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A Comparative Study of State-of-the-Art Meshless Methods for Flow and Transport Simulation in Porous Media 认领 引用
1
作者 T.I.Eldho Sanjukta Das +1 位作者 Aatish Anshuman Tinesh Pathania 《Computer Modeling in Engineering & Sciences》 SCIE EI 2026年第5期828-852,共25页
In recent years,meshless methods have been increasingly applied to the simulation of various engineering problems due to their inherent advantages over traditional mesh-based approaches,including greater flexibility,i... In recent years,meshless methods have been increasingly applied to the simulation of various engineering problems due to their inherent advantages over traditional mesh-based approaches,including greater flexibility,independence from predefined meshing,simpler adaptive analysis,improved automation,and suitability for complex problems.Several meshless methods have been used for porous media simulation,and are broadly categorized into collocation,global weak form and local weak form methods.In this study,a comprehensive comparison of the applicability of these three categories of meshless methods for simulating coupled flow and transport problems in porous media is presented.The Radial Point Collocation Method(RPCM)(strong form),the Element Free Galerkin Method(EFGM)(global weak form)and the Meshless Local Petrov Galerkin(MLPG)method(local weak form)are implemented and systematically compared.These methods are applied to the analysis of flow in a synthetic regular domain aquifer,flow and non-reactive contaminant transport in a synthetic irregular boundary porous media problem and groundwater flow in a field aquifer located in India.The simulated groundwater heads are compared with analytical solution,observed field data and results obtained from widely used MODFLOW-MT3DMS models.The deviation of the solutions from the analytical solution is in the range of O.67%to O.l6%for the hypothetical case study.For the field-scale case study,mean absolute error of 0.183%,0.18l%and 0.188%are obtained for the RPCM,EFGM and MLPG models,respectively,outperforming MODFLOW,which exhibits a deviation of 0.254%from observed values.Overall,the present study reaffirms the practical applicability of these meshless methods for real-world groundwater problems and provides valuable insights into the utilization of each category of meshless method,with respect to problem type,computational efficiency and accuracy requirements. 展开更多
关键词 Meshless methods groundwater flow contaminant transport radial point collocation method element free Galerkin method meshless local Petrov Galerkin method
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A new complex variable meshless method for transient heat conduction problems 认领 引用 被引量：11
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作者 王健菲 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第12期42-50,共9页
In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is pres... In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper. 展开更多
关键词 meshless method improved complex variable moving least-square approximation com-plex variable meshless method transient heat conduction problem
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New complex variable meshless method for advection-diffusion problems 认领 引用 被引量：11
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作者 王健菲 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第3期92-98,共7页
In this paper,an improved complex variable meshless method（ICVMM） for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square（ICVMLS） approximation.The equi... In this paper,an improved complex variable meshless method（ICVMM） for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square（ICVMLS） approximation.The equivalent functional of two-dimensional advection-diffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for twopoint boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advection-diffusion problems,and has a good convergent character,accuracy,and computational efficiency. 展开更多
关键词 meshless method improved complex variable moving least-square approximation improved complex variable meshless method advection-diffusion problem
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A meshless method for the nonlinear generalized regularized long wave equation 认领 引用 被引量：13
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作者 王聚丰 白福浓 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第3期35-42,共8页
This paper presents a meshless method for the nonlinear generalized regularized long wave （GRLW） equation based on the moving least-squares approximation. The nonlinear discrete scheme of the GRLW equation is obtain... This paper presents a meshless method for the nonlinear generalized regularized long wave （GRLW） equation based on the moving least-squares approximation. The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method. A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm. Compared with numerical methods based on mesh, the meshless method for the GRLW equation only requires the.scattered nodes instead of meshing the domain of the problem. Some examples, such as the propagation of single soliton and the interaction of two solitary waves, are given to show the effectiveness of the meshless method. 展开更多
关键词 generalized regularized long wave equation meshless method moving least-squares approximation convergence
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A meshless method for the compound KdV-Burgers equation 认领 引用 被引量：23
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作者 程荣军 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第7期41-46,共6页
The element-free Galerkin （EFG） method for numerically solving the compound Korteweg-de Vries-Burgers （KdVB） equation is discussed in this paper. The Galerkin weak form is used to obtain the discrete equation and ... The element-free Galerkin （EFG） method for numerically solving the compound Korteweg-de Vries-Burgers （KdVB） equation is discussed in this paper. The Galerkin weak form is used to obtain the discrete equation and the essential boundary conditions are enforced by the penalty method. The effectiveness of the EFG method of solving the compound Korteweg-de Vries-Burgers （KdVB） equation is illustrated by three numerical examples. 展开更多
关键词 element-free Galerkin （EFG） method meshless method compound Korteweg-de Vries-Burgers （KdVB） equation solitary wave
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A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation 认领 引用 被引量：5
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作者 葛红霞 程荣军 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第4期91-97,共7页
Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the movi... Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging inter- polation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail. 展开更多
关键词 meshless method moving Kriging interpolation time-fractional diffusion equation
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GALERKIN MESHLESS METHODS BASED ON PARTITION OF UNITY QUADRATURE 认领 引用 被引量：3
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作者 曾清红 卢德唐 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第7期893-899,共7页
Numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature （PUQ）,for Galerkin meshless methods was presented. The technique is b... Numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature （PUQ）,for Galerkin meshless methods was presented. The technique is based on finite covering and partition of unity. There is no need to decompose the physical domain into small cell. It possesses remarkable integration accuracy. Using Element-free Galerkin methods as example, Galerkin meshless methods based on PUQ were studied in detail. Meshing is always not required in the procedure of constitution of approximate function or numerical quadrature, so Galerkin meshless methods based on PUQ are “truly” meshless methods. 展开更多
关键词 Galerkin meshless method finite cover partition of unity numerical quadrature
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The Space-Time Meshless Methods for the Solution of One-Dimensional Klein-Gordon Equations 认领 引用 被引量：2
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作者 ZHANG Zhiqiang WANG Fuzhang ZHANG Juan 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2022年第4期313-320,共8页
A simple direct space-time meshless scheme,based on the radial or non-radial basis function,is proposed for the onedimensional Klein-Gordon equations.Since these equations are time-dependent,it is worthwhile to presen... A simple direct space-time meshless scheme,based on the radial or non-radial basis function,is proposed for the onedimensional Klein-Gordon equations.Since these equations are time-dependent,it is worthwhile to present two schemes for the basis functions from radial and non-radial aspects.The first scheme is fulfilled by considering time variable as normal space variable,to construct an"isotropic"space-time radial basis function.The other scheme considered a realistic relationship between space variable and time variable which is not radial.The timedependent variable is treated regularly during the whole solution process and the Klein-Gordon equations can be solved in a direct way.Numerical results show that the proposed meshless schemes are simple,accurate,stable,easy-to-program and efficient for the Klein-Gordon equations. 展开更多
关键词 radial basis functions meshless method space-time
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MESHLESS METHOD OF DUAL RECIPROCITY HYBRID RADIAL BOUNDARY NODE METHOD FOR ELASTICITY 认领 引用 被引量：2
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作者 Fei Yan Xiating Feng Hui Zhou 《Acta Mechanica Solida Sinica》 SCIE EI 2010年第5期447-458,共12页
Combining the radial point interpolation method(RPIM),the dual reciprocity method(DRM)and the hybrid boundary node method(HBNM),a dual reciprocity hybrid radial boundary node method(DHRBNM)is proposed for linear elast... Combining the radial point interpolation method(RPIM),the dual reciprocity method(DRM)and the hybrid boundary node method(HBNM),a dual reciprocity hybrid radial boundary node method(DHRBNM)is proposed for linear elasticity.Compared to DHBNM,RPIM is exploited to replace the moving least square(MLS)in DHRBNM,and it gets rid of the deficiency of MLS approximation,in which shape functions lack the delta function property,the boundary condition can not be applied easily and directly and it's computational expense is high.Besides,different approximate functions are discussed in DRM to get the interpolation property,in which the accuracy and efficiency for different basis functions are compared.Then RPIM is also applied in DRM to replace the conical function interpolation,which can greatly improve the accuracy of the present method.To demonstrate the effectiveness of the present method,DHBNM is applied for comparison,and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM. 展开更多
关键词 meshless method hybrid boundary node method dual reciprocity method radial point interpolation method elasticity
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APPLICATION OF WAVELET THEORY IN RESEARCHON WEIGHT FUNCTION OF MESHLESS METHOD 认领 引用 被引量：1
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作者 张红 张选兵 葛修润 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第5期662-666,共5页
Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is ort... Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given. 展开更多
关键词 meshless method weight function spline wavelet multiresolution analysis
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A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains 认领 引用 被引量：1
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作者 Chengxin Zhang Chao Wang +1 位作者 Shouhai Chen Fajie Wang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第6期2407-2424,共18页
This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method(LKM)with the dual reciprocity method(DRM).Firstly,the temporal derivative is discretized by... This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method(LKM)with the dual reciprocity method(DRM).Firstly,the temporal derivative is discretized by a finite difference scheme,and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation.Secondly,the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution.And then,the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation,respectively.The LKM is a recently proposed local radial basis function collocationmethod with themerits of being simple,accurate,and free ofmesh and integration.Compared with the traditional domain-type and boundary-type schemes,the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains.Numerical experiments,including two-and three-dimensional heat transfer models,demonstrated the effectiveness and accuracy of the new methodology. 展开更多
关键词 Local knot method transient heat conduction dual reciprocity method meshless method
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MESHLESS METHOD FOR 2D MIXED-MODE CRACK PROPAGATION BASED ON VORONOI CELL 认领 引用 被引量：1
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作者 Lou Luliang Zeng Pan 《Acta Mechanica Solida Sinica》 SCIE 2003年第3期231-239,共9页
A meshless method integrated with linear elastic fracture mechanics(LEFM)is presented for 2D mixed-mode crack propagation analysis.The domain is divided automatically into sub-domains based on Voronoi cells,which are ... A meshless method integrated with linear elastic fracture mechanics(LEFM)is presented for 2D mixed-mode crack propagation analysis.The domain is divided automatically into sub-domains based on Voronoi cells,which are used for quadrature for the potential energy. The continuous crack propagation is simulated with an incremental crack-extension method which assumes a piecewise linear discretization of the unknown crack path.For each increment of the crack extension,the meshless method is applied to carry out a stress analysis of the cracked structure.The J-integral,which can be decomposed into mode Ⅰ and mode Ⅱ for mixed-mode crack,is used for the evaluation of the stress intensity factors(SIFs).The crack-propagation direction,predicted on an incremental basis, is computed by a criterion defined in terms of the SIFs. The flowchart of the proposed procedure is presented and two numerical problems are analyzed with this method.The meshless results agree well with the experimental ones,which validates the accuracy and efficiency of the method. 展开更多
关键词 meshless method crack propagation mixed-mode crack Voronoi cell
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Numerical Implementation of Meshless Method for Electromagnetic Field Governing Equations 认领 引用
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作者 阳恩会 王石刚 +2 位作者 莫锦秋 徐威 曹家勇 《Journal of Shanghai Jiaotong university(Science)》 EI 2010年第5期535-540,共6页
For electromagnetic governing equations formulated by magnetic vector potential and electric scalar potential,its detailed numerical implementation is achieved by using meshless method and Galerkin approach.And essent... For electromagnetic governing equations formulated by magnetic vector potential and electric scalar potential,its detailed numerical implementation is achieved by using meshless method and Galerkin approach.And essential boundary and interface condition of electromagnetic field are imposed by means of Lagrange multiplier method.Furthermore,the influences of interpolation point number at essential boundary and interface on computational results are also discussed.Examples are given to validate the effects of meshless method and Lagrange multiplier approach for electromagnetic field. 展开更多
关键词 meshless method electromagnetic equations Lagrange multiplier magnetic vector potential
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Stabilization meshless method for convection-dominated problems 认领 引用
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作者 张小华 欧阳洁 王建瑜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第8期1067-1075,共9页
It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY iss... It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal refinement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all. 展开更多
关键词 meshless method convection-diffusion problem stability method
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The Space-Time Semi-Analytical Meshless Methods for Coupled Burgers'Equations 认领 引用
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作者 ZHANG Zhiqiang WANG Fuzhang 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2024年第6期572-578,共7页
In this paper,a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers'equations.During the whole solution procedure,two different schemes are c... In this paper,a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers'equations.During the whole solution procedure,two different schemes are considered in terms of radial and non-radial basis functions.The time-dependent variable in the first radial scheme is directly considered as the normal space variables to formulate an"isotropic"space-time radial basis function.The second non-radial scheme considered relationship between time-dependent and spacedependent variables.Under such circumstance,we can get a one-step space-time meshless scheme.The numerical findings demonstrate that the proposed meshless schemes are precise,user-friendly,and effective in solving the coupled Burgers'equations. 展开更多
关键词 radial basis functions coupled Burgers'equations meshless methods numerical simulation
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Application of meshless method to electromagnetic NDT 认领 引用
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作者 黄作英 Que Peiwen Tao Zhengshu 《High Technology Letters》 EI CAS 2006年第2期150-153,共4页
In this paper, a meshless method is introduced for NDT computation. Compared with the conventional FEM, it can avoid the onerous mesh generation and updating, only a distribution of points and the description of the b... In this paper, a meshless method is introduced for NDT computation. Compared with the conventional FEM, it can avoid the onerous mesh generation and updating, only a distribution of points and the description of the boundaries are needed. The mathematical background for moving least square approximation employed in the method is given, and the numerical implementation is discussed. Application of the method for MFL computation and comparison with the results from FEM are also presented. 展开更多
关键词 meshless method moving least square NDT finite element method
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An Efficient Meshless Method for Hyperbolic Telegraph Equations in (1 + 1) Dimensions 认领 引用 被引量：2
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作者 Fuzhang Wang Enran Hou +2 位作者 Imtiaz Ahmad Hijaz Ahmad Yan Gu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第8期687-698,共12页
Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions.The purpose of this paper is to propose a simple novel direct meshless scheme for s... Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions.The purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations.This is fulfilled by considering time variable as normal space variable.Under this scheme,there is no need to remove time-dependent variable during the whole solution process.Since the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function method.We propose a simple shifted domain method,which can avoid the full-coefficient interpolation matrix easily.Numerical experiments performed with the proposed numerical scheme for several second-order hyperbolic telegraph equations are presented with some discussions. 展开更多
关键词 Radial basis functions telegraph equation shifted domain method meshless method
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HIGH PERFORMANCE SPARSE SOLVER FOR UNSYMMETRICAL LINEAR EQUATIONS WITH OUT-OF-CORE STRATEGIES AND ITS APPLICATION ON MESHLESS METHODS 认领 引用 被引量：1
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作者 苑维然 陈璞 刘凯欣 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第10期1339-1348,共10页
A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method ... A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests. 展开更多
关键词 sparse matrices linear equations meshless methods high performance computation
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Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method 认领 引用 被引量：1
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作者 Xin Liu Kai Yan +3 位作者 Bo Fang Xiaoyu Sun Daqiang Feng Li Yin 《Fluid Dynamics & Materials Processing》 EI 2024年第7期1539-1552,共14页
In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering comp... In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production. 展开更多
关键词 Weighted least squares method meshless method numerical simulation of low permeability tight reservoirs oil-water two-phase flow fracture half-length
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Quadric SFDI for Laplacian Discretisation in Lagrangian Meshless Methods 认领 引用 被引量：1
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作者 Shiqiang Yan Q.W.Ma Jinghua Wang 《Journal of Marine Science and Application》 CSCD 2020年第3期362-380,共19页
In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),... In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities(such as the viscous stresses).In some meshless applications,the Laplacians are also needed as stabilisation operators to enhance the pressure calculation.The particles in the Lagrangian methods move following the material velocity,yielding a disordered(random)particle distribution even though they may be distributed uniformly in the initial state.Different schemes have been developed for a direct estimation of second derivatives using finite difference,kernel integrations and weighted/moving least square method.Some of the schemes suffer from a poor convergent rate.Some have a better convergent rate but require inversions of high order matrices,yielding high computational costs.This paper presents a quadric semi-analytical finite-difference interpolation(QSFDI)scheme,which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices,i.e.3×3 for 3D cases,compared with 6×6 or 10×10 in the schemes with the best convergent rate.Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations.The convergence,accuracy and robustness of the present schemes are compared with the existing schemes.It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures,particularly for estimating the Laplacian of given functions. 展开更多
关键词 Laplacian discretisation Lagrangian meshless methods QSFDI Random/disordered particle distribution Poisson’s equation Patch tests
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