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Acta Mechanica Sinica 2018年第6期34卷 1124-1135页

作者： Nuttawit Wattanasakulpong Arisara Chaikittiratana Sacharuck Pornpeerakeat Department of Mechanical Engineering Mahanakom University of TechnologyNongchokBangkok 10530Thailand Department of Mechanical and Aerospace Engineering King Mongkut’s University of Technology North BangkokBangkok 10800Thailand Department of Teacher Training in Civil Engineering King Mongkut’s University of Technology North BangkokBangkok 10800Thailand Research Centre for Advanced Computational and Experimental Mechanics(RACE) King Mongkut’s University of Technology North BangkokBangkok 10800nailand

In this paper,vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation *** beams have uniform and non-uniform porosity distributions across their thickness and both ends are supported by rotational and translational *** material properties of the beams such as elastic moduli and mass density can be related to the porosity and mass coefficient utilizing the typical mechanical features of open-cell metal *** Chebyshev collocation method is applied to solve the governing equations derived from Hamilton's principle,which is used in order to obtain the accurate natural frequencies for the vibration problem of beams with various general and elastic boundary *** on the numerical experiments,it is revealed that the natural frequencies of the beams with asymmetric and non-uniform porosity distributions are higher than those of other beams with uniform and symmetric porosity distributions.

关键词： Functionally graded porous beam Vibration analysis Chebyshev collocation method Elastic boundary condition

MESHLESS METHOD BASED ON collocation WITH CONSISTENT COMPACTLY SUPPORTED RADIAL BASIS FUNCTIONS

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Acta Mechanica Sinica 2004年第5期20卷 551-557页

作者：宋康祖张雄陆明万 Department of Engineering Mechanics Tsinghua UniversityBeijing 100084China

Based on our previous study,the accuracy of derivatives of interpolating functions are usually very poor near the boundary of domain when Compactly Supported Radial Basis Functions (CSRBFs)are used,so that it could result in significant error in solving partial differential equations with Neumann boundary *** overcome this drawback,the Consistent Compactly Supported Radial Basis Functions(CCSRBFs)are developed,which satisfy the predetermined consistency con- *** method based on point collocation with CCSRBFs is developed for solving partial differential *** studies show that the proposed method improves the accuracy of approximation significantly.

关键词： radial basis function collocation meshless

BITS: an efficient transport solver based on a collocation method with B-spline basis

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Plasma Science and Technology 2023年第2期25卷 27-35页

作者：肖小涛王少杰叶磊戴宗良潘成康任启龙 Institute of Plasma Physics Chinese Academy of ScienceHefei 230031People's Republic of China Department of Modern Physics University of Science and Technology of ChinaHefei 230026People's Republic of China

A B-spline Interpolation Transport Solver(BITS) based on a collocation method is developed. It solves transport equations as a generalized interpolation problem, taking the first-order accuracy in time and the second-order accuracy in space along with a predictor–corrector or under-relaxation iteration method. Numerical tests show that BITS can solve one-dimensional transport equations for tokamak plasma more accurately without additional computation cost, compared to the finite difference method transport solver which is widely used in existing tokamak transport codes.

关键词： plasma simulation transport equation collocation B-spline tokamak

Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation

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Chinese Physics B 2015年第5期24卷 177-190页

作者： Reza Mohammadi Department of Mathematics University of Neyshabur

The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank-Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stable. It is shown that the method is convergent with an order of θ（k2 ＋ h2）. Our scheme leads to a tri-diagonal nonlinear system. This new method has lower computational cost in comparison to the Sinc-collocation method. Finally, numerical examples demonstrate the stability and accuracy of this method.

关键词： solitary waves GRLW equation exponential B-spline collocation

Evaluating the uncertainty of Darcy velocity with sparse grid collocation method

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Science China(Technological Sciences) 2009年第11期52卷 3270-3278页

作者： SHI LiangSheng YANG JinZhong ZHANG DongXiao State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan UniversityWuhan 430072China Department of Energy and Resources Engineering College of EngineeringPeking UniversityBeijing 100871China

Spatial variability of Darcy velocity is presented due to the heterogeneity of aquifer parameters. The uncertainty qualification of velocity suffers great challenge in the complex porous media. This work focuses on the use of sparse grid collocation method in velocity simulation. Since the sparse grid collocation method provides a non-intrusive way to incorporate any existing deterministic solver, the mixed finite element method is combined as the deterministic solver to retain the local continuity of Darcy velocity. We decompose the error of the velocity into three components, and illustrate that the Karhunen-Loeve truncation brings more error into velocity approximation than into head. The convergence properties of velocity moments restrict the application of sparse grid collocation method in the problems with small correlation lengths. This work provides insights towards the application of sparse grid collocation method to velocity modeling. It is demonstrated that for which problems the sparse grid collocation method is expected to be competitive with the Monte Carlo simulation. Further work about the anisotropic sparse grid collocation method should be extended to circumvent the obstacle of dimensionality.

关键词： stochastic velocity uncertainty collocation sparse grid

A Novel Spacetime collocation Meshless Method for Solving Two- Dimensional Backward Heat Conduction Problems

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Computer Modeling in Engineering & Sciences 2019年第1期118卷 229-252页

作者： Chihyu Liu Chengyu Ku Jingen Xiao Weichung Yeih Department of Harbor and River Engineering National Taiwan Ocean UniversityKeelung20224Taiwan Center of Excellence for Ocean Engineering National Taiwan Ocean UniversityKeelung20224Taiwan.

In this article,a meshless method using the spacetime collocation for solving the two-dimensional backward heat conduction problem(BHCP)is *** spacetime collocation meshless method(SCMM)is to derive the general solutions as the basis functions for the two-dimensional transient heat equation using the separation of *** solutions of the heat conduction problem are expressed as a series using the addition *** the basis functions are the general solutions of the governing equation,the boundary points may be collocated on the spacetime boundary of the *** proposed method is verified by conducting several heat conduction *** also carry out numerical applications to compare the SCMM with other meshless *** results show that the SCMM is accurate and ***,it is found that the recovered boundary data on inaccessible boundary can be obtained with high accuracy even though the over specified data are provided only at a 1/6 portion of the spacetime boundary.

关键词： Spacetime collocation meshless method backward heat conduction problem basis functions.

A Jacobi Spectral collocation Scheme Based on Operational Matrix for Time-fractional Modified Korteweg-de Vries Equations

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Computer Modeling in Engineering & Sciences 2015年第3期104卷 185-209页

作者： A.H.Bhrawy E.H.Doha S.S.Ezz-Eldien M.A.Abdelkawy Department of Mathematics Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia Department of Mathematics Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt Department of Mathematics Faculty of ScienceCairo UniversityGizaEgypt Department of Mathematics Faculty of ScienceAssiut UniversityNew Valley BranchEl-Kharja 72511Egypt

In this paper,a high accurate numerical approach is investigated for solving the time-fractional linear and nonlinear Korteweg-de Vries(KdV)*** equations are the most appropriate and desirable definition for physical *** spectral collocation method and the operational matrix of fractional derivatives are used together with the help of the Gauss-quadrature formula in order to reduce such problem into a problem consists of solving a system of algebraic equations which greatly simplifying the *** approach is based on the shifted Jacobi polynomials and the fractional derivative is described in the sense of *** addition,the presented approach is applied also to solve the timefractional modified KdV *** testing the accuracy,validity and applicability of the developed numerical approach,we apply it to provide high accurate approximate solutions for four test problems.

关键词： KdV equation Jacobi polynomials Operational matrix Gauss quadrature collocation spectral method Caputo derivative

Radial point collocation method (RPCM) for solving convection-diffusion problems

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第6期7卷 1061-1067页

作者： LIU Xin Department of Mechanics Zhejiang University Hangzhou 310027 China

In this paper, Radial point collocation method （RPCM）, a kind of meshfree method, is applied to solve convectiondiffusion problem. The main feature of this approach is to use the interpolation schemes in local supported domains based on radial basis functions. As a result, this method is local and hence the system matrix is banded which is very attractive for practical engineering problems. In the numerical examination, RPCM is applied to solve non-linear convection-diffusion 2D Burgers equations. The results obtained by RPCM demonstrate the accuracy and efficiency of the proposed method for solving transient fluid dynamic problems. A fictitious point scheme is adopted to improve the solution accuracy while Neumann boundary conditions exist. The meshfree feature of the nresent method is verv attractive in solving comnutational fluid nroblems.

关键词： Radial basis functions Radial point collocation method (RPCM) collocation Meshfree Convection-diffusion

A LINEAR IM PLICIT Ll-LEGENDRE GALERKIN CHEBYSHEV collocation M ETHOD FOR GENERALIZED TIME- AND SPACE-FRACTIONAL BURGERS EQUATION

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Journal of Computational Mathematics 2019年第5期37卷 629-644页

作者： Yubo Yang Heping Ma Nanhu College Jiaxing UniversityJiaxing 314001 China Department of Mathematics Shanghai UniversityShanghai 200444China

In this paper, a linear implicit Ll-Legendre Galerkin Chebyshev collocation method for the generalized time-and space-fractional Burgers equation is developed. A linear implicit finite difference scheme based on the L 1-algorithm for the Caputo fractional derivative is proposed for temporal discretization. And the Legendre Galerkin Chebyshev collocation method, based on the Legendre-Galerkin variational form, but the nonlinear term and the right-hand term are treated by Chebyshev-Gauss interpolation, is proposed for spatial discretization. Rigorous stability and convergence analysis are developed. Numerical examples are shown to demonstrate the accuracy, stability and effectiveness of the method.

关键词： Generalized fractional Burgers equation Stability and convergence analysis Legendre Galerkin Chebyshev collocation method Finite difference method

Local collocation Approach for Solving Turbulent Combined Forced and Natural Convection Problems

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Advances in Applied Mathematics and Mechanics 2011年第3期3卷 259-279页

作者： Robert Vertnik Bozidar Sarler Technical Development Sˇtore-Steel d.o.o.Z elezarska 3SI-3220StoreSlovenia 2 Laboratory for Multiphase ProcessesUniversity of Nova GoricaVipavska 13SI-5000Nova GoricaSlovenia

An application of the meshless Local Radial Basis Function collocation Method(LRBFCM)[22,30–33]in solution of incompressible turbulent combined forced and natural convection is for the first time explored in the present *** turbulent flow equations are described by the low-Re number k−εmodel with Launder and Sharma[23]and Abe et al.[1]closure *** involved temperature,velocity,pressure,turbulent kinetic energy and dissipation fields are represented on overlapping 5-noded sub-domains through the collocation by using multiquadrics Radial Basis Functions(RBF).The involved first and second order partial derivatives of the fields are calculated from the respective derivatives of the RBF’*** involved equations are solved through the explicit time *** pressure-velocity coupling is based on Chorin’s fractional step method[11].The adaptive upwinding technique,proposed by Lin and Atluri[27],is used because of the convection dominated *** solution procedure is represented for a 2D upward channel flow with differentially heated *** results have been assessed by achieving a reasonable agreement with the direct numerical simulation of Kasagi and Nishimura[20]for Reynolds number 4494,based on the channel width,and Grashof number 9.6×*** advantages of the represented mesh-free approach are its simplicity,accuracy,similar coding in 2D and 3D,and straightforward applicability in non-uniform node arrangements.

关键词： Turbulent combined convection two-equation turbulence model radial basis function collocation meshless method upward channel flow