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On Triangular Lattice Boltzmann Schemes for Scalar Problems

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Communications in Computational Physics 2013年第3期13卷 649-670页

作者： Francois Dubois Pierre Lallemand Conservatoire National des Arts et Metiers Department of MathematicsParisand Department of MathematicsUniversity Paris-SudBat.425F-91405 Orsay CedexFrance Centre National de la Recherche Scientifique ParisFrance

We propose to extend the d’Humi`eres version of the lattice Boltzmann scheme to triangular *** use Bravais lattices or more general lattices with the property that the degree of each internal vertex is supposed to be *** such meshes,it is possible to define the lattice Boltzmann scheme as a discrete particle method,without need of finite volume formulation or Delaunay-Voronoi hypothesis for the *** test this idea for the heat equation and perform an asymptotic analysis with the Taylor expansion method for two schemes named D2T4 and *** results show a convergence up to second order accuracy and set new questions concerning a possible super-convergence.

关键词： Laplacian operator heat equation d’Humi`eres scheme D2T4 D2T7

Exponential Stability of a Coupled heat-ODE System 25th

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Exponential Stability of a Coupled Heat-ODE System

Numerical Study on Single and Multi-Dimensional Boundary Value Problems by the Method of Weighted Residual

第25届中国控制与决策会议

作者： Dong-Xia Zhao Jun-Min Wang the Department of Mathematics Beijing Institute of Technology the Department of Mathematics North University of China the Department of Mathematics Beijing Institute of Technology

ISBN: (纸本)9781467355339

This paper addresses the feedback stabilization of an interconnected heat-ODE system with the Dirichlet interconnection. The "interconnection" between the heat equation and the ODE are bi-directional, in which the Dirichlet boundary observation of the heat equation is fed into the ODE, and the velocity of ODE is flowed into the boundary of the heat equation. The semigroup approach is adopted in investigation. By a detailed analysis, we obtain the asymptotic expressions of eigenvalues and eigenfunctions. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. This deduces the spectrumdetermined growth condition for the C0-semigroup, and as a consequence, the exponential stability of the system is then followed. Numerical simulations are presented.

关键词： heat equation Dirichlet interconnection Riesz basis Exponential stability

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American Journal of Computational Mathematics 2020年第2期10卷 230-251页

作者： Humaira Farzana Md. Abdul Alim Department of Arts & Sciences Ahsanullah University of Science & Technology Dhaka Bangladesh Department of Mathematics Bangladesh University of Engineering & Technology Dhaka Bangladesh

The Galerkin method of weighted residual (MWR) for computing natural frequencies of some physical problems such as the Helmholtz equation and some second-order boundary value problems has been revised in this article. The use of one and two-dimensional characteristic Bernstein polynomials as the basis functions have been presented by the Galerkin MWR. The vibration of non-homogeneous membranes with Dirichlet type boundary conditions is also studied here. The useful properties of Bernstein polynomials, its derivatives and function approximations have also been illustrated. Besides, the efficiency and applicability of the proposed technique have been demonstrated through some numerical experiments.

关键词： Eigenvalues heat equation Wave equation Bernstein Polynomials Galerkin MWR

一类非线性Burgers方程组的基于Hopf-Cole变换的直接间断Galerkin有限元方法

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高等学校计算数学学报 2015年第2期37卷 141-155页

作者：赵国忠蔚喜军包头师范学院数学科学学院北京应用物理与计算数学研究所计算物理实验室

1引言Burgers方程可以作为描述许多物理现象的数学模型,如交通流、激波、扰流问题和连续的随机过程.它还可以用于检验数值方法的效率.由于其具有较广的实用范围,一些学者对其近似解进行了较多的研究.如Adomian分解方法、混合有限差分和... 详细信息

1引言Burgers方程可以作为描述许多物理现象的数学模型,如交通流、激波、扰流问题和连续的随机过程.它还可以用于检验数值方法的效率.由于其具有较广的实用范围,一些学者对其近似解进行了较多的研究.如Adomian分解方法、混合有限差分和边界元方法、样条有限元方法、精确显式有限差分方法、Douglas有限差分格式,直接变分方法和变分迭代方法被用于Burgers方程近似解的研究.Hopf-Cole变换是研究Burgers方程较好的分析工具,利用它可以获得Burgers方程一些精确解.近年来,人们意识到该变换也是一个很好的数值工具并利用其得到了一

关键词： Burgers’ equations DDG finite element method Hopf-Cole transformation heat equation

Approximate Analytical Solutions to the heat and Stokes equations on the Half-Line Obtained by Fokas’ Transform

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Journal of Applied Mathematics and Physics 2021年第4期9卷 809-833页

作者： Mohamed Lachaab Marius Beceanu University of Tunis Tunis Tunisia University at Albany New York USA

In this paper, we evaluate the integrals that are solutions of the heat and Stokes’ equations obtained by Fokas’ transform method by deriving exact formulas. Our method is more accurate and efficient than the contour deformation and parametrization used by Fokas to compute these integrals. In fact, for the heat equation, our solution is exact up to the imaginary error function and for the Stokes equation, our solution is exact up to the incomplete Airy function. In addition, our solutions extend to the lateral boundary without convergence issues, allow for asymptotic expansions, and are much faster than those obtained by other methods.

关键词： heat equation Stokes equation Fokas’ Transform Asymptotic Expansion Hilbert Transform Incomplete Airy Function Imaginary Error Function

Indirect Control of Linear Plant via heat Diffusion

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Indirect Control of Linear Plant via Heat Diffusion

Study on Reconstruction of heat Flux in Moving Boundary

第24届中国控制与决策会议

作者： Ailiang Zhao, Chengkang Xie the School of Mathematics and System Science, Southwest University

It is considered that a linear plant is indirectly controlled via a heat equation. A backstepping transformation is introduced to design a control law. Stability of the closed loop is achieved. Simulation results are ... 详细信息

关键词： Linear plant Indirect control heat equation

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Study on Reconstruction of Heat Flux in Moving Boundary