This research has been conducted to investigate a numerical solution for the Allen–Cahn equation featuring the generalized fractional time derivative. The finite difference method is employed to discretize the equation in the time variable. Subsequently, an error estimate is derived for the proposed method in Lp,μ,q space. Furthermore, a meshless technique based on radial point interpolation is used

Accurate modeling of basin structures and quantitative analysis of basin amplification effects are critical for seismologists and engineers. The Indirect Boundary Element Method (IBEM), developed from the Boundary Element Method (BEM), is particularly well-suited for these tasks due to its capability to manage layers with lateral inhomogeneities. However, current IBEM studies mostly focus on wavefields

A two-dimensional time domain coupled model is developed to analyze the interaction between fully nonlinear waves and floating bodies over variable topography. The whole calculation domain is divided into an inner domain close to the structure and two outer domains far away from the structure. The fully nonlinear free surface boundary conditions are used in each sub-domain. Irrotational Green-Naghdi

This work presents a new and robust formulation for studying the effect of point heat sources on three-dimensional thermomechanical contact problems. The aim of this work is to accurately analyze heat dissipation in microchips with known heat sources. To achieve this, the Boundary Element Method (BEM) has been used to calculate the thermomechanical influence coefficients. The traditional BEM has been

This study presents a novel volume compensation model for multi-resolution moving particle method simulating free surface flows. The volume-compensation model is developed to conserve volume when simulating free surface flow using multi-resolution particles, a topic that has been rarely discussed for multi-resolution simulations in previous literature. The free surface is reconstructed by a linear

The characterization and understanding of cracking propagation behaviors in non-uniform geological structures are crucial for predicting the mechanical response of rock-like materials under varying loading conditions. In this study, an improved Peridynamics (PD) model with degree of heterogeneity characterized by random pre-breaking "bond" ratio is introduced to capture the intricacies of crack initiation

Although kernel functions play a pivotal role in meshfree approximation, the selection of kernel functions is often experience-based and lacks a theoretical basis. As an attempt to resolve this issue, a rational matching between kernel functions and nodal supports is proposed in this work for Galerkin meshfree methods, where the quadratic through quintic B-spline kernel functions are particularly investigated

In this paper, we propose a numerical formula to calculate time-harmonic electromagnetic field interacting with three-dimensional elastic body. The formula is based on the method of fundamental solutions. Firstly, we perform Helmholtz decomposition on the displacement field. The problem will transform into a coupled bounded problem including a scaler Helmholtz equation, a vector Helmholtz equation

In this paper, a series of novel sphere elements are proposed in the boundary element method (BEM). These elements are designed as isoparametric closure elements to simulate spherical geometries with greater accuracy and fewer nodes than conventional boundary elements. Constructed similarly to multi-dimensional Lagrange elements, these sphere elements utilize trigonometric bases for each dimension

In this paper, a novel spatial-temporal collocation solver is proposed for the solution of 2D and 3D long-time diffusion problems with source terms varying over time. In the present collocation solver, a series of semi-analytical spatial-temporal fundamental solutions are used to approximate the solutions of the time-dependent diffusion equations with only the node discretization of the initial and

The submarine's sail, as the largest appendage structure, is more susceptible to turbulence induced vibrations during medium to high-speed navigation, making it a critical area for the generation of flow-induced noise, significantly impacting the stealth and safety of submarine. Considering the excellent mechanical properties and high damping characteristics of lightweight composite sandwich structures

This study is concerned with rigid-body responses and elastic motion of floating offshore wind turbines (FOWTs) under combined wave, current and wind loads. A numerical approach is developed in frequency domain based on the linear diffraction theory with a Green function for small current speeds and the blade-element momentum method for hydrodynamic and aerodynamic analysis, respectively. This approach

Nanostructures play a vast role in the current Internet of NanoThings (IoNT) era due to remarkable properties and features that precisely impart their desired application functions in catalysis, energy and other fields. The exploration in understanding their minute features caused by the flexibility of compositional and complex atomic arrangement from the synthesis reaction widely opens for the in-depth

Ice-water coupling is a unique fluid-solid interaction problem characterized by collisions and hydrodynamic interaction between multiple bodies, accompanied by significant changes in the free surface. This paper presents a novel numerical model that achieves two-way coupling between the moving particle semi-implicit (MPS) method and the non-smooth discrete element method (NDEM) to simulate ice-water

Piezoelectric materials are extensively used in engineering for the fabrication of sensors, transducers, and actuators. Due to the coupling characteristics, anisotropy, and arbitrariness of polarization directions, the tasks of mesh generation, numerical integration, and global equation formulation involved in numerical computations are complex and nontrivial. To solve electrostatic and electroelastic

In recent years, Physics-Informed Neural Networks (PINN) have emerged as powerful meshless numerical methods for solving partial differential equations (PDEs) in engineering and science, including the field of structural vibration. However, PINN struggles due to the spectral bias when the target PDEs exhibit high-frequency features. In this work, a meshless Runge-Kutta-based PINN (R-KPINN) framework

This study focuses on the numerical simulation of bubble growth in microchannels and addresses the interfacial deformations associated with phase transitions in the Volume of Fluid (VOF) method. In order to avoid the blurred deformation of the interface during bubble growth, a gradient-constrained algorithm is proposed to simulate bubble growth with sharp interface. The algorithm proposed in this paper

This paper introduces an efficient hybrid numerical discretization method designed to address the coupled mechanical challenges of geomechanics and fluid flow during pressure depletion in tight reservoirs. Utilizing the extended finite element method, this approach solves the elastic deformation of rock, while the mixed boundary element method precisely calculates the unsteady fluid exchange between

Recently, deep learning has been tried to improve the efficiency of compressed ghost imaging. However, these current learning-based ghost imaging methods have to modify and retrain the learning model to cope with different sampling ratios. This will consume a lot of computing resources and energy. In this paper, we propose a deep learning-based compressed ghost imaging method that can adapt to arbitrary

An accurate and stable weighted-least-squares multi-physical particle-based (WLS-MPP) hybrid model is developed to simulate the incompressible generalized Newtonian two-phase magnetohydrodynamics (MHD) flows, and then it is extended to predict a bubble rising process in shear-thinning MHD flow with large density difference, for the first time. The development of WLS-MPP hybrid model for two-phase MHD

This paper develops an improved weakly compressible smoothed particle hydrodynamics (SPH) method for simulating multiphase flows with complex interface and large density ratios. Surface tension is computed using a continuum surface force method along with a kernel gradient correction algorithm, thereby improving the numerical precision of normal vectors and curvatures. To maintain a uniform particle

To explore the rockburst proneness of rock materials, coarse-grained granite, red sandstone and white marble were selected for uniaxial compression laboratory tests. Applying the rockburst proneness criterion based on the peak strength strain storage index, numerical models of the three rocks were constructed according to the three-dimensional Clump (3D-Clump) modelling method using the three-dimensional

In this study, a Hybrid Spectral Element Method (HSEM) integrated with Equivalent Static Load (ESL) in the frequency domain is suggested. This integration aims to enhance the computational efficiency of dynamic topology optimization. In comparison with existing techniques, the proposed HSEM transforms the governing equation of dynamic analysis into a spectral element equation within the frequency domain

In the research of explosion shock theory and engineering application, the convergence of detonation waves can be realized by using multiple initiation points to utilize the detonation energy and pressure effectively. To study the propagation process of detonation wave and the distribution law of impact energy of the explosive with multiple initiation points, a detonation calculation model of the explosive

Grouting is a widely used technique in underground engineering by enhancing mechanical properties of jointed rock mass. Understanding the shear characteristics of jointed coal mass after grouting reinforcement is crucial for optimizing grouting parameters and advancing grouting mechanism. This study proposed a grout-filled jointed coal (GJC) direct shear discrete element model (GJCS-DEM). The model

Floating ice can be damaged by the bubble loads generated by releasing high-pressure gas underwater using an air-gun, so ice-breaking by underwater high-pressure bubble loads is becoming one of the effective ice-breaking technologies. A numerical model was established to study the motion and damage of floating ice subjected to high-pressure bubble loads. Empirical formulas were used to calculate the

In this paper, formulations for asymptotic homogenization method based on the boundary element method (BEM) are presented for the estimations for effective parameters of unidirectional fiber reinforced composites in the 2D plane strain case. The boundaries are discretized by shape functions of non-uniform rational B-splines (NURBS) according to the features of isogeometric analysis and the related

The problem of concentrating electromagnetic fields into a nanotube from an ambient source of light, is considered. An isogeometric analysis approach, in a boundary element method setting, is employed to evaluate the local electric field, which is represented with the exact same basis functions used in the geometric representation of the nanotube. Subsequently, shape optimization of the nanotubes is

A novel fundamental solution based finite element method (HFS-FEM) is proposed to analyze heat conduction problem of two-dimensional composite materials. In the proposed method, a linear combination of fundamental solutions at source points is taken as intra-element trial functions to construct the interior temperature field. The required fundamental solution is established by the charge simulation

In this paper, we improve the traditional space-time radial basis function (RBF) collocation method for solving three-dimensional elastodynamic problems. The proposed approach arranges source points outside the entire space-time domain by introducing space and time amplification factors, rather than locating them within the computational domain. Additionally, a multiple-scale technique is developed

A generalization of a recently introduced recursive numerical method (Gumerov et al., 2023) for the exact evaluation of integrals of regular solid harmonics and their normal derivatives over simplex elements in R3 is presented. The original Quadrature to Expansion (Q2X) method (Gumerov et al., 2023) achieves optimal per-element asymptotic complexity for computing O(ps2) integrals of all regular solid

This paper presents a fluid topology optimization method utilizing a quadtree scaled boundary finite element method (SBFEM). The method aims to minimize energy dissipation during fluid flow by employing quadtree mesh refinement in the design domain, integrating both velocity and pressure fields. Finer meshes are used near the fluid-structure interface and coarser meshes elsewhere. By leveraging the

Defect identification is an important issue in structural health monitoring. Herein, originated from inverse techniques, a merging approach is established by the numerical manifold method (NMM) and whale optimization algorithm-back propagation (WOA-BP) cooperative neural network to identify hole defects in heat conduction problems. On the one hand, the NMM can simulate varying hole configurations on

We consider the problem of approximating a linear differential operator on several specific stencils using the radial basis function method in the finite difference scheme. We prove a linear convergence order on a non-equispaced five-point stencil. Then, we discuss how the convergence rate can be boosted up to the second-order on an equispaced stencil. Moreover, we show that including additional nearby

In this article, a new high-order, local meshless technique is presented for numerically solving multi-dimensional Sobolev equation arising from fluid dynamics. In the proposed method, Hermite radial basis function (RBF) interpolation technique is applied to approximate the operators of the model over local stencils. This leads to compact RBF generated finite difference (RBF-FD) formula, which provides

The development of new numerical methods for fluid flow simulations is challenging but such tools may help to understand flow problems better. Here, the Boundary-Domain Integral Method is applied to simulate laminar fluid flow governed by a dimensionless velocity–vorticity formulation of the Navier–Stokes equation. The Reynolds number is chosen in all examples small enough to ensure laminar flow conditions

In this paper, the T-matrix method is applied to investigate the monostatic and bistatic far-field acoustic scattering patterns of underwater elastic multi-obstacles, which is a semi-analytical method and its results can be used to verify the accuracy of various numerical methods. The T-matrix formula for underwater multi-obstacle acoustic scattering is obtained by utilizing the addition theorem of

This study aims to find a solution for crack propagation in 2D brittle elastic material using the local radial basis function collocation method. The staggered solution of the fourth-order phase field and mechanical model is structured with polyharmonic spline shape functions augmented with polynomials. Two benchmark tests are carried out to assess the performance of the method. First, a non-cracked

The present work aims to study the free vibration behaviour of bio-inspired helicoidal laminated composite spherical, toroid, and conical shell panels using a single-output Support Vector Machine (SVM) algorithm trained in the chassis of parabolic shear deformation theory under thermal conditions. Different helicoidal lamination schemes are adopted, such as Fibonacci, semi-circular, exponential, recursive

In this paper, a novel weak-form meshless method, Galerkin Free Element Collocation Method (GFECM), is proposed for the mechanical analysis of thin plates. This method assimilates the benefits of establishing spatial partial derivatives by isoparametric elements and forming coefficient matrices node by node, which makes the calculation more convenient and stable. The pivotal aspect of GFECM is that

Porous structures are extensively used in engineering, and current designs of porous structures are constructed based on linear assumptions. In engineering, deformation cannot be ignored, so it is necessary to consider the effect of geometric nonlinearity in structural design. For the first time, this paper performs the geometrically nonlinear topology optimization of porous structures. This paper

This paper presents a novel and efficient approach for the computation of energy eigenvalues in quantum semiconductor heterostructures. Accurate determination of the electronic states in these heterostructures is crucial for understanding their optical and electronic properties, making it a key challenge in semiconductor physics. The proposed method is based on utilizing series expansions of zero-order

Numerous simulations have shown that Smoothed Finite Element Method (S-FEM) performs better than the standard FEM. However, there is lack of rigorous mathematical proof on such a claim. This task is challenging since there are so many variants of S-FEM and the standard FEM theory in Sobolev space does not work for S-FEM because of the Smoothed Gradient. Another long-standing open problem is to establish

Thermoelastic problems are prevalent in various practical structures, wherein thermal stresses are of considerable concern for product design and analysis. Solving these thermal and thermoelastic problems for intricate geometries and boundary conditions often requires numerical computations. This study develops a node's residual descent method (NRDM) for solving steady-state thermal and thermoelastic

In this paper, a quadratic time interpolation for temperature and a linear time interpolation for fluxes are implemented for the parabolic (time-dependent) fundamental solution-based scheme for solving transient heat transfer problems with sources using the subdomain BEM (boundary element method), which is the main innovation of this paper. The approach described in this work to incorporate the quadratic

In this work, the scaled boundary finite element method (SBFEM) is used to predict the frequency response of an acoustic cavity with a porous layer based on Biot–Allard theory. For the porous material, both the solid and the fluid displacements are considered as the primary variables. Scaled boundary shape functions are used to interpolate the acoustic pressure within the acoustic cavity, and the solid

The spatial Solow model can take into account the geographical interdependence and the spatial organization of economic activities, and offers a better understanding of economic growth. In this work, governing equations of the spatial Solow model were solved by using the Physics Informed Neural Networks (PINNs) method, and both the forward and inverse problems were considered. For the forward problems

Accurate knowledge of the inner wall defect shape of industrial thermal equipment (ITE) plays a crucial role in safety inspections. However, direct observation and measurement are challenging due to the high-temperature environment within ITE. To address this issue, the identification of irregular inner wall defect shape based inverse technology is studied in this work. A novel particle swarm optimization

The present study investigates the thermoelastic response of a heterogeneous piezoelectric sphere under thermal shock loading. Boundary conditions as well as loading are considered as symmetric; thus, the response of the sphere is expected to be symmetric. All of the properties of the thick-walled sphere, including mechanical, electrical and thermal properties, are considered dependent on the radial

For engineering analysis of 3D problems, common difficulty to apply the boundary element method (BEM) is the so called “nearly singular integrals” that arise when the object is thin or the internal points of analysis are close to the boundary. In the present work, the local integration domain is sub-divided into 4 quadrants at the projection of the source point. By use of the FG-Squircular Mapping

The main objective of this paper is to develop effective numerical methods to solve hypersingular integral equations arising in various physical and mechanical applications. Both surface and contour integrals are considered. The novelty of the proposed approach lies in the exact formulas obtained for an arbitrary planar polygon in hypersingular integral estimations. A one-dimensional hypersingular

Robust and reliable numerical models are vital to solve the Richards’ equation, which depicts the variably saturated flows in porous media. In this study, the Richards’ equation is discretized spatially with the numerical manifold method (NMM) and temporally with the backward Euler scheme, in which the under-relaxation and mass lumping techniques are introduced to keep the numerical stability and mass

This paper proposes the Boundary Knot Method with ghost points (BKM-G), which enhances the performance of the BKM for solving 2D (3D) high-order Helmholtz-type partial differential equations in domains with multiple cavities. The BKM-G differs from the conventional BKM by relocating the source points from the boundary collocation nodes to a random region, such as a circle (sphere) encompassing the

We propose an online interactive physics-informed adversarial network (IPIAN) to address mean field games (MFGs) from the perspective of physics-informed interaction. In this study, we model the interaction between agents as a physics-informed exchange process, quantifying the evolution and distribution of individual strategy choices. We utilize the variational dyadic structure of MFGs to transform

Seismic-induced damage, integral to the safety evaluations of major engineering projects, persists as a key focus of research worldwide. Based on the Scaled Boundary Finite Element Method (SBFEM) and the Phase-Field Method (PFM), a coupled algorithm tailored for reciprocal loading was introduced in this paper, integrating strategies including "closure constraints," "numerical threshold strategy," and

The paper establishes the pure boundary integral equations of the isogeometric boundary element method (IGABEM) based on isotropic fundamental solutions to solve three-dimensional (3D) general anisotropic elastic problems including various complex cavities. The residual method is employed which introduces the fictitious body force causing the domain integral. Subsequently, the radial integration method

In the issue of significant prediction deviations in fatigue crack predictions, the parameter uncertainties are usually neglected. To deal with this drawback, this paper proposes a crack growth evaluation method which takes parameter uncertainties into account to predict crack fatigue life. Firstly, the life model of crack growth is established through the combination of extended finite element method

The identification method based on the traditional Proper Orthogonal Decomposition (POD) reduced-order model has the problem of low efficiency, due to the large amount of both data and computation, when dealing with complicated problems with a large number of spatially distributed nodes. To deal with this issue, an improved POD reduced-order model is proposed in this work. The improved POD reduced-order