Heng Cheng

• Taiyuan University of Science and Technology

This study introduces a hybrid element‐free Galerkin (HEFG) method to analyze the 3D steady convection–diffusion‐reaction equation. By introducing the dimension‐splitting method, the governing equation can be split into 2D form in each layer. The 2D form can be solved using the improved element‐free Galerkin (IEFG) method with improved moving least...

This paper uses the physical information neural network (PINN) model to solve a 3D anisotropic steady-state heat conduction problem based on deep learning techniques. The model embeds the problem’s governing equations and boundary conditions into the neural network and treats the neural network’s output as the numerical solution of the partial diff...

In this study, by introducing the finite element method (FEM) into the improved element-free Galerkin (IEFG) method, the dimension coupling method (DCM) is proposed for solving three-dimensional (3D) Helmholtz and Poisson’s equations efficiently. The dimensional splitting method is introduced into the corresponding governing equations, thus 3D equa...

In order to obtain the numerical results of 3D convection-diffusion-reaction problems with variable coefficients efficiently, we select the improved element-free Galerkin (IEFG) method instead of the traditional element-free Galerkin (EFG) method by using the improved moving least-squares (MLS) approximation to obtain the shape function. For the go...

In this study, the hybrid element-free Galerkin (HEFG) method is studied to solve the 3D Helmholtz equations. The idea of the dimension splitting method (DSM) is introduced into the improved element-free Galerkin (IEFG) method, thus a sequence of 2D forms can be obtained by splitting the problem domain of 3D Helmholtz equation, each 2D form can be...

In this paper, we considered the improved element-free Galerkin (IEFG) method for solving 2D anisotropic steady-state heat conduction problems. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty method is applied to enforce the boundary conditions, thus the final discretized equations of...

The improved element-free Galerkin (IEFG) method is proposed in this paper for solving 3D Helmholtz equations. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty technique is used to enforce the essential boundary conditions. Thus, the final discretized equations of the IEFG method for 3D...

Based on the dimension splitting method (DSM) and the improved complex variable element-free Galerkin (ICVEFG) method, the hybrid complex variable element-free Galerkin (HCVEFG) method for three-dimensional (3D) elasticity is proposed in this paper. The equilibrium equation of a 3D elasticity is written as three sets of equations, which contains th...

By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin (DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin (IEFG) method is used for 2D transient heat conduction problems, and the finite difference method is applied in the splitting directio...

In this paper, combining the dimension splitting method with the improved complex variable element-free Galerkin (ICVEFG) method, we present a fast ICVEFG method for three-dimensional wave propagation problems. Using the dimension splitting method, the equations of three-dimensional wave propagation problems are translated into a series of two-dime...