*;Li, J.

期刊： Mathematics and Computers in Simulation,2020年177:500-515 ISSN：0378-4754

通讯作者： Dou, Fangfang

作者机构： [Dou, Fangfang; Shen, Shu-Hui; Chen, C. S.] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China.;[Chen, C. S.] Univ Southern Mississippi, Sch Math & Nat Sci, Hattiesburg, MS 39406 USA.;[Li, J.] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China.

通讯机构： [Dou, Fangfang] U;Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China.

关键词： Boundary conditions;Functions;Partial differential equations;Dirichlet;Fourth order partial differential equations;Fourth-order PDEs;Method of particular solution;Polynomial basis functions;Second order pdes;Polynomials

摘要： Due to certain difficulties in solving fourth-order partial differential equations (PDEs) using localized methods, the given differential equation is normally split into two decoupled second order PDEs. Such an approach is only feasible for Dirichlet and Laplace boundary conditions. In this paper the localized method of particular solutions is applied to fourth-order PDEs directly using polynomial basis functions. The effectiveness of the proposed algorithms is demonstrated by considering four numerical examples. © 2020 International Association for Mathematics and Computers in Simulation (IMACS)

语种： 英文

作者： Li, J.;Sladek, J.;Sladek, V;Wen, P. H.*

期刊： European Journal of Mechanics A-Solids,2020年83:104023 ISSN：0997-7538

通讯作者： Wen, P. H.

作者机构： [Li, J.] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.;[Sladek, V; Sladek, J.] Slovak Acad Sci, Inst Construct & Architecture, Bratislava 84503, Slovakia.;[Wen, P. H.] Queen Mary Univ London, Sch Engn & Mat Sci, London E1 4NS, England.

通讯机构： [Wen, P. H.] Q;Queen Mary Univ London, Sch Engn & Mat Sci, London E1 4NS, England.

关键词： Boundary element method;Crack growth;Meshless method;Static and dynamic loadings;Stress intensity factors

摘要： This paper investigated a hybrid Meshless Displacement Discontinuity Method (MDDM) for a cracked plate subjected to static and dynamic loadings. The purpose of MDDM is to model displacement discontinuity on a cracked surface by the displacement discontinuity method in an infinite plate. This was achieved by considering a meshless approach, the equilibrium equations, and the boundary conditions for a domain with an irregular nodes distribution. Also, by imposing the principle of superposition, accurate and convergent solutions can be obtained. In this paper, the static and dynamic stress intensity factors, and the crack growth for different initial crack length and crack slant angles are investigated. The Laplace transform method is applied to deal with dynamic problems and the time-dependent values are obtained by the Durbin inversion technique. Validations of the presented technique are demonstrated by four numerical examples of plates with a central embedded crack. © 2020

语种： 英文

作者： Li, Jiao;Ying, Jinyong*

期刊： JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,2020年16(1):357-369 ISSN：1547-5816

通讯作者： Ying, Jinyong

作者机构： [Li, Jiao] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.;[Ying, Jinyong] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.

通讯机构： [Ying, Jinyong] C;Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.

关键词： Boltzmann equation;C++ (programming language);Computer software;Continuum mechanics;Dissociation;Electrostatics;Nonlinear equations;Compromising solutions;Dielectric continuum model;Dielectric modeling;Ionic solvents;Non-linear solver;Numerical tests;Poisson-Boltzmann equations;Relaxation methods;Poisson equation

摘要： The nonlocal mofied Poisson-Boltzmann equation (NMPBE) is one important variant of a commonly-used dielectric continuum model, Poisson-Boltzmann equation (PBE). In this paper, we use a nonlinear block relaxation method to develop a new nonlinear solver for the nonlinear equation of Φ and thus a new NMPBE solver, which is then programmed as a software package in C\C++, Fortran and Python for computing the electrostatics of a protein in a symmetric 1:1 ionic solvent. Numerical tests validate the new package and show that the new solver can improve the efficiency by at least 40% than the finite element NMPBE solver without compromising solution accuracy. © 2020, American Institute of Mathematical Sciences.

语种： 英文

作者： Li, Jianliang;Helin, Tapio;Li, Peijun*

期刊： Communications in Partial Differential Equations,2020年45(10):1335-1380 ISSN：0360-5302

通讯作者： Li, Peijun

作者机构： [Li, Jianliang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.;[Helin, Tapio] LUT Univ, Sch Engn Sci, Lappeenranta, Finland.;[Li, Peijun] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA.

通讯机构： [Li, Peijun] P;Purdue Univ, Dept Math, W Lafayette, IN 47907 USA.

关键词： Elastic wave equation;Gaussian random function;Helmholtz equation;inverse source problem;uniqueness

摘要： This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a domain away from the source region. The source is assumed to be a microlocally isotropic generalized Gaussian random function such that its covariance operator is a classical pseudo-differential operator. Given such a distributional source, the direct problem is shown to have a unique solution by using an integral equation approach and the Sobolev embedding theorem. For the inverse problem, we demonstrate that the amplitude of the scattering field averaged over the frequency band, obtained from a single realization of the random source, determines uniquely the principle symbol of the covariance operator. The analysis employs asymptotic expansions of the Green functions and microlocal analysis of the Fourier integral operators associated with the Helmholtz and Navier equations.

语种： 英文

作者： Li, Jianliang*;Li, Peijun

期刊： SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2019年51(6):4570-4603 ISSN：0036-1410

通讯作者： Li, Jianliang

作者机构： [Li, Jianliang] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal, Sch Math & Stat, Changsha 410114, Peoples R China.;[Li, Peijun] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA.

通讯机构： [Li, Jianliang] C;Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal, Sch Math & Stat, Changsha 410114, Peoples R China.

关键词： inverse source problem;elastic wave equation;Lippmann--Schwinger integral equation;Gaussian random function;uniqueness;78A46;65C30

摘要： Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with a linear load. The source is modeled as a microlocally isotropic generalized Gaussian random function whose covariance operator is a classical pseudodifferential operator. The goal is to recover the principal symbol of the covariance operator from the displacement measured in a domain away from the source. For such a distributional source, we show that the direct problem has a unique solution by introducing an equivalent Lippmann-Schwinger integral equation. For the inverse problem, we demonstrate that, with probability one, the principal symbol of the covariance operator can be uniquely determined by the amplitude of the displacement averaged over the frequency band, generated by a single realization of the random source. The analysis employs the Born approximation, asymptotic expansions of the Green tensor, and microlocal analysis of the Fourier integral operators. © 2019 Society for Industrial and Applied Mathematics.

语种： 英文

作者： Li, Jiao;Ying, Jinyong*;Xie, Dexuan

期刊： Nonlinear Analysis: Real World Applications,2019年47:188-203 ISSN：1468-1218

通讯作者： Ying, Jinyong

作者机构： [Li, Jiao] Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.;[Ying, Jinyong] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.;[Xie, Dexuan] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53211 USA.

通讯机构： [Ying, Jinyong] C;Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.

关键词： Electrochemistry;Electrostatics;Free energy;Ions;Poisson equation;Electric double layer;Electrostatic free energy;Electrostatic solvation free energies;Ion size;Ion size effects;Ionic concentrations;Solution existence;Variational methods;Boltzmann equation

摘要： In this paper, an improved electrostatic free energy functional is presented as an extension of the one proposed in Xie and Li (2015) to reflect ion size effects. It is then shown to have a unique minimizer, resulting in the solution existence and uniqueness of one commonly-used ion size-modified Poisson–Boltzmann equation (SMPBE). As for applications, SMPBE is used to calculate the electrostatic solvation free energy with the new derived well-defined formula and simulate an electric double layer numerically to demonstrate the advantage of SMPBE over the classic Poisson–Boltzmann equation in the prediction of ionic concentrations. © 2018 Elsevier Ltd

语种： 英文

作者： Liu, Fawang*;Feng, Libo;Vo Anh;Li, Jing

期刊： Computers & Mathematics with Applications,2019年78(5):1637-1650 ISSN：0898-1221

通讯作者： Liu, Fawang

作者机构： [Liu, Fawang; Feng, Libo] Queensland Univ Technol, Sch Math Sci, GPO Box 2434, Brisbane, Qld 4001, Australia.;[Liu, Fawang] Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350116, Fujian, Peoples R China.;[Vo Anh] Swinburne Univ Technol, Fac Sci Engn & Technol, POB 218, Hawthorn, Vic 3122, Australia.;[Li, Jing] Changsha Univ Sci & Technol, Sch Math Sci, Changsha 410114, Hunan, Peoples R China.

通讯机构： [Liu, Fawang] Q;Queensland Univ Technol, Sch Math Sci, GPO Box 2434, Brisbane, Qld 4001, Australia.

关键词： Multi-term time-space fractional;Bloch-Torrey equations;Riesz fractional operator;Unstructured mesh;Irregular domains;Galerkin finite element method

摘要： Models based on partial differential equations containing time–space fractional derivatives have attracted considerable interest in the past decade because of their ability to model anomalous transport phenomena. These phenomena are strongly connected to the interactions within complex and non-homogeneous media exhibiting spatial heterogeneity. The class of equations with multi-term time–space derivatives of fractional orders has been found to be very useful in the description of such interactions. This motivates the extension of the classical Bloch–Torrey equation through the application of the operators of fractional calculus to new multi-term time–space fractional Bloch–Torrey equations with Riesz fractional operators. In this paper, we firstly propose an unstructured-mesh Galerkin finite element method for the two-dimensional multi-term time–space fractional diffusion equation with Riesz fractional operators on irregular convex domains. Secondly, we rigorously establish the stability and convergence of the numerical scheme. Thirdly, we extend the computational model to solve a system of coupled two-dimensional multi-term time–space fractional Bloch–Torrey equations. Finally, some numerical results are given to demonstrate the versatility and application of the models. © 2019 Elsevier Ltd

语种： 英文

作者： Li, Jianliang*

期刊： Inverse Problems in Science and Engineering,2019年27(1):17-36 ISSN：1741-5977

通讯作者： Li, Jianliang

作者机构： [Li, Jianliang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China.

通讯机构： [Li, Jianliang] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China.

关键词： Integral equations;Inverse problems;Surface measurement;Impedance boundary conditions;Inverse scattering;Multi frequency;Nonlinear integral equations;Rough surfaces;Surface scattering

摘要： In this paper, we consider an inverse rough surface scattering problem in near-field optical imaging. This problem is actually to reconstruct the scattering surface as well as its impedance coefficient from multifrequency near-field data, and can be reduced into an integral scheme by employing an integral representation. We solve this integral scheme by a non-linear integral equation method, and further develop a fast inversion algorithm for reconstructing both the rough surface and the impedance coefficient. Numerical experiments are presented to illustrate the effectiveness of the algorithm. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

语种： 英文

作者： Li, Jiao;Ying, Jinyong*;Lu, Benzhuo

期刊： Journal of Computational Physics,2019年396:193-208 ISSN：0021-9991

通讯作者： Ying, Jinyong

作者机构： [Li, Jiao] Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.;[Ying, Jinyong] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.;[Lu, Benzhuo] Chinese Acad Sci, Natl Ctr Math & Interdisciplinary Sci, Acad Math & Syst Sci, State Key Lab Sci Engn Comp, Beijing 100190, Peoples R China.

通讯机构： [Ying, Jinyong] C;Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.

关键词： Biomolecules;Boltzmann equation;Continuum mechanics;Dissociation;Electrostatic force;Forecasting;Poisson equation;Recovery;Software testing;Continuum model;Flux jump;Flux preserving;Gradient recovery;Gradient recovery technique;Implicit continuum model;Poisson-Boltzmann equations;Recovery techniques;Solvated biomolecules;Total electrostatic force;Numerical methods

摘要： Poisson-Boltzmann equation (PBE) and its variants are important implicit continuum models for predicting the electrostatics of solvated biomolecules. In this paper, in order to accurately predict the gradient of electrostatics, we propose a new flux-jump preserved gradient recovery method and then fulfill it in the program using Python and Fortran. Two numerical tests with available analytical solutions are presented to well validate the new program. Then the new proposed method is applied to recover the gradient of a simple dipole case as well as two protein cases using the numerical solutions of both PBE and SMPBE. © 2019 Elsevier Inc.

语种： 英文

作者： Li, Y.*;Li, J.;Wen, P. H.

期刊： Applied Mathematical Modelling,2019年68:306-326 ISSN：0307-904X

通讯作者： Li, Y.

作者机构： [Li, Y.] Southwest Jiaotong Univ, Sch Mech & Engn, Chengdu, Sichuan, Peoples R China.;[Li, J.] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China.;[Wen, P. H.] Queen Mary Univ London, Sch Engn & Mat Sci, London, England.

通讯机构： [Li, Y.] S;Southwest Jiaotong Univ, Sch Mech & Engn, Chengdu, Sichuan, Peoples R China.

关键词： Functionally graded materials;Infinite block;Meshless technique;Polynomial interpolation;Weak-form block Petrov–Galerkin method

摘要： This paper presents a novel weak-form block Petrov–Galerkin method (BPGM) for linear elastic and crack problems in functionally graded materials with bounded and unbounded problem domains. The main idea of this approach is to combine the meshless local Petrov–Galerkin method with block method. Once the problem domain is discretized into several sub-regions, named blocks, which can be mapped into normalized square domains. The weak-form Petrov–Galerkin method and polynomial series of interpolations are employed in each block. The computational efficiency is rigorously examined against the strong-form finite block method, the finite element technique and meshless approaches. Numerical results demonstrate that the BPGM possesses the following important properties: (1) only a few blocks are required for calculating problems in unbounded regions which saves tedious work of meshing; (2) the displacements and stresses are continuous at the interfaces of neighboring blocks; (3) due to the use of weak formulation, the continuity requirements of the approximation functions are reduced and numerical results are stable; (4) because of using Lagrange polynomial interpolation, highly accurate solutions can be obtained with a small amount of nodes in each block. © 2018 Elsevier Inc.

语种： 英文

作者： Li, Jianliang;Sun, Guanying;Zhang, Bo*

期刊： Applicable Analysis,2017年96(1):85-107 ISSN：0003-6811

通讯作者： Zhang, Bo

作者机构： [Li, Jianliang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China.;[Sun, Guanying] North China Univ Technol, Dept Math, Beijing, Peoples R China.;[Zhang, Bo] Chinese Acad Sci, AMSS, LSEC, Beijing, Peoples R China.;[Zhang, Bo] Chinese Acad Sci, AMSS, Inst Appl Math, Beijing, Peoples R China.

通讯机构： [Zhang, Bo] C;Chinese Acad Sci, AMSS, LSEC, Beijing, Peoples R China.;Chinese Acad Sci, AMSS, Inst Appl Math, Beijing, Peoples R China.

关键词： Helmholtz equation;Inverse scattering;locally rough interface;the Kirsch-Kress approach;transmission problem

摘要： This paper is concerned with the inverse problem of reconstructing an infinite, locally rough interface from the scattered field measured on line segments above and below the interface in two dimensions. We extend the Kirsch-Kress method originally developed for inverse obstacle scattering problems to the above inverse transmission problem with unbounded interfaces. To this end, we reformulate our inverse problem as a nonlinear optimization problem with a Tikhonov regularization term. We prove the convergence of the optimization problem when the regularization parameter tends to zero. Finally, numerical experiments are carried out to show the validity of the inversion algorithm.

语种： 英文

作者： Li, J.;Huang, T.*;Yue, J. H.;Shi, C.;Wen, P. H.*

期刊： JOURNAL OF STRAIN ANALYSIS FOR ENGINEERING DESIGN,2017年52(7):422-433 ISSN：0309-3247

通讯作者： Huang, T.;Wen, P. H.

作者机构： [Li, J.] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China.;[Huang, T.] Changsha Univ Sci & Technol, Sch Traff & Transportat Engn, Changsha 410114, Hunan, Peoples R China.;[Yue, J. H.] Taiyuan Univ Technol, Coll Math, Taiyuan, Peoples R China.;[Wen, P. H.; Shi, C.] Queen Mary Univ London, Sch Engn & Mat Sci, London E1 4NS, England.

通讯机构： [Huang, T.] C;[Wen, P. H.] Q;Changsha Univ Sci & Technol, Sch Traff & Transportat Engn, Changsha 410114, Hunan, Peoples R China.;Queen Mary Univ London, Sch Engn & Mat Sci, London E1 4NS, England.

关键词： Beams and girders;Elasticity;Fracture;Fracture mechanics;Laplace transforms;Shear stress;Stress intensity factors;Time domain analysis;Anti-plane;Displacement method;Fundamental solutions;Inversion methods;Laplace transform techniques;Mass densities;Mode III fractures;Time-dependent variables;Functionally graded materials

摘要： In this article, the fundamental solutions for anti-plane elasticity are derived using the Fourier transform and the Laplace transform techniques, with the shear modulus and the mass density varying exponentially for functionally graded materials. It has been shown that the transformed fundamental solutions both in the Laplace space and in the time domain have the same order of singularities as that in the static case. The time-dependent variables including the displacement and the shear stresses for anti-plane elasticity are obtained with Durbin's inversion method for the Laplace transform. The discontinuity displacement method is formulated from the fundamental solutions and applied to the mode III fracture problems. © IMechE 2017.

语种： 英文