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Numerical Mathematics(Theory,methods and Applications) 2023年第1期16卷 242-276页

作者： Xiaopeng Zhu Zhizhang Wu Zhongyi Huang Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China Department of Mathematics The University of Hong KongPokfulam RoadHong Kong SARChina

In this paper,we generalize the direct Method of Lines for linear elasticity problems of composite materials in star-shaped domains and consider its application to inverse elasticity problems.We assume that the boundary of the star-shaped domain can be described by an explicit C 1 parametric curve in the polar coordinate.We introduce the curvilinear coordinate,in which the irregular star-shaped domain is converted to a regular semi-infinite strip.The equations of linear elasticity are discretized with respect to the angular variable and we solve the resulting semidiscrete approximation analytically using a direct method.The eigenvalues of the semi-discrete approximation converge quickly to the true eigenvalues of the elliptic operator,which helps capture the singularities naturally.Moreover,an optimal error estimate of our method is given.For the inverse elasticity problems,we determine the Lam´e coefficients from measurement data by minimizing a regularized energy functional.We apply the direct Method of Lines as the forward solver in order to cope with the irregularity of the domain and possible singularities in the forward solutions.Several numerical examples are presented to show the effectiveness and accuracy of our method for both forward and inverse elasticity problems of composite materials.

关键词： Composite materials linear elasticity problems inverse elasticity problems starshaped domains Method of Lines

A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems

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Advances in Applied Mathematics and Mechanics 2013年第4期5卷 548-568页

作者： Tao Lin Yanping Lin Xu Zhang Department of Mathematics Virginia TechBlacksburgVA 24061USA Department of Applied Mathematics Hong Kong Polytechnic UniversityHung HomHong Kong Department of Mathematical and Statistics Science University of AlbertaEdmonton ABT6G 2G1Canada

This article extends the finite element Method of Lines to a parabolic initial boundary value problem whose diffusion coefficient is discontinuous across an interface that changes with respect to time.The method presented here uses immersed finite element(IFE)functions for the discretization in spatial variables that can be carried out over a fixedmesh(such as a Cartesianmesh if desired),and this featuremakes it possible to reduce the parabolic equation to a system of ordinary differential equations(ODE)through the usual semi-discretization procedure.Therefore,with a suitable choice of the ODE solver,this method can reliably and efficiently solve a parabolic moving interface problem over a fixed structured(Cartesian)mesh.Numerical examples are presented to demonstrate features of this new method.

关键词： Immersed finite element moving interface Method of Lines Cartesian mesh

An Efficient Tide-Surge Interaction Model for the Coast of Bangladesh

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China Ocean Engineering 2020年第1期34卷 56-68页

作者： M.Mizanur RAHMAN Gour Chandra PAUL Ashabul HOQUE Department of Mathematics Shahjalal University of Science&TechnologySylhet 3114Bangladesh Department of Mathematics University of RajshahiRajshahi-6205Bangladesh

The numerical Method of Lines(MOLs)in coordination with the classical fourth-order Runge Kutta(RK(4,4))method is used to solve shallow water equations(SWEs)for foreseeing water levels owing to the nonlinear interaction of tide and surge accompanying with a storm along the coast of Bangladesh.The SWEs are developed by extending the body forces with tide generating forces(TGFs).Spatial variables of the SWEs along with the boundary conditions are approximated by means of finite difference technique on an Arakawa C-grid to attain a system of ordinary differential equations(ODEs)of initial valued in time,which are being solved with the aid of the RK(4,4)method.Nested grid technique is adopted to solve coastal complexities closely with least computational cost.A stable tidal solution in the region of our choice is produced by applying the tidal forcing with the major tidal constituent M2(lunar semi-diurnal)along the southern open-sea boundary of the outer scheme.Numerical experimentations are carried out to simulate water levels generated by the cyclonic storm AILA along the coast of Bangladesh.The model simulated results are found to be in a reasonable agreement with the limited available reported data and observations.

关键词： Bangladesh coast shallow water equations Method of Lines tide-surge interaction islands tide generating forces inverse barometer

Application of method-of-lines to Charging-Up Process in Pipelines with Entrapped Air

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Tsinghua Science and Technology 2006年第3期11卷 324-331页

作者：张永良 K.Vairavamoorthy State Key Laboratory of Hydroscience and Hydraulic Engineering Department of Hydraulic Engineering Tsinghua University Beijing 100084China Department of Civil and Building Engineering Loughborough University Leicestershire LE11 3TUUK

A mathematical model is presented for the charging-up process in an air-entrapped pipeline with moving boundary conditions. A coordinate transformation technique is employed to reduce fluid motion in time-dependent domains to ones in time-independent domains. The nonlinear hyperbolic partial differential equations governing the unsteady motion of fluid combined with an equation for transient shear stress between the pipe wall and the flowing fluid are solved by the Method of Lines. Results show that ignoring elastic effects overestimates the maximum pressure and underestimates the maximum front velocity of filling fluid. The peak pressure of the entrapped air is sensitive to the length of the initial entrapped air pocket.

关键词： transient flow charging-up process pipelines entrapped air Method of Lines

Heat Transfer within Direct Heating Integrated Moving Bed Torrefier by Method of Lines

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Journal of Sustainable Bioenergy Systems 2021年第1期11卷 1-13页

作者： Bosikawa Mosi Fabrice Sumuna Temo Vertomene Mbuyi Katshiatshia Haddy Laboratory of New and Renewable Energy Université de Kinshasa Kinshasa Democratic Republic of Congo

This work deals with the determination of the temperature profile within a direct heating moving bed torrefier in order to determine its minimum column height. A thermal model based on eulerian-eulerian two-phase solid-gas theory was performed and solved with the method of lines. In addition, this study allows to investigate the effect of the biomass particle size on the minimum torrefier column height. This investigation was performed by changing, simultaneously, the diameter of particles and the minimum fluidization velocity of the bed. Then, the calculations were made for a counter-current torrefaction reactor of 30 cm in diameter and for 5 kg/h of the feed rate of raw sugarcane bagasse. Results show that the height of the reactor column must be at least 30 cm for that are 1 mm in diameter and 108 cm for particles that are 2 mm in diameter.

关键词： Torrefaction Biomass Sugarcane Bagasse Moving Bed Method of Lines

Method of Lines for the Chiral Nonlinear Schrödinger Equation

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Applied Mathematics 2020年第6期11卷 447-459页

作者： K. S. AL-Basyouni M. S. Ismail Department of Math. College of Science King Abdulaziz University Jeddah Saudi Arabia

In this paper, we solve chiral nonlinear Schrodinger equation (CNSE) numerically. Two numerical methods are derived using the explicit Runge-Kutta method of order four and the linear multistep method (Predictor-Corrector method of fourth order). The resulting schemes of fourth order accuracy in spatial and temporal directions. The CNSE is non-integrable and has two kinds of soliton solutions: bright and dark soliton. The exact solutions and the conserved quantities of CNSE are used to display the efficiency and robustness of the numerical methods we derived. Interaction of two bright solitons for different parameters is also displayed.

关键词： Method of Lines Linear Multistep method Chiral Soliton Interaction of Two Solitons

THE VIBRATION AND STABILITY ANALYSIS OF MODERATE THICK PLATES BY THE Method of Lines

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Applied Mathematics and Mechanics(English Edition) 1992年第6期13卷 523-531页

作者：唐寿高袁驷 Tongji University Shanghai Qinghua University Beijing

The Method of Lines based on Hu Hai-chang 's theory for the vibration and stability of moderate thick plates is developed. The standard nonlinear ordinary differential equation (ODE) system for natural frequencies and critical load is given by use of ODE techniques, and then any indicated eigenvalue could be obtained directly from ODE solver by employing the so-called initial eigenfunction technique instead of the mode orthogonality condition. Numerical examples show that the present method is very effective and reliable.

关键词： moderate thick plate vibration stability Method of Lines

Method of Lines with Different Discretization on Layers

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Method of Lines with Different Discretization on Layers

ANALYSIS OF 2-D EM PROBLEMS ON A COMPOUND RECTANGULAR REGION BY THE Method of Lines

2002 3rd International Conference on Microwave and Millimeter Wave Technology

作者： Guo-Lin Li Zheng-He Feng State Key Lab on Microwave and Digital Communications Tsinghua UniversityEE Dept.

＜正＞The behavior and reasons of numerical instability of the Method of Lines（MOL） is discussed. Strategy of different layer different discretization with linear interpolation on the interfaces is adopted.More thic... 详细信息

ISBN: (纸本)078037486X

关键词： Method of Lines numerical stability interpolation Method of Lines discretization numerical instability linear interpolation layer interface

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电子科学学刊(英文版) 1988年第3期5卷 189-196页

作者：洪伟 Nanjing Institute of Technology Nanjing

In this paper an extended Method of Lines for analyzing the electromagnetic boundary valueproblems is presented and applied to the waveguide with a compound rectangular cross-section.A number ofnumerical results are given for the higher mode analysis in a rectangular waveguide with ridges or fins,and in ashielded stripline.In the computation practice,the random errors caused by the discretization of theboundary conditions are decreased by a least-square procedure.

关键词： Elctronmagnetic field Boundary value problem Method of Lines

Storm surge simulation along the Meghna estuarine area:an alternative approach

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Acta Oceanologica Sinica 2018年第1期37卷 40-49页

作者： PAUL Gour Chandra SENTHILKUMAR Sukumar PRIA Rana Department of Mathematics University of Rajshahi School of Mathematical Sciences Universiti Sains Malaysia Mathematics Discipline Khulna University

In this study, numerical prediction of surges associated with a storm was made through the Method of Lines（MOL） in coordination with the newly proposed RKARMS（4, 4） method for the meghna estuarine region, along the coast of Bangladesh. For this purpose, the vertically integrated shallow water equations（SWEs） in Cartesian coordinates were firstly transformed into ordinary differential equations（ODEs） of initial valued, which were then soloved using the new RKARMS（4, 4） method. Nested grid technique was employed for resolving the complexities of the region of interest with minimum cost. Fresh water discharge through the lower Meghna River was taken into account along the north east corner of the innermost child scheme. Numerical experiments were performed with the severe cyclone on April 1991 that crossed the coast over the study area. Simulated results by the study were found to be in good agreement with some reported data and were found to compare well with the results obtained by the MOL in addition with the classical 4th order Runge-Kutta（RK（4, 4）） method and the standard finite difference method（FDM）.

关键词： Method of Lines storm surge nested grid finite difference method RKARMS （4, 4） method truncation errors