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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
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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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Numerical Simulation Method of Meshless Reservoir Considering Time-Varying Connectivity Parameters 认领 引用
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作者 Yuyang Liu Wensheng Zhou +4 位作者 Zhijie Wei Engao Tang Chenyang Shi Qirui Zhang Zifeng Chen 《Energy Engineering》 EI 2025年第10期4245-4260,共16页
After a long period of water flooding development,the oilfield has entered the middle and high water cut stage.The physical properties of reservoirs are changed by water erosion,which directly impacts reservoir develo... After a long period of water flooding development,the oilfield has entered the middle and high water cut stage.The physical properties of reservoirs are changed by water erosion,which directly impacts reservoir development.Conventional numerical reservoir simulation methodologies typically employ static assumptions for model construction,presuming invariant reservoir geological parameters throughout the development process while neglecting the reservoir’s temporal evolution characteristics.Although such simplifications reduce computational complexity,they introduce substantial descriptive inaccuracies.Therefore,this paper proposes a meshless numerical simulation method for reservoirs that considers time-varying characteristics.This method avoids the meshing in traditional numerical simulation methods.From the fluid flow perspective,the reservoir’s computational domain is discretized into a series of connection units.An influence domain with a certain radius centered on the nodes is selected,and one-dimensional connection units are established between the nodes to achieve the characterization of the flow topology structure of the reservoir.In order to reflect the dynamic evolution of the reservoir’s physical properties during the water injection development process,the time-varying characteristics are incorporated into the formula of the seepage characteristic parameters in the meshless calculation.The change relationship of the permeability under different surface fluxes is considered to update the calculated connection conductivity in real time.By combining with the seepage control equation for solution,a time-varying meshless numerical simulation method is formed.The results show that compared with the numerical simulationmethod of the connection elementmethod(CEM)that only considers static parameters,this method has higher simulation accuracy and can better simulate the real migration and distribution of oil and water in the reservoir.Thismethod improves the accuracy of reservoir numerical simulation and the development effect of oilfields,providing a scientific basis for optimizing the water injection strategy,adjusting the production plan,and extending the effective production cycle of the oilfield. 展开更多
关键词 Meshless method parameters’time-varying numerical simulation production optimization block application
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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 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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NUMERICAL ANALYSIS OF MINDLIN SHELL BY MESHLESS LOCAL PETROV-GALERKIN METHOD 认领 引用 被引量：5
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作者 Di Li Zhongqin Li Shuhui Li 《Acta Mechanica Solida Sinica》 SCIE EI 2008年第2期160-169,共10页
The objectives of this study are to employ the meshless local Petrov-Galerkin method （MLPGM） to solve three-dimensional shell problems. The computational accuracy of MLPGM for shell problems is affected by many fact... The objectives of this study are to employ the meshless local Petrov-Galerkin method （MLPGM） to solve three-dimensional shell problems. The computational accuracy of MLPGM for shell problems is affected by many factors, including the dimension of compact support domain, the dimension of quadrture domain, the number of integral cells and the number of Gauss points. These factors＇ sensitivity analysis is to adopt the Taguchi experimental design technology and point out the dimension of the quadrature domain with the largest influence on the computational accuracy of the present MLPGM for shells and give out the optimum combination of these factors. A few examples are given to verify the reliability and good convergence of MLPGM for shell problems compared to the theoretical or the finite element results. 展开更多
关键词 meshless methods meshless local Petrov-Galerkin method moving least square shell
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h-ADAPTIVE ANALYSIS BASED ON MESHLESS LOCAL PETROV-G ALERKIN METHOD WITH B SPLINE WAVELET FOR PLATES AND SHELLS 认领 引用 被引量：1
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作者 Di Li Zhongqin Lin 《Acta Mechanica Solida Sinica》 SCIE EI 2009年第4期337-346,共10页
Using the two-scale decomposition technique, the h-adaptive meshless local Petrov- Galerkin method for solving Mindlin plate and shell problems is presented. The scaling functions of B spline wavelet are employed as t... Using the two-scale decomposition technique, the h-adaptive meshless local Petrov- Galerkin method for solving Mindlin plate and shell problems is presented. The scaling functions of B spline wavelet are employed as the basis of the moving least square method to construct the meshless interpolation function. Multi-resolution analysis is used to decompose the field variables into high and low scales and the high scale component can commonly represent the gradient of the solution according to inherent characteristics of wavelets. The high scale component in the present method can directly detect high gradient regions of the field variables. The developed adaptive refinement scheme has been applied to simulate actual examples, and the effectiveness of the present adaptive refinement scheme has been verified. 展开更多
关键词 meshless methods meshless local Petrov-Galerkin method multi-resolution analysis adaptive analysis plate and shell
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Meshless Local Discontinuous Petrov-Galerkin Method with Application to Blasting Problems 认领 引用
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作者 强洪夫 高巍然 《Transactions of Tianjin University》 EI CAS 2008年第5期376-383,共8页
A meshiess local discontinuous Petrov-Galerkin （MLDPG） method based on the local symmetric weak form （LSWF） is presented with the application to blasting problems. The derivation is similar to that of mesh-based R... A meshiess local discontinuous Petrov-Galerkin （MLDPG） method based on the local symmetric weak form （LSWF） is presented with the application to blasting problems. The derivation is similar to that of mesh-based Runge-Kutta Discontinuous Galerkin （RKDG） method. The solutions are reproduced in a set of overlapped spherical sub-domains, and the test functions are employed from a partition of unity of the local basis functions. There is no need of any traditional nonoverlapping mesh either for local approximation purpose or for Galerkin integration purpose in the presented method. The resulting MLDPG method is a meshless, stable, high-order accurate and highly parallelizable scheme which inherits both the advantages of RKDG and meshless method （MM）, and it can handle the problems with extremely complicated physics and geometries easily. Three numerical examples of the one-dimensional Sod shock-tube problem, the blast-wave problem and the Woodward-Colella interacting shock wave problem are given. All the numerical results are in good agreement with the closed solutions. The higher-order MLDPG schemes can reproduce more accurate solution than the lower-order schemes. 展开更多
关键词 meshless method discontinuous Galerkin method meshless local discontinuous Petrov-Galerkin （MLDPG） method finite-volume particle method convection-dominated flow
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The complex variable meshless local Petrov-Galerkin method of solving two-dimensional potential problems 认领 引用 被引量：1
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作者 杨秀丽 戴保东 张伟伟 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第10期49-55,共7页
Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential proble... Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method. 展开更多
关键词 meshless method complex variable moving least-square method complex variable meshless local Petrov-Galerkin method potential problems
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A meshless moving morphable component-based method for structural topology optimization without weak material 认领 引用 被引量：6
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作者 Linyuan Li Chang Liu +2 位作者 Zongliang Du Weisheng Zhang Xu Guo 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2022年第5期72-87,I0002,共16页
Traditional topology optimization methods often introduce weak artificial material to mimic voids to avoid the singularity of the global stiffness matrix and carry out topology optimization with a fixed finite element... Traditional topology optimization methods often introduce weak artificial material to mimic voids to avoid the singularity of the global stiffness matrix and carry out topology optimization with a fixed finite element(FE)mesh.This treatment,however,may not only increase the computational cost for structural analysis but also lead to unfavorable numerical instabilities,especially when large deformations and dynamic/buckling behaviors are involved.In the present work,a new meshless moving morphable component-based method(ML-MMC),which structural analysis is carried out only on the solid region occupied by components,is proposed.In this approach,the coupling of discrete components is achieved through the adaptively constructed influence domain of the meshless shape function.Therefore,the singularity problem of the stiffness matrix can be naturally avoided without introducing weak artificial material.Compared with traditional methods,the number of degrees of freedoms(DOFs)can be reduced substantially under this treatment.The effectiveness of the proposed approach is also illustrated by some representative examples. 展开更多
关键词 Topology optimization Moving morphable components(MMCs) Meshless method Influence domain Numerical integration
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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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Meshless Surface Wind Speed Field Reconstruction Based on Machine Learning 认领 引用 被引量：3
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作者 Nian LIU Zhongwei YAN +6 位作者 Xuan TONG Jiang JIANG Haochen LI Jiangjiang XIA Xiao LOU Rui REN Yi FANG 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2022年第10期1721-1733,共13页
We propose a novel machine learning approach to reconstruct meshless surface wind speed fields,i.e.,to reconstruct the surface wind speed at any location,based on meteorological background fields and geographical info... We propose a novel machine learning approach to reconstruct meshless surface wind speed fields,i.e.,to reconstruct the surface wind speed at any location,based on meteorological background fields and geographical information.The random forest method is selected to develop the machine learning data reconstruction model(MLDRM-RF)for wind speeds over Beijing from 2015-19.We use temporal,geospatial attribute and meteorological background field features as inputs.The wind speed field can be reconstructed at any station in the region not used in the training process to cross-validate model performance.The evaluation considers the spatial distribution of and seasonal variations in the root mean squared error(RMSE)of the reconstructed wind speed field across Beijing.The average RMSE is 1.09 m s−1,considerably smaller than the result(1.29 m s−1)obtained with inverse distance weighting(IDW)interpolation.Finally,we extract the important feature permutations by the method of mean decrease in impurity(MDI)and discuss the reasonableness of the model prediction results.MLDRM-RF is a reasonable approach with excellent potential for the improved reconstruction of historical surface wind speed fields with arbitrary grid resolutions.Such a model is needed in many wind applications,such as wind energy and aviation safety assessments. 展开更多
关键词 data reconstruction meshless machine learning surface wind speed random forest
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Meshless analysis of three-dimensional steady-state heat conduction problems 认领 引用 被引量：14
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作者 程荣军 葛红霞 《Chinese Physics B》 SCIE EI CAS 2010年第9期36-41,共6页
Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attr... Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson＇s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method （RKPM）. A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples. 展开更多
关键词 reproducing kernel particle method meshless method steady-state heat conduction problem
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MESHLESS METHOD BASED ON COLLOCATION WITH CONSISTENT COMPACTLY SUPPORTED RADIAL BASIS FUNCTIONS 认领 引用 被引量：3
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作者 宋康祖 张雄 陆明万 《Acta Mechanica Sinica》 SCIE EI CAS 2004年第5期551-557,共7页
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 re... 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 conditions.To overcome this drawback,the Consistent Compactly Supported Radial Basis Functions(CCSRBFs)are developed,which satisfy the predetermined consistency con- ditions.Meshless method based on point collocation with CCSRBFs is developed for solving partial differential equations.Numerical studies show that the proposed method improves the accuracy of approximation significantly. 展开更多
关键词 radial basis function collocation meshless
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ELASTIC DYNAMIC ANALYSIS OF MODERATELY THICK PLATE USING MESHLESS LRPIM 认领 引用 被引量：4
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作者 Ping Xia Shuyao Long Hongxue Cui 《Acta Mechanica Solida Sinica》 SCIE EI 2009年第2期116-124,共9页
A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using ... A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using a locally weighted residual method. It uses a radial basis function （RBF） coupled with a polynomial basis function as a trial function,and uses the quartic spline function as a test function of the weighted residual method. The shape function has the properties of the Kronecker delta function,and no additional treatment is done to impose essen-tial boundary conditions. The Newmark method for solving the dynamic problem is adopted in computation. Effects of sizes of the quadrature sub-domain and influence domain on the dynamic properties are investigated. The numerical results show that the presented method can give quite accurate results for the elastic dynamic problem of the moderately thick plate. 展开更多
关键词 meshless method moderately thick plate local radial point interpolation method,dynamic analysis Newmark method
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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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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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Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems 认领 引用 被引量：4
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作者 唐耀宗 李小林 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第3期215-225,共11页
We first give a stabilized improved moving least squares （IMLS） approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin... We first give a stabilized improved moving least squares （IMLS） approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis. 展开更多
关键词 meshless method moving least squares approximation element-free Galerkin method error esti-mate
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AN ASSESSMENT OF THE MESHLESS WEIGHTED LEAST-SQUARE METHOD 认领 引用 被引量：4
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作者 PanXiaofei SzeKimYim ZhangXiong 《Acta Mechanica Solida Sinica》 SCIE 2004年第3期270-282,共13页
The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high e?ciency. Moreover, the... The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high e?ciency. Moreover, the coe?cient matrix obtained is symmetric and semi- positive de?nite. In this paper, the method is further examined critically. The e?ects of several parameters on the results of MWLS are investigated systematically by using a cantilever beam and an in?nite plate with a central circular hole. The numerical results are compared with those obtained by using the collocation-based meshless method (CBMM) and Galerkin-based meshless method (GBMM). The investigated parameters include the type of approximations, the type of weight functions, the number of neighbors of an evaluation point, as well as the manner in which the neighbors of an evaluation point are determined. This study shows that the displacement accuracy and convergence rate obtained by MWLS is comparable to that of the GBMM while the stress accuracy and convergence rate yielded by MWLS is even higher than that of GBMM. Furthermore, MWLS is much more e?cient than GBMM. This study also shows that the instability of CBMM is mainly due to the neglect of the equi- librium residuals at boundary nodes. In MWLS, the residuals of all the governing equations are minimized in a weighted least-square sense. 展开更多
关键词 meshless meshfree least-square weighted residual
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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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