Article
Mathematics
Jufeng Wang, Fengxin Sun, Rongjun Cheng
Summary: The DS-IMLS method utilizes dimension splitting to reduce matrix dimension and computational complexity in calculating shape functions, achieving high accuracy in approximations and derivatives. It is utilized in an improved IEFG method for two-dimensional potential problems, resulting in high accuracy in numerical solutions.
Article
Engineering, Multidisciplinary
Fengxin Sun, Jufeng Wang, Qi Wei, Yong Wu
Summary: In this paper, an improved element-free Galerkin method (IEFGM) is proposed to solve two-dimensional elasticity problems. The IEFGM utilizes the dimension-splitting moving least squares (DS-MLS) method for constructing trial functions and the Galerkin variational weak form with integral coordinate transformation to obtain discrete equations for the elastic problems. The DS-MLS method, developed from dimensional splitting and moving least squares approximation, reduces the dimension and complexity of matrix operations, thus improving calculation efficiency. Several examples demonstrate the effectiveness of the improved meshless method in terms of reduced CPU time and higher accuracy solution compared to the EFG method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Zhijuan Meng, Yanan Fang, Yumin Cheng
Summary: In this paper, a fast FEFG method is proposed for solving 3D elasticity problems. The method combines the IEFG method and the DSM, and converts the 3D problem into a series of 2D problems. The effectiveness and advantages of the FEFG method are demonstrated through numerical experiments, and the convergence and relative error norm of the method are studied.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2022)
Article
Mechanics
Heng Cheng, Jiao Zhang, Zebin Xing
Summary: This study investigates the hybrid element-free Galerkin method for solving the 3D Helmholtz equations, with the introduction of dimension splitting method in the improved element-free Galerkin method. The numerical results demonstrate that the HEFG method can significantly save computational resources without compromising computational accuracy.
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
(2022)
Article
Mathematics
Heng Cheng, Miaojuan Peng
Summary: This paper proposes an improved element-free Galerkin method for solving 3D Helmholtz equations. The method utilizes the improved moving least-squares approximation and penalty technique to ensure accurate solutions. Numerical results demonstrate that the proposed method enhances computational speed and eliminates the singular matrix phenomenon.
Article
Mechanics
Fengxin Sun, Jufeng Wang, Yong Wu, Qi Wei
Summary: In this paper, a DS-MLS method is proposed by introducing dimension splitting into the moving least-squares approximation. By coupling with Galerkin weak form, an IEFGM method based on the DS-MLS method is proposed for solving 2D potential problems on irregular domains. Numerical results demonstrate that the IEFGM method consumes less CPU time and has higher computational accuracy compared to the EFG method.
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
(2022)
Article
Mathematics
Heng Cheng, Zebin Xing, Yan Liu
Summary: In order to efficiently obtain numerical results of 3D convection-diffusion-reaction problems with variable coefficients, the improved element-free Galerkin (IEFG) method is chosen instead of the traditional element-free Galerkin (EFG) method, using the improved moving least-squares (MLS) approximation to derive the shape function. The governing equation of the 3D convection-diffusion-reaction problems is used to derive the corresponding equivalent functional, with essential boundary conditions imposed using the penalty method, resulting in the obtained equivalent integral weak form. By introducing the IMLS approximation, the final solved linear equations for the convection-diffusion-reaction problem can be derived. Numerical examples discuss the scale parameter and penalty factor of the IEFG method for such problems, numerically proving convergence and verifying the calculation efficiency of the IEFG method through four numerical examples.
Article
Mathematics
Fengxin Sun, Jufeng Wang, Xiang Kong, Rongjun Cheng
Summary: The DS-GIEFG method combines the dimension splitting method with GEFG and IIMLS methods to analyze numerical solutions of singularly perturbed steady CDR problems, effectively dividing the problem into lower-dimensional ones and achieving high computational efficiency and accuracy.
Article
Engineering, Multidisciplinary
Jufeng Wang, Yong Wu, Ying Xu, Fengxin Sun
Summary: In this paper, a new method combining dimensional splitting and multiscale interpolating element-free Galerkin is proposed for solving three-dimensional singular perturbed convection-diffusion problems. By decomposing the problem into a series of 2D problems and constructing discrete equations using least squares method, the method effectively solves the 3D problem with high computational stability.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Mathematics, Applied
Quan Shen, Rui Ding, Yuan Yao
Summary: The element-free Galerkin method is proposed for the variational-hemivariational inequality of the dynamic Signorini-Tresca contact problems with friction in elastic materials. The Dirichlet boundary conditions and the constrained conditions are imposed by the penalty method. The error estimates of the element-free Galerkin method indicate that the convergence order depends on various factors, including the spatial step, the time step, the largest degree of basis functions in the moving least-squares approximation, and the penalty factor. Numerical examples confirm the validity of our theoretical results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics
Fengbin Liu, Mingmei Zuo, Heng Cheng, Ji Ma
Summary: In this study, we propose the Dimension Coupling Method (DCM) as an efficient alternative to the Improved Element-Free Galerkin (IEFG) method for solving three-dimensional (3D) Laplace problems using meshless methods. The DCM divides the 3D problem domain into multiple two-dimensional (2D) problems, which are solved using the IEFG method, and combines the solutions in the third direction using the Finite Element Method (FEM). Numerical verification shows that the DCM improves computational speed while maintaining computational accuracy compared to the IEFG method. Therefore, the DCM significantly reduces computational time and costs, expanding the applicability of the dimension splitting EFG method.
Article
Computer Science, Interdisciplinary Applications
Qian Wu, Miaojuan Peng, Yumin Cheng
Summary: This paper proposes the IDSEFG method for 3D potential problems, which utilizes 2D subdomain splitting and the improved IMLS method to construct shape functions, obtains discretized equations using the dimension splitting method, couples subdomains through the finite difference method, and can directly enforce essential boundary conditions.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mathematics, Applied
Mostafa Abbaszadeh, Mehdi Dehghan, Mahmoud A. Zaky, Ahmed S. Hendy
Summary: This research presents a numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative through finite difference approximation. The energy method is utilized to investigate the convergence rate and stability of temporal discretization. Additionally, the interpolation of moving Kriging technique is applied for approximating the space derivative, leading to a meshless numerical formulation. Finally, theoretical findings are confirmed through numerical experiments.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Engineering, Multidisciplinary
Hulun Guo, Xuelin Du, Krzysztof Kamil Zur
Summary: This paper investigates the vibration characteristics of rotating functionally graded graphene nanoplatelets reinforced composite cylindrical shells, analyzing the effects of factors such as cracks, material parameters, and size on the critical rotating speed and natural frequency of the shell using improved mathematical models and algorithms.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mechanics
Zhijuan Meng, Yuye Ma, Xiaofei Chi, Lidong Ma
Summary: This paper presents an improved interpolating dimension splitting element-free Galerkin method for solving three-dimensional potential problems. Compared to other methods, it has the advantages of having fewer undetermined coefficients in the shape function and being able to directly enforce essential boundary conditions. The computational accuracy and efficiency of this method are better than existing methods, as demonstrated in numerical examples.
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
(2021)
Article
Engineering, Multidisciplinary
H. Cheng, M. J. Peng, Y. M. Cheng
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2019)
Article
Engineering, Multidisciplinary
Z. J. Meng, H. Cheng, L. D. Ma, Y. M. Cheng
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2019)
Article
Physics, Multidisciplinary
ZhiJuan Meng, Heng Cheng, LiDong Ma, YuMin Cheng
SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY
(2019)
Article
Engineering, Multidisciplinary
P. P. Peng, Q. Wu, Y. M. Cheng
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2020)
Article
Engineering, Multidisciplinary
D. Liu, Y. M. Cheng
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2019)
Article
Engineering, Multidisciplinary
Lidong Ma, Zhijuan Meng, Jinfei Chai, Yumin Cheng
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2020)
Article
Mechanics
Binhua Wang, Yongqi Ma, Yumin Cheng
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
(2019)
Article
Engineering, Multidisciplinary
Q. Wu, F. B. Liu, Y. M. Cheng
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2020)
Article
Engineering, Multidisciplinary
Qiang Wu, PiaoPiao Peng, YuMin Cheng
Summary: The paper introduces the IEFG method for solving 2D elastic large deformation problems, which provides higher computational efficiency and accuracy compared to the traditional EFG method, thanks to its ability to apply displacement boundary conditions directly.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2021)
Article
Engineering, Civil
Heng Cheng, Miaojuan Peng, Yumin Cheng, Zhijuan Meng
ENGINEERING STRUCTURES
(2020)
Article
Mechanics
Guodong Zheng, Yumin Cheng
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
(2020)
Article
Engineering, Multidisciplinary
P. P. Peng, Y. M. Cheng
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2020)
Article
Materials Science, Multidisciplinary
D. Liu, Y. M. Cheng
RESULTS IN PHYSICS
(2020)
Article
Mechanics
Piaopiao Peng, Yida Fu, Yumin Cheng
Summary: In this paper, a hybrid reproducing kernel particle method (HRKPM) for three-dimensional advection-diffusion problems is proposed, which transforms the 3D problem into a series of related 2D problems through dimension splitting and establishes discrete equations through the RKPM method coupled by difference method. Numerical results show that the HRKPM has higher computational efficiency than the RKPM when solving 3D advection-diffusion problems.
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
(2021)
Editorial Material
Mathematics
Yumin Cheng
