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

This paper proposes an O(N) fast direct solver for two-dimensional elastic wave scattering problems. The proxy surface method is extended to elastodynamics to obtain shared coefficients for low-rank approximations from discretized integral operators. The proposed method is a variant of the Martinsson–Rokhlin–type fast direct solver. Our variant avoids the explicit computation of the inverse of the

Piezoelectric intelligent materials are pivotal in a multitude of fields. In this work, the numerical manifold method (NMM) is developed to model piezoelectric solids with arbitrarily shaped cavities. The superiority of this method roots in its dual-cover systems, namely, the mathematical and physical covers, which enable the NMM to straightforwardly discretize physical domain with non-conforming mathematical

The current work concerns to introduce a new numerical solution based upon a supervised learning algorithm with the shape functions of reproducing kernel particle method (RKPM). In the developed technique a least-squares support vector regression is extended for the numerical solution of the Cahn–Hilliard (CH) model in two- and three-dimensional domains. First, the time derivative is approximated by

The time-fractional viscoelastic wave equation plays a crucial role in geophysical exploration by accurately modeling wave attenuation and velocity dispersion in Earth’s media. However, solving this equation is challenging due to the stress–strain relationship governed by the Caputo fractional derivative of small orders and the complexity of irregular surface topographies. The requirement for significant

Brain tumors are among the deadliest types of cancer and the most challenging to treat. Predicting the growth behavior of tumors can help physicians choose the best treatment program. Herein, a numerical technique based on the meshless radial point interpolation methods is presented for simulating the growth of brain tumors under the effects of radiotherapy and chemotherapy. In this work, the stress

This study adopts the indirect boundary integral equation method (IBIEM) to solve the scattering of spherical P-waves by a three-dimensional (3D) cavity in an elastic half-space. Specifically, the free field of the spherical wave is obtained by the method of full space superposition. Based on the single-layer potential theory, the scattered field is constructed using concentrated force sources applied

In this article, a hybrid FEM-MESHLESS method for dynamic analysis of homogeneous and inhomogeneous structures is developed. This hybrid method has already been shown by El Kadmiri et al (2021, 2022, 2024) for static analysis of homogeneous and inhomogeneous structures. To verify the proposed method for studying the dynamic response of homogeneous and inhomogeneous structures, a study based on small

This study introduces a comprehensive multiscale and multiphysical numerical approach for analyzing sandwich three-phase nanocomposite plate with multiferroic facesheets in its upper and lower surfaces. The proposed research investigates the zigzag effect and quasi-3D sinusoidal shear deformation, capturing the complex interactions between the core and multiferroic facesheets across multiple physical

Multi-ship encountering results in complex interactions that significantly modify the surrounding flow field, particularly in the presence of incident waves. Due to the disturbing effect of the complex wave system, the behavior of each ship during the encounter is influenced by the wave characteristics and the relative motions between the ships. This paper establishes a model for ship-to-ship encountering

Because of the nonlinearity, three-dimensional (3D) elastoplastic problems are very important for any numerical method. In this study, the improved interpolating element-free Galerkin (IIEFG) method based on nonsingular weight functions for elastoplastic problems is presented. An improved interpolating moving least-squares (IIMLS) method with nonsingular weight functions is applied to construct the

This paper develops a stable numerical method based on RBFs to solve two-dimensional time-fractional partial integro-differential equations with singular kernels. The spatial discretization uses an RBF-generated Hermite finite difference approach, which applies a geometric greedy sparse approximation technique for node selection, ensuring accuracy and controlling consistency errors. The temporal direction

Peridynamic is an effective method for addressing fracture problems. However, the non-local theory makes it time-consuming. Although some techniques have been developed to improve computational efficiency, the acceleration effect remains relatively limited. This paper introduces a parallel algorithm for bond-based peridynamic using the GPU parallel CUDA programming technology. The calculation process

This paper presents some results on steady-state thermal analysis with variable thermal conductivity under general boundary conditions and other internal constraints using isogeometric methods. Non-Uniform Rational B-splines (NURBS) serve as basis functions for representing both the geometry of the physical domains and the solution. While both isogeometric collocation method and Galarkin formulation

This study proposes a sensitivity analysis framework for Transverse Magnetic polarized electromagnetic scattering problems, with a focus on Perfectly Electric Conductors (PEC). To enable seamless integration of Computer-Aided Design and Computer-Aided Engineering, the isogeometric boundary element method based on the Galerkin scheme is employed. This method utilizes Non-Uniform Rational B-splines to

This paper proposes a novel numerical method based on the cell-based smoothed radial point interpolation method (CS-RPIM) combined with second-order cone programming to perform lower bound limit analysis of elastic-perfectly-plastic thin plates, using only deflection as nodal variable. The problem domain is initially discretized using a simple triangular background mesh, where each triangular cell

The finite block method (FBM) in the Cartesian coordinate system is developed to deal with the problems of the bi-materials V-notches in functionally graded materials (FGM) under static and dynamic loads. The first partial differential matrix is established via Lagrange series. Higher-order derivatives can be deduced from the first order partial differential matrix directly. In order to obtain the

This paper investigates the two-dimensional unsteady Stokes equation with general additive noise. The primary contribution is the derivation of the relevant estimate of Green’s tensor, which provides a fundamental representation for the solution of this stochastic equation. We demonstrate the crucial role of Green’s function in understanding the stability and perturbation characteristics of the stochastic

A new semi-analytical and semi-numerical approach is proposed to investigate the scaling law of in-plane roughness due to the fracture of a heterogeneous interface involving spatial correlation of disorders. The model is considered as a composite structure composed of two cantilever rectangular plates bonded with an interfacial layer. Based on the theory of solid mechanics, the dynamic process of interfacial

The seafloor is mostly made up of soft silt, and seismic waves collide with particles before scattering during their propagation. Moreover, the ocean terrain includes basins, seamounts, islands and reefs, contributing to the intricate propagation of seismic waves in seawater. This study proposes a two-dimensional wave simulation algorithm for the marine seismic site effect based on the indirect boundary

In this work, an effective and stable immersed cell-based smoothed finite element method (ICS-FEM) together with mean value coordinate (MVC) projection using quadrilateral elements is presented for 2D fluid-structure interaction (FSI) problems. In an immersed-based algorithm, the entire system can be divided into three components: large-deformed nonlinear structure, incompressible viscous fluid, and

A boundary element formulation is developed based on consistent couple stress flexoelectricity. The formulation is used here to study the flexoelectric response of a two-dimensional isotropic bimaterial consisting of a flexoelectric dielectric thin film on a non-flexoelectric dielectric material. Flexoelectric phenomenon is a coupled problem of mechanical and electrostatic effects, each specified by

Solid–fluid numerical simulations involving open channels are usually complicated, especially for large solid displacements. An extended three–dimensional discontinuous deformation analysis (3D DDA) method incorporating depth-integrated two-dimensional fluid dynamics was proposed to evaluate solid movement considering fluid actions. In this method, two types of fluid forces on solid blocks, buoyancy

This paper proposes a novel algorithm, the symplectic time-domain finite element method (ST-FEM), for solving the equation of motion within the peridynamics (PD) framework, with a focus on dynamic impact problems and crack propagation prediction. An iterative scheme for the PD equation of motion is established using the time-domain finite element method (T-FEM), with symplectic conservation of the

Periodic structures are ubiquitous in nature and engineering, offering unique properties that inspire a range of applications. This paper explores the mathematical modeling of periodic structures in rarefied gas flows using the coupled constitutive relations (CCR) model. The method of fundamental solutions (MFS), known for its meshfree nature and computational efficiency, is utilized as a numerical

This study presents an end-to-end deep learning framework for nonlinear reduced-order modeling and prediction, combining Variational Autoencoders (VAE) for feature extraction and Long Short-Term Memory (LSTM) networks for temporal prediction. The framework simplifies the modeling process by integrating multiple steps into a unified architecture, improving both design and training efficiency. The VAE

Isogeometric analysis (IGA) employs NURBS basis functions as shape functions, possessing geometric accuracy, high precision and high-order continuity, thereby making it very suitable for analyzing complex curved surface structures. By taking advantage of these benefits, this paper presents a geometrically nonlinear electro-mechanical coupled IGA model for accurately predicting the post-buckling behavior

This study evaluates the performance of a pair of inverted trapezoidal pile-rock breakwaters (PRB) placed at a finite distance from the floating dock and connected to a partially reflecting seawall under the oblique wave incidence. The PRB consists of pile shields to protect the rock core from the displacements due to incident wave stroke. The porous boundary conditions, such as continuity of pressure

The 3D-NDDACP method (nodal-based 3D discontinuous deformation analysis method with contact potential) shows its capability to simulate discontinuous deformation of rock block systems. Due to the adoption of contact potential for contact treatment and Newmark method for time integration, 3D-NDDACP method inherits attractive advantages from both FEM-DEM and discontinuous deformation analysis (DDA) method

Recent growth in the aeronautical and oil industries has increased the demand for efficient repair techniques that offer shorter maintenance periods, greater durability, and reduced costs. Bonded composite repairs have emerged as an excellent solution, enabling the restoration of components without compromising structural integrity. By the first attempt, the coupling of the 3D boundary element method

In this communication, a novel strategy is presented for addressing advection–conduction problems with solid↔liquid phase change by using a modified implementation of the improved element-free Galerkin (IEFG) method. The approach involves a deferred inclusion of non-linear effects related to temperature-dependent material properties and the latent heat exchanged during phase change, incorporated within

In this article, we apply an error estimation technique to assess the numerical error of seven kinds of method of layer potentials for solving the Stokes flow problem governed by the biharmonic equation. The new error estimation technique allows us to estimate numerical errors in situations where analytical solutions are not available. Additionally, it enables us to determine the optimal solution for

To systematically quantify certain uncertainties within the vibro-acoustic coupling problems, we propose a framework for sampling the acceleration and uncertainty quantification based on a Deep Neural Network (DNN). Coupling the Finite Element Method (FEM) and Boundary Element Method (BEM) with Catmull–Clark subdivision surfaces to generate samples for DNN training and testing. Constructing various

The tensile strength of rocks is a critical information in the design of operational blasting and support systems in rock engineering. However, it is important to note that in rock dynamic, the measured tensile strength in the BD test may be higher than the real value due to the overload effect. In this study, the overload effect and dynamic tensile strength correction are investigated by comparing

Pile groups in saturated soils frequently encounter transient dynamic loads from earthquakes, waves, and winds. This study uses the coupled boundary element method-finite element method (BEM-FEM) to investigate the transient interaction between pile groups and layered saturated soils. The analytical layer element solution for the stratified saturated soils is used as the kernel function to establish

The analysis of complex multipatch structures has been solved with numerical tools, however, isogeometric shape optimization has not yet been applicable for designing free-form surface. Benefiting from the key concept of isogeometric analysis (IGA) for integration of design and analysis, a morphogenesis method is presented for shape optimization of complex free-form surfaces, especially built with

Explicit surface reconstruction is useful for treating challenging boundary-related problems in smoothed particle hydrodynamics (SPH), for example, high-accuracy contact treatment. In this work, an efficient local surface reconstruction method (LSRM) is proposed. It first identifies boundary layer particles and then employs the Delaunay triangulation technique to reconstruct explicit surfaces from

The Generalized Interpolation Material Point method (GIMP), based on both material-point discretization and Eulerian space meshing, which is appropriate for nonlinear problems. However, it is difficult to identify physical boundaries and material interfaces, leading to numerical oscillations in the thermal analysis. Therefore, an Element Mapping Material Point method (EMMP) is proposed to handle with

This paper presents a novel simplified approach to achieving smooth boundaries on structural shape optimizations when combining Genetic Algorithms (GA) with the Boundary Element Method (BEM) by applying a simple polynomial fitting technique for boundary smoothing. The methodology focuses on the challenges of reducing material usage while maintaining constructability. The integration of polynomial fitting

Nowadays, adhesively bonded joints are widely used in high-end industries due to their valuable advantages over traditional joining techniques. Nevertheless, predicting the mechanical behaviour of adhesively bonded joints with accuracy and efficiency still represents a major challenge reducing structure weight, material usage, and computational cost. In this work, a fracture propagation algorithm based