The traditional boundary element method (BEM) often faces challenges in efficiently solving inhomogeneous problems, particularly in thin-walled geometries, due to the need for domain discretization and the handling of nearly singular integrals. In this study, we propose an efficient hybrid algorithm that combines the BEM with physics-informed neural networks (PINNs) to solve inhomogeneous potential

Numerical simulation of slope instability remains a critical challenge in geotechnical engineering, particularly for large deformations and long-term seepage. The traditional finite element method (FEM) is prone to mesh distortion in large-deformation modeling, while the material point method (MPM) is less efficient for small deformations associated with long-term seepage. To overcome these limitations

This research introduces a dual reciprocity boundary element method (BEM) designed to analyze the transient scattering of vertically travelling incident P-SV waves. By using static fundamental solutions and appropriate predictor operations, the domain inertia integrals from the equilibrium equation were transformed into boundary integral equations. The computable format of the integral equations was

In this work, the ZZ-BD recovered stress field is first used to enhance the data transferred from the global to the local scale models in the Generalized Finite Element Method with Global–Local enrichments (GFEMgl). The recovered stress field is constructed by solving a block-diagonal system of equations resulting from an L2 approximate function projection associated with the singular stress field

The problem of radiation diffusion is extremely challenging due to the complex physical processes and nonlinear characteristics of the equation involved. In this paper, we propose a class of high-precision meshless methods for 3D nonlinear radiation diffusion equations applicable to spherical and cylindrical walls. Firstly, when the energy density is linearly related to temperature, we use a full-implicit

In this study, a new virtual material point peridynamic model (abbreviated as VMPPD) is proposed to capture the fracture behavior of composite laminates with arbitrary fiber orientation. The unique feature is that virtual material points serve as intermediate variables to achieve load transfer in a regularized discrete grid. As a result, a PD model for describing the reinforcement characteristics of

The paper introduces a novel methodology based on a generalized formulation and higher-order-theories for the fully-coupled multifield analysis of laminated curved structures subjected to thermal, magnetic, and mechanical loads. The formulation follows the Equivalent Single Layer approach, taking into account a generalized through-the-thickness expansion of displacement field components, scalar magnetic

Artificial Neural Networks (ANNs) have revolutionized machine learning by enabling systems to learn from data and generalize to new, unseen examples. As biologically inspired models, ANNs consist of interconnected neurons organized in layers, mimicking the human brain’s functioning. Their ability to model complex, nonlinear processes makes them powerful tools in various domains. In this study, the

Traditional model for composite laminae based on bond-based peridynamics (BB-PD) involves only two material parameters, which is insufficient to fully describe the complicated engineering properties of composite laminae. This limitation results in constrained Poisson's ratio and shear modulus in the PD model. In this study, a novel fracture model for composite laminae is proposed based on BB-PD, which

The generalized nth-order perturbation method for the quantitative uncertainty analysis in half-space acoustic problems proposed in this study is based on the isogeometric boundary element method, where the acoustic wave frequency is defined as a stochastic variable. We derive the Taylor series expansion and the kernel function formulation of the acoustic boundary integral equation for the half-space

Numerical solutions of initial value problems (IVPs) for stiff differential equations via explicit methods such as Euler’s method, trapezoidal method and Runge–Kutta methods suffer from stability issues and demand unacceptably small time steps. Backward differentiation formulas (BDF), a class of implicit methods, have been successfully used for resolving stiff IVPs. Classical BDF methods are derived

Fracture initiation in solids fundamentally arises from pre-existing discontinuities, such as crack networks and void distributions, which are ubiquitously observed in engineering structures. This paper presents an innovative unsupervised learning framework, termed Kolmogorov–Arnold representation theorem enhanced peridynamic-informed neural network (PD-KINN), designed to address challenges in elastic

The Mechatronic Electro-Hydraulic Coupler (MEHC) integrates a swashplate axial piston pump with a permanent magnet synchronous motor, enabling flexible conversion between mechanical, electrical, and hydraulic energy. The efficiency of the MEHC plays a crucial role in the selection of loading and control strategy. However, specific research on its hydraulic energy loss is lacking. This paper proposes

Detailed studies of peculiar wave phenomena in piezoelectric metamaterials require advanced and accurate numerical methods. An extended boundary integral equation method based on the employment of the Fourier transform of Green’s matrices and the Bubnov–Galerkin method is presented for the wave motion simulation of a multi-layered piezoelectric laminate with electrode arrays connected pairwise via

In this paper, we consider the numerical solutions of three-dimensional axisymmetric nonlinear boundary integral equations with logarithmic kernel. A numerical algorithm with using extrapolation twice is developed to solve the equations, which possesses the low computing complexities and high accuracy. The asymptotic compact operator theory is used to prove the convergence of the algorithm. The efficiency

Understanding the Site-City Interaction (SCI) induced by surface wave is vital for accurate seismic analysis and urban planning. Based on the elastodynamics theory and wave equations, this paper proposes a semi-analytical method to investigate SCI effect induced by Rayleigh wave. The proposed approach integrates the Dynamic Stiffness Matrix Method (DSMM) with substructure method, and can effectively

This study introduces an online reduced-order methodology designed to avoid the need for generating additional samples during the offline phase, a requirement typically associated with the classical reduced basis method. The proposed methodology is implemented for accelerating the sensitivity analysis in the dynamic topology optimization. The dominant Proper Orthogonal Mode (POM) of the adjoint sensitivity

A novel fully nonlinear circular numerical wave basin is developed based on potential flow theory and high-order boundary element methods (HOBEM). By controlling the vector input of wave velocity from wave-making sources uniformly distributed on the three-dimensional cylindrical surface, the wave basin is capable of generating waves in all directions. The wave basin is used to simulate nonlinear waves

The combined effect of dual rigid structures over non-periodic bottom morphologies is examined through a boundary value problem to characterize the scattering phenomenon. Three different types of bottom morphologies: (a) monotonically decreasing oscillatory, (b) exponential decreasing oscillatory and (c) Gaussian oscillatory are taken into consideration. Utilizing the boundary element method (BEM)

This study considers transient response of sandwich beams produced from functionally graded graphene platelets-reinforced composite faces and functionally graded porous core under the action of various types of moving distributed masses. The equations of motion are developed by the energy method using a von Kármán type nonlinear strain-displacement relationship. Different micromechanical models are

Earthquakes can occur onshore and offshore. When it occurs offshore, an analytical model is needed where both the water layers and rock layers have to be considered. In this paper, we develop such a new solution when a general dislocation source is located in any layer of the transversely isotropic and elastic rock media. This novel and comprehensive method is based on the Fourier-Bessel series system

Boundary element methods for elliptic partial differential equations typically lead to boundary integral operators with translation-invariant kernel functions. Taking advantage of this property is not straightforward if general unstructured meshes and general basis functions are used, since we need the supports of these basis functions to be contained in a hierarchy of subdomains with translational

Multiphase flow simulations are complex due to the intricate interactions between phases when high density and viscosity ratios are involved. These complexities often lead to challenges in capturing sharp interfaces and managing pressure jumps across phases, which can induce numerical instability. Extending the Lagrangian Differencing Dynamics (LDD) method which differs from other meshless methods

Dynamic response of a transversely isotropic layered half-space composed of alternatively arbitrary poroelastic and elastic materials is numerically investigated through the Meshless Local Petrov–Galerkin (MLPG) method. The governing equations of the porous layers are the u−p formulation of the Biot’s theory, and the equations of motion for single-phase elastic media are considered for pure elastic

The blast threats have become a global safety concern for the ecosystems. Rigorous research using blasts over infrastructures improves the assessment methods, damages and failure modes, either experimentally or numerically. However, experimental blast analysis over a full-scale bridge is not feasible and is against the country's federal law. Alternatively, numerical analysis with experimentally validated

In this study, we derived a three-dimensional scaled boundary finite element formulation for heat conduction problems. By incorporating Wachspress shape functions, a polyhedral scaled boundary finite element method (PSBFEM) was proposed to address heat conduction challenges in complex geometries. To address the complexity of traditional methods, this work introduced polygonal discretization techniques

Tunnel engineering is one of the hot spots of research in the field of geotechnical engineering, and the seepage analysis of tunnels is an important research direction at present. In recent years, physics-informed deep learning based on priori fusion data has become a cross-disciplinary hotspot for solving forward and inverse problems based on partial differential equations (PDEs). In this paper, physics-informed

It has recently been demonstrated that turbulent flow could be described by the fractional Laplacian Reynolds-averaged Navier–Stokes equations fL-RANS equations, (Epps and Cushman-Roisin, 2018). In this paper, we propose a numerical approach for solving the equations, and then provide a deep-learning based approach for inferring the unknown parameters of the equations. First, we construct a lattice

The study presents an adapted MeshGraphNet for real-time field prediction in digital twins, surpassing traditional FEM in efficiency and boundary condition adaptability but falling short of real-time computational demands. Trained with true labels, MeshGraphNet accurately predicts nodal variables on coarse graphs and reduces simulation time through parallel sub-mesh processing. Applied to a 1D mesh

An efficient numerical integration technique, namely the Element Midpoint(EM) Method, is successfully applied to meshless methods to solve the fracture problem, which is modeled using the Radial point interpolation method. The results were compared with standard (3×3) points Gauss quadrature and (6×6) points Gauss quadrature in 2D to validate the presented numerical methods. To demonstrate the efficiency

Discontinuous numerical methods have been widely applied to investigate rock deformation and failure behavior in rock engineering scenarios such as tunnel excavation and oil/gas exploitation. Compared to discontinuous numerical methods with explicit formulations, discontinuous deformation analysis (DDA) has the advantages of unconditional stability and strict contact convergence with its implicit formulation

In large-scale water diversion projects, the rapid and accurate evaluation of pumping station unit performance is crucial to ensure that flow rates meet delivery requirements. Computational fluid dynamics (CFD) is effective in analyzing unit performance but is constrained by its high computational complexity and time consumption. Reduced-order models (ROMs) partially alleviate these issues; however

In the study of the stability of gravity dam, the situation of dam and rock mass is complicated, there may be pore water and various kinds of heterogeneous materials to affect the stability of rock mass, among which the deformation and failure of the dam cannot be ignored. In this paper, an improved high-order covering function is applied to the Numerical Manifold Method (NMM), and the Hermite form

Due to the many applications of shape memory alloys (SMAs) to make the structures more intelligent, these materials are getting great attention of researchers. Meanwhile, the nonlinear dynamic analysis of curved beams made of SMAs has not been investigated so far. Therefore, this work focuses on a nonlinear dynamic analysis of SMA curved beams under transverse impulse loading taking into account the

We introduce a novel semi-analytic method for solving singularly perturbed reaction–diffusion problems in a smooth domain using neural network architectures. To manage steep solution transitions near the boundary, we utilize the boundary-fitted coordinates and perform boundary layer analysis to construct a corrector function which describes the singular behavior of the solution near the boundary. By

A novel computational framework based on modified bond-based peridynamics is proposed for viscoelastic laminas. The framework accurately captures deformations, damage initiation, and propagation under mechanical and thermal loads. It reduces numerical complexity by directly assessing viscoelastic strains each time step, eliminating real-time increment constraints. Constitutive component models, including

We consider various method of fundamental solution (MFS) formulations for the numerical solution of two-dimensional boundary value problems (BVPs) governed by the homogeneous biharmonic equation. The motivation for employing the proposed techniques comes from the corresponding boundary integral representations. These are carefully analyzed in the case the domain of the BVP under consideration is a

Numerical manifold method (NMM) is a powerful unified continuous-discontinuous method due to its dual cover systems and the flexibility of the cover types. In this work, to better solve problems with various discontinuity geometry characteristics by NMM, the finite element method (FEM) mesh and the NMM traditional regular mathematical mesh are employed to construct finite covers for NMM, respectively

Modeling the structural failures induced by fluid-structure interaction (FSI) are crucial because it dominates many engineering problems. In this paper, a nonlocal general particle dynamic (NGPD) method is proposed to solve the FSI problems considering the structural failure. In this framework, the governing equations for fluid and solid are reformulated by introducing nonlocal theories. The tensile

Slag accumulation is one of the key and most difficult problems in solid rocket motor (SRM) having submerged nozzles, which may cause severe ablation of insulation and even has a great influence on the interior ballistic performance. This study aims to establish a computational framework mainly based on a Lagrangian-Euler coupled particle model, which consider granular flow as a combination of smoke

A new thermoelastic model is introduced to reveal equivalent mechanical and thermal properties of randomly oriented (RO), agglomerated carbon nanotube (CNT) inclusions within a matrix material. Thereafter, a bio-inspired FG-CNTR-TPMS material model is established through three typical triply periodic minimal surfaces (TPMS) microstructures reinforced with CNTs and functionally graded (FG) schemes.

Neural network (NN) methods have been developed to solve interface problems recently. In comparison with conventional techniques (e.g., finite element method), the NN method enjoys the merits of meshless features, powerful ability to approximate complex interface geometries, and high accuracy. The current NN studies are mostly focused on elliptic interface problems. The methodology will cause difficulties

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in their loss function. While PINNs are successfully used for solving forward and inverse problems, their accuracy decreases significantly for parameterized systems

Underwater reinforced concrete is vulnerable to chloride corrosion, which reduces the durability of underwater concrete structures. In this paper, by introducing time-varying chloride ion diffusion and non-uniform corrosion expansion failure model, a chemical-hydraulic-mechanical coupling peridynamic model of reinforced concrete corrosion expansion failure process in actual underwater environment is

In this study, a nonlinear eigenvalue solver for the numerical solution of thermoviscous acoustic problems based on the equivalent source method (ESM) is developed. By using the idea of the ESM, the solutions to the thermoviscous formulations are coupled on the surface of the structure through the isothermal and non-slip conditions. The frequency-dependent nature of the transfer matrix in the system

In recent years, with the development of quantum machine learning, Quantum Neural Networks (QNNs) have gained increasing attention in the field of Natural Language Processing (NLP) and have achieved a series of promising results. However, most existing QNN models focus on the architectures of Quantum Recurrent Neural Network (QRNN) and Quantum Self-Attention Mechanism (QSAM). In this work, we propose

The shape parameter c and the fictitious radius R are important parameters that affect the performance of the polynomial-augmented RBF collocation method (RBFCM) with fictitious centers. It is known that the RBFCM can reduce the accuracy dependency on shape parameter by using extra polynomial constraints. Moreover, we find that calculation inaccuracies exhibit a strong association with the effective

The meshless global radial basis reproducing kernel particle method (GRB-RKPM), constructed based on the global radial basis function and the reproducing kernel particle method (RKPM), is extended to the investigation of the three-dimensional (3D) elastoplastic problem of bi-directional functional gradient materials (BDFGMs). The discrete equations in the incremental form are established based on the

Key features for the versatile industrial applications of smoothed particle hydrodynamics (SPH) are numerical accuracy and stability, computational efficiency, and ease of implementation. To meet these requirements, this study presents a straightforward algorithm to treat large-strain elastoplasticity within Total Lagrangian SPH (TLSPH) framework. In terms of accuracy and stability, the total Lagrangian

This paper develops the Zonal Free Element Method (ZFREM) to solve transient nonlinear heat conduction problems. As a novel meshless method, ZFREM utilizes the shape functions of isoparametric elements, which contribute to its enhanced stability compared to other meshless methods. Moreover, through domain partitioning, this method effectively handles complex geometric configurations. Another distinguishing

Discontinuous deformation analysis (DDA), a representative discontinuum-based numerical method, has been successfully developed to simulate the important problem of fracturing failures in rock mechanics through a sub-block approach. In the present work, a refinement algorithm of the Voronoi sub-block elements for DDA simulations of rock fracturing is proposed to simultaneously improve the simulation

This study introduces a rapid methodology based on recursive skeletonization factorization (RSF), for the determination of origin intensity factors (OIFs) at Neumann boundaries within the framework of the singular boundary method (SBM). The conventional formula for OIFs, which is derived using the subtracting and adding-back technique (SABT), is reformulated into a matrix-vector product representation

The oblique entry process of a vehicle not only generates strong axial forces, but also generates significant normal force due to the asymmetry of air and cavity flows, which poses a great threat to the local and overall strength of the vehicle. This paper employs a multiphase δ-smoothed particle hydrodynamics (δ-SPH) method to analyze the flow field evolution and pressure distribution on the vehicle

The problem of enhancing the electromagnetic (EM) scattering for almost transparent nanotubes via shape modification of their cross section, is studied in this work. An isogeometric analysis approach, in a boundary element method setting, is employed to evaluate the local electric field, which is expressed in terms of the exact same basis functions utilized in the geometric representation of the cylinder

Within the framework of scaled boundary finite element method (SBFEM) and inspired by isogeometric analysis (IGA), the NURBS-enhanced semi-analytical method, referred to as the scaled boundary isogeometric analysis (SBIGA), is extended for solving nonlinear liquid sloshing analysis in storage structures. This method leverages the advantages of Non-Uniform Rational B-Splines (NURBS), offering a highly

This paper studies and assesses different Neumann boundary conditions (BC) implementations in the radial basis function generated finite difference (RBF-FD) method. We analyse four BC implementations by solving a phase-field model for single dendrite growth in supercooled pure melts. In the first BC implementation, the BC are satisfied when constructing interpolation problems in the local support domains

In computational electromagnetics, numerical methods are generally optimized for triangular or tetrahedral meshes. However, typical objects of general interest in electronics, such as diode packages or antennas, have a Manhattan-type geometry that can be modeled with orthogonal and rectangular meshes. The advantage of orthogonal meshes is that they allow analytic solutions of the integral equations

Enhancing the efficiency of chat models in multi-turn dialogue systems is a critical challenge in Artificial Intelligence. Multi-turn dialogues often span diverse topics, with irrelevant dialogue turns frequently degrading the quality of the model’s responses. This study addresses this challenge by proposing a novel method for the automated identification and selection of contextually relevant dialogue