This study proposes a non-uniform meshing strategy for finite element (FE) discretization aimed at improving mechanical accuracy under controlled nodal budgets in structural analyses with localized field gradients. Unlike quasi-uniform meshing, the p...
In this work, stable and convergent numerical schemes on nonuniform time meshes are proposed, for the solution of distributed-order diffusion equations. The stability and convergence of the numerical methods are proven, and a set of numerical results...
This paper presents a novel non-uniform, non-stationary Loop subdivision that directly interpolates arbitrary initial triangular meshes. This subdivision is derived by assigning distinct parameters for “vertex-point” and “edge-point...
The use of multiple-level non-uniform rectangular mesh in coupled flow and sediment transport modeling is preferred to achieve high accuracy in important region without increasing computational cost greatly. Here, a robust coupled hydrodynamic and no...
This paper develops a compact analytical framework for multiquadric radial basis function–Hermite finite difference (MQ RBF–HFD) approximations on nonuniform meshes. The main contributions are a unified local operator formulation, uniform...
In this paper, we are interested in the effective numerical schemes of the time-fractional Black–Scholes equation. We convert the original equation into an equivalent integral-differential equation and then discretize the time-integral term in...
The finite-difference time-domain (FDTD) method is a versatile electromagnetic simulation technique, widely used for solving various broadband problems. However, when dealing with complex structures and large dimensions, especially when applying perf...
This paper develops a fully discrete finite element scheme for the fractional wave equation with order
In this paper, efficient methods seeking the numerical solution of a time-fractional fourth-order differential equation with Caputo’s derivative are derived. The solution of such a problem has a weak singularity near the initial time
A neural-network-assisted numerical method is proposed for the solution of Laplace and Poisson problems. Finite differences are applied to approximate the spatial Laplacian operator on nonuniform grids. For this, a neural network is trained to comput...
In this paper, we consider a nonlinear fractional superdiffusion equation involving a Caputo derivative of order
For non-uniform control polygons, a parameterized four-point interpolation curve ternary subdivision scheme is proposed, and its convergence and continuity are demonstrated. Following curve subdivision, a non-uniform interpolation surface ternary sub...
A finite-difference approach with non-uniform meshes was presented for simulating magnetotelluric responses in 2D structures. We presented the calculation formula of this scheme from the boundary value problem of electric field and magnetic field, an...
The present paper deals with the numerical solution of time-fractional advection–diffusion equations involving the Caputo derivative with a source term by means of an unconditionally-stable, implicit, finite difference method on non-uniform gri...
We consider the predictor-corrector numerical methods for solving Caputo–Hadamard fractional differential equations with the graded meshes
In this paper, we introduce the development of the Finite Difference Matrix Operators (FDMO) algorithm for solving the three-dimensional (3D) electromagnetic problem governed by the Laplace–Poisson equation. Specifically, we propose a novel approach...
This paper aims to numerically study the time-fractional Allen-Cahn equation, where the time-fractional derivative is in the sense of Caputo with order
An efficient approximation is developed for the Laplacian operator by merging the advances of finite difference and finite element approximations. This approach is applicable to a general quadrilateral grid. The optimal coefficients for the approxima...
Rolling-horizon energy management systems (EMSs) and model predictive control (MPC) for microgrids in smart cities face a fundamental trade-off: finer temporal discretization improves operational performance but rapidly increases the size of the opti...
Acoustic pyrometry (AP) is a promising methodology for high-quality temperature field reconstruction, which is widely used in the monitoring of atmosphere, room, and furnace. However, most of the existing acoustic reconstruction algorithms are develo...
The lattice Boltzmann method (LBM) has two key steps: collision and streaming. In a conventional LBM, the streaming is exact, where each distribution function is perfectly shifted to the neighbor node on the uniform mesh arrangement. This advantage m...
Nonuniform mesh is beneficial to reduce computational cost and improve the resolution of the interest area. In the paper, a cell-based adaptive mesh refinement (AMR) method was developed for bearing cavitation simulation. The bearing mesh can be opti...
Digital image correlation (DIC) is a popular photomechanics method for deformation measurement. The conventional subset-based DIC method obtains the displacement vectors at the subset centers, but cannot calculate the deformation on the specimen edge...
A parameterization modeling method based on finite element mesh to create complex large-scale lattice structures for AM is presented, and a corresponding approach for size optimization of lattice structures is also developed. In the modeling method,...
This paper considers the multi-term subdiffusion equation with weakly singular solutions. In order to use sparser meshes near the initial time, a novel scheme (which we call the corrected L1 scheme) on graded meshes is constructed to estimate the mul...
The paper is aimed at an assessment of the importance of the coordinate system (Cartesian vs. cylindrical) assumed for simulations of free-round jets. The research is performed by applying the large eddy simulation method with spatial discretisation...
Pipe bend is a critical integral component, widely used in slurry pipeline systems involving various engineering applications, including natural gas hydrate production. The aim of this study is to assess the capability of RANS-based CFD models to cap...
Three-dimensional (3D) orebody boundary modeling primarily relies on spatial interpolation methods, such as radial basis functions (RBFs). However, these methods struggle with large datasets and require gradient or normal constraints for stable geome...
This paper presents a ε-uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of the analytical solution are given, and the finite difference s...
To evaluate the influence of tooth surface wear on face gear dynamics, this study proposes a coupled wear–dynamics modeling method. A phase-dependent backlash model is developed to preserve the meshing-phase modulation induced by nonuniform wea...
Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article. The second-order derivative is multiplied by a small parameter which gives rise to bou...
A nonlinear fractional differential equation with a Caputo derivative of order
Helical gear transmissions in wind turbine gearboxes operate under high torque, variable speed, and complex rolling–sliding contact conditions, where friction-induced wear evolves in a spatially non-uniform manner. However, most existing dynami...
Numerical simulations are crucial for fast and accurate estimations of the flow characteristics in many engineering applications such as atmospheric boundary layers around buildings, external aerodynamics around vehicles, and pollutant dispersion. In...
Mesh generation is a critical preprocessing step in Computational Fluid Dynamics. In ship hydrodynamics, existing mesh generation methods lack adaptability to complex hull surface geometries, necessitating repeated optimization. To address these issu...
A structured mesh generation method based on an improved ray-tracing technique is proposed for finite time difference domain (FDTD) simulation in this paper. This method converts the triangular faces provided by the STL file into the structured mesh...
In this work, we propose a fast scheme based on higher order discretizations on graded meshes for resolving the temporal-fractional partial differential equation (PDE), which benefits the memory feature of fractional calculus. To avoid excessively in...
In deep shale gas fracturing, the narrow width of micro fractures presents a challenge for conventional proppants (40/70 mesh, 70/140 mesh), which often fail to enter branch fractures, resulting in inadequate effective support volume. To address this...
High-speed and accurate simulations of landslide-generated tsunamis are of great importance for the understanding of generation and propagation of water waves and for prediction of these natural disasters. A three-dimensional numerical model, based o...
The convolutional neural networks (CNNs) functioning on geometric learning for the urban large-scale 3D meshes are indispensable because of their substantial, complex, and deformed shape constitutions. To address this issue, we proposed a novel Geome...
In the clock network design, the trade-off between power consumption and timing closure is an important and difficult issue. The clock tree architecture has a shorter wire length and better power consumption, but it is more difficult to achieve timin...
8 November 2026
Repeated computational fluid dynamics (CFD)-based aerodynamic optimization requires both a compact design space and an inexpensive mesh-update procedure. This study presents a reduced-parameter-to-mesh framework in which low-dimensional variables act...
To study the aerodynamic and vibration characteristics of iced conductors under the influence of wind fluctuations, a harmonic superposition method is used to simulate nonuniform wind speeds. A user-defined function is written on the basis of the sec...
Mechanical equipment in the field of aerospace that is used only once is called disposable machinery. As a piece of typical disposable machinery, disposable harmonic gear exhibit stiffness failure with a large load. This manuscript distinguishes disp...
Stiffness is the main internal excitation of gear system vibration and is the basis for studying the static and dynamic characteristics of the system. Based on the relationship between thermal stress and strain in plane strain theory and combined wit...
The engineering applications of two-dimensional (2D) hydrodynamic models are restricted by the enormous number of meshes needed and the overheads of simulation time. The aim of this study is to improve computational efficiency and optimize the balanc...
In this study, a numerical solution for degenerate space–time fractional advection–dispersion equations is proposed to simulate atmospheric dispersion in vertically inhomogeneous planetary boundary layers. The fractional derivative exists...
The influence of obstacles in the form of polymer chains on the diffusion of a low-molecular-weight solvent was the subject of this research. Studies were performed by computer simulations. A Monte Carlo model—the Dynamic Lattice Liquid algorit...
A numerical gear rolling test (NGRT) method for actual tooth surfaces was proposed. The non-uniform rational B-spline (NURBS) fitting method was adapted to reconstruct the actual tooth surface, and the instant meshing point as well as the transmissio...
Five-G heterogeneous network overlaid by millimeter-wave (mmWave) access employs mmWave meshed backhauling as a promising cost-efficient backhaul architecture. Due to the nature of mobile traffic distribution in practice which is both time-variant an...
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