The primary objective of this study is to present the local radial basis function (RBF)-finite difference method with a goal to solve Korteweg–de Vries (KdV) model with dual power law nonlinearity. First, Crank–Nicolson difference scheme is applied for time derivative and the local RBF collocation method is utilized to estimate the spatial derivatives. Also, the stability and convergence of KdV model is analyzed in [Formula: see text] and [Formula: see text] spaces. This approach is effective and has minimal computational cost. Four instances are provided that illustrate the accuracy of the presented method and found efficient results.

This study presents an efficient Monte Carlo simulation method to solve multivariate uncertainty problems in structural dynamic systems. The full model is obtained by the adaptive time-step material point method, and the multivariate surrogate model is built and analyzed for uncertainty by the adaptive sparse polynomial chaos expansion. The cubic spline interpolation method serves as a bridge between the original full model and the multivariate surrogate model, which improves the sampling efficiency of Monte Carlo simulation. Numerical results show that the proposed algorithm can significantly improve the efficiency and accuracy of uncertainty analysis.

The objective of this work is to develop a one-way partitioned coupling computational method to account for aerodynamic effects, dynamic structural deformation, and fatigue damage of a 5[Formula: see text]MW wind turbine blade. We accurately reproduce a wind flow field using a large eddy simulation (LES)-based computational fluid dynamics (CFD) approach with a rotating high-fidelity wind turbine model. A high-fidelity finite element structural model of the blade is also constructed, where laminated composite solid elements are used for mesh discretization. A dynamic finite element method is employed for blade deformation analysis. The aerodynamic loading history calculated by the LES analysis is applied onto the blade surface as a loading boundary condition of the dynamic structural analysis via a one-way partitioned fluid–structure interaction (FSI) method. A fatigue damage distribution of the whole blade structure is finally estimated using an engineering fatigue life model with the help of stress history information outputted from the structural analysis. Based on the developed method, a high-performance computational system that combines a parallel finite element LES code named FrontFlow/Blue (FFB), a parallel data coupling tool named REVOCAP_Coupler, a parallel structural analysis code named ADVENTURE_Solid, and a fatigue evaluation tool named ADVENTURE_Fatigue is established on a latest high-performance computing environment (i.e., Supercomputer Fugaku). The effectiveness and accuracy of the computational system are first validated in terms of aerodynamic results and dynamic behaviors of the blade model. Finally, some parametric studies are performed to investigate the effects of gravitational and centrifugal forces, shear of atmospheric boundary layer, and tip speed ratios on structural behaviors and fatigue damages of the 5[Formula: see text]MW turbine blade.

This article explores the application of Kumar-Sloan technique based Legendre spectral Galerkin, collocation and multi-Galerkin methods to solve non-linear Volterra Hammerstein integral equations, and demonstrate significant advancements in superconvergence results in both infinity as well as L 2 norms. It is concluded that without going to the iterated versions, we obtain the improved superconvergence rates for Legendre spectral Galerkin, collocation and multi-Galerkin methods as higher as that of Legendre spectral iterated Galerkin, iterated collocation and iterated multi-Galerkin methods. Numerical results are given to show the efficiency of the proposed technique.

This paper presents an enhanced formulation of the Fragile Points Method (FPM), a truly meshless approach for efficiently modeling implicit interfaces in two-dimensional differential equations involving non-homogeneous materials. The proposed framework eliminates the need for specialized numerical integration techniques and provides a systematic mathematical foundation for solving interface problems. Discontinuities in both primary and secondary variables across interfaces are naturally handled through the inherently discontinuous shape functions of FPM. Unlike conventional Galerkin methods, FPM employs simple, local, pointbased polynomial trial and test functions constructed via a generalized finite difference approach. These discontinuous functions bypass the continuity requirements of standard Galerkin frameworks. To address the resulting inconsistency due to discontinuities, we incorporate numerical flux corrections inspired by the discontinuous Galerkin method. The proposed method is validated through several benchmark problems, demonstrating its efficiency and robustness.

To address the issues of mismatched temporal and spatial accuracy as well as the high computational cost associated with nonlinear iterative procedures in existing high-order numerical methods for the two-dimensional Generalized Benjamin-Bona-Mahony-Burgers equation, this paper proposes a novel linearized high-order finite difference scheme. This method integrates the fourth-order backward difference formula in time with the fourth-order compact scheme in space, and constructs a fully linear numerical scheme through the interpolation-based linearization technique. The main innovations are: (1) achieving uniform fourth-order convergence in both time and space, thereby maintaining high accuracy and numerical stability even under relatively large time step sizes; (2) significantly enhancing computational efficiency for high-dimensional problems through the proposed linearization strategy; (3) providing rigorous theoretical analysis, including proofs of the existence and uniqueness of the numerical solution and the linear stability of the scheme. Comprehensive numerical experiments are conducted to demonstrate the effectiveness and reliability of the proposed method.

In this paper, an H 1 - Galerkin mixed finite element method for the fourth order Rosenau equation is studied, where three auxiliary variables are introduced as intermediate functions, which split the equation into four first order equations. Further an appropriate weak formulation is chosen for all the equations. In both semi-discrete and fully-discrete analysis, optimal error estimates are obtained. Furthermore, numerical experiments are used to validate the effectiveness of the method. In this method optimal error estimates of the unknown variable, it’s first derivative, second derivative and the third derivative are obtained simultaneously, which is an added advantage.

In this paper, we propose a novel augmented Lagrangian preconditioner based on the global Arnoldi method for accelerating the convergence of Krylov subspace solvers applied to linear systems with a block three-by-three structure. Such systems typically arise from mixed finite element discretizations of the Stokes equations. In practice, the velocity components are approximated using a common finite element space. More specifically, in two dimensions, our approach relies on a standard scalar finite element basis to discretize the velocity space. This componentwise splitting naturally induces the desired block three-by-three structure. We establish spectral analyses for the exact versions of the proposed preconditioners. Numerical experiments further demonstrate that the new approach is more robust and efficient for solving discrete Stokes problems. In particular, efficiency is assessed in terms of reduced computational time, confirming the practical advantages of our method.

The ammunition manipulator is an important actuator of the modern self-propelled ammunition supply and delivery system. The positioning accuracy reliability (PAR) directly affects the firing stability of the entire artillery system. Therefore, it is of great significance to accurately and efficiently evaluate the PAR. This paper aims to conduct an in-depth analysis of the PAR for ammunition manipulator. First, a rigid–flexible coupling dynamic model of the artillery manipulator was established; Subsequently, a reliability evaluation strategy for positioning accuracy of ammunition manipulator was developed by combining the second-order approximation of the limit-state function (LSF) and the mixture importance sampling (MIS) method. Meanwhile, the effectiveness of the constructed model was verified through experimental testing. Finally, the influence of the clearance coefficient on the positioning accuracy of the ammunition manipulator was studied in detail by analyzing three cases.

In this paper, a nonconforming quadtree finite element method (FEM) with Wachspress shape functions (WSFs) is proposed for the nonlinear analysis of elastoplastic behavior. The adaptive quadtree mesh technique used for bilinear quadrilateral (Q4) elements can result in hanging nodes along refined edges, which necessitates the construction of multiple corresponding shape functions. This paper employs the WSF within the polygonal framework to construct a unified shape function for nonconforming quadtree meshes, thereby eliminating issues related to hanging nodes. Within the framework of continuum mechanics, an implicit implementation of the von Mises elastoplastic model is proposed, and the stiffness matrix, formulated using the FEM with WSFs, is divided into elastic and plastic components, with only the plastic matrix updated during Newton–Raphson iteration, improving computational efficiency. Both homogeneous and multi-material slope stability examples are presented, validating the high accuracy and convergence of the FEM with WSFs in comparison to traditional FEM techniques. Moreover, the method exhibits excellent adaptability and robustness in handling adaptive quadtree mesh refinement with hanging nodes.