In the current work, an efficient and powerful computational technique is implemented to simulate an anomalous mobile-immobile solute transport process. The process is mathematically modelled as a time-fractional mobile-immobile diffusion equation in the sense of Riemann-Liouville derivative. Firstly, an implicit time integration procedure is used to semi-discretize the model in the time direction

This paper presents a boundary moving least squares method (BMLS) for solving 3D linear elasticity problems. In the proposed method, moving least squares interpolant is used to construct the 1D shape function employing the boundary discrete points in each axis. Then, the Kronecker product is introduced to generate the tensor product points in the regular region coving the problem domain, which simply

In this paper, the Hermite-type radial point interpolation method (RPIM) is proposed to develop the meshless numerical wave tank (NWT) for simulating the propagation of fully nonlinear water waves. The Hermite-type interpolation scheme, the radial basis functions (RBFs), and the polynomial functions are used to construct shape functions. These shape functions have better stability and can use any distribution

Currently, accurate simulations of fluid structure interaction (FSI) problems still remain a challenging task in the academic community. The purpose of this work is to develop a three-dimensional (3D) coupling algorithm to achieve the end, where the explicit moving particle simulation method (MPS) and the finite element method (FEM) are respectively employed to account for fluid flows and structural

The Radial Point Interpolation Mixed Collocation (RPIMC) method is proposed in this paper for transient analysis of diffusion problems. RPIMC is an efficient purely meshfree method where the solution of the field variable is obtained through collocation. The field function and its gradient are both interpolated (mixed collocation approach) leading to reduced C-continuity requirement compared to strong-form

This article presents an applications of boundary element method (BEM) in engineering to numerically analyse the water percolation velocity inside an earth dam structure from a temperature measurement device inside. This device is known like distributed temperature sensing (DTS) and recent articles points it as a promising system for the safety monitoring of large structures such as gas pipelines,

In this paper, to improve the computational speed of the reproducing kernel particle method (RKPM), the dimension splitting reproducing kernel particle method (DSRKPM) is presented for solving three-dimensional (3D) transient heat conduction problems. The idea of the proposed method is transforming the 3D problem into a series of two-dimensional (2D) ones by using the finite difference method in the

This study presents an eXtended Boundary Element Method (XBEM) formulation for simulating the linear elastic crack growth in two-dimensional domains. A displacement approximation enrichment based on the Williams first-order expansions is used to represent the near-tip square root behavior predicted by the linear elastic fracture mechanics. This strategy also enables the direct evaluation of the Stress

The coupled advection-dominated diffusion-reaction equations which arise in the prevention of groundwater contamination problem are approximated by the compact local integrated radial basis function (CLIRBF) method. To efficiently solve the resulting nonlinear system of advection-diffusion equations, we use the integrated radial basis function (IRBF) for discretizing the spatial variables. Afterwards

In this work, two new techniques of the Boundary Elements Method are coupled for solving eigenvalues in three-dimensional piecewise scalar problems. The Domain Superposition Technique (DST) is used to approach the sectorial homogeneities, modeling the domain as a sum of a homogeneous surrounding sector and other complementary ones with different constitutive properties. The Direct Interpolation Technique

We study accurate and stable approximations for highly oscillatory integrals (HOIs) which are demanding in computational engineering, especially for high frequency. In literature, the Levin method with radial basis functions (RBFs) is considered for better accuracy instead of stability of the algorithm. In this work, we demonstrate an accurate and stable Levin method for a class of RBFs. In addition

The fluid-structure interaction phenomenon is often encountered in the ocean engineering field. In the present work, a non-local numerical model is developed for the simulations of weakly compressible viscous fluid and elastic structure interactions. The peridynamic theory is adopted for both the structure and fluid modelling. The elastic structure is described by using the ordinary state-based peridynamics

In this paper, a coupled FEM-BEM method is applied to simulate the magneto-mechanical behavior of a single-crystalline Ni-Mn-Ga sample. First, based on some kinematic and constitutive assumptions, the governing system for modeling the response of the Ni-Mn-Ga sample is formulated, which is composed of the magnetic and mechanical field equations, the evolution laws of the internal variables and the

This paper presents an axisymmetric boundary element analysis of one-layered transversely isotropic material of halfspace extent with either ellipsoidal or spherical cavity. This analysis uses the fundamental solution of a transversely isotropic bi-material fullspace subject to the body force uniformly concentrated at a circular ring. The finite and infinite boundary elements are, respectively, used

This study improved two parts of the virtual element method (VEM) to ensure that the stability of a stony soil slope, especially under excavation conditions, could be better studied. One of the improvements was the specific realization of the excavation algorithm, including the determination of how to identify polygonal elements that needed to be excavated, and the “deactivate and reactivate polygonal

In this paper, a meshless BEM based on the radial integration method is developed to solve transient non-homogeneous convection-diffusion problem with spatially variable velocity and time-dependent source term. The Green function served as the fundamental solution is adopted to derive the boundary domain integral equation about the normalized field quantity. The two-point backward finite difference

In this paper, the meshless element-free Galerkin method (EFGM) based coupled model is developed to simulate the groundwater flow and multispecies reactive transport coupled with sequential decay reactions in unconfined aquifers. The use of moving least squares (MLS) approximation in approximating the head and concentration variables in EFGM tends to provide the solutions with better numerically stability

We present a new numerical algorithm combining the dual reciprocity method with the dual interpolation boundary face method for solving the two-dimensional Poisson equations. In this new combined approach, the boundary physical variables and particular solutions are approximated by dual interpolation elements which include source and virtual points. Additionally, this algorithm is implemented by employing

A novel efficient technique is presented for the evaluation of domain integrals that appear in the boundary element method (BEM). Herein, the source term is approximated with the use of radial basis functions, as in the dual reciprocity BEM. The proposed technique, called the Kriging Integration Method (KIM), comprises the use of the Simple Kriging Method in non-overlapping patches for obtaining the

This contribution establishes a coupled numerical method to show its effectiveness in the simulation of LEFM problems. The semi-meshless method uses the MLPG1 meshfree theory to discrete governing equations while geometry is modeled by simple CPS3 triangular cells. The cells help to propose an efficient neighboring method for meshfree interpolations. Three benchmark homogeneous cases are considered

The paper is devoted to issues of numerical simulation of free surface elevations in rigid circular cylindrical fluid-filled tanks under external vertical and horizontal loadings with usage boundary element methods. The liquid in reservoirs is assumed to be ideal and incompressible, and its flow is irrotational. The influence of horizontal and vertical baffle installation is considered and damping

The key challenge faced by engineers is how to design a subsea pipeline to ensure that the production fluid is safely and economically transported from the reservoir all the way downstream to the processing plants. Transient thermal analysis is essential for flow assurance design and operating strategies of deepwater subsea pipelines. This work presents a numerical analysis of heat transport in sandwich

In the present paper, a novel computational model of non-uniform eigenstrain formulation of boundary integral equations (BIEs) with corresponding iterative solution procedures is presented for simulating solids with multiple rectangular inhomogeneities in elastic range. The computational model is developed by introducing the concepts of the equivalent inclusion of Eshelby with eigenstrains into BIEs

A Kansa–radial basis function (RBF) collocation method is applied to two–dimensional second and fourth order nonlinear boundary value problems. The solution is approximated by a linear combination of RBFs, each of which is associated with a centre and a different shape parameter. As well as the RBF coefficients in the approximation, these shape parameter values are taken to be among the unknowns. In

In the present work, local radial basis function (RBF) collocation method is used to solve the Stokes problem numerically. Benefits of the local meshless method is its flexibility of handling complex computational domain and interface. Local meshless method produces sparse coefficient matrix, though its structure is depending on the placement of nodes, and type of boundary conditions. The Stokes equations

Smoothed particle hydrodynamics (SPH) is adopted to simulate the peak impact load, the water entry process and the water entry characteristics of a re-entry capsule with the complex capsule motions modelled by a developed six degrees of freedom fluid-solid coupling model. Diffused particle distribution is developed and used in the simulations to decrease memory and computational cost. The results show

In order to solve multi-medium nonlinear transient heat conduction problems, based on interface integration boundary element method, a new approach, which can convert the multi-domain integrals to the boundary integrals with high precision, is firstly proposed in this paper. The boundary element method with the internal and exterior source is used to establish the interface integral equation of the

In this paper, some steady infiltration problems from periodic channels into two-layered soils are considered. The problems are governed by a system of Richards’ equations with boundary interface conditions. To solve the problems, the system of Richards’ equations with respect to some boundary conditions are transformed into a system of steady diffusion-convection equations with respect to transformed

The collocation-based impedance-to-scattering matrix method recently developed in conjunction with the boundary element method (BEM) for large silencer analysis is reformulated by using the reciprocal identity integral. The reciprocal identity integral also forms the foundation of the classical theory of acoustic reciprocity for silencers. Contrary to the conventional wisdom, when the inlet and the

The Contact Theory proposed by Shi in 2015 is expected to solve the contact detection problem of discrete blocks in a perfect and universal manner. In the present paper, a contact detection algorithm for arbitrary polygonal blocks based on the Contact Theory is proposed and coupled into the two-dimensional DDA (2D-DDA). Four different methods to determine the contact entrance lines are presented, and

The numerical solutions of boundary integral equations by the Boundary Element Method (BEM) have been applied in several areas of computational engineering and science such as elasticity and fracture mechanics. The BEM formulations often require the evaluation of complex singular and hypersingular integrals. Therefore, BEM requires special integration schemes for singular elements. The Subtraction

Nonlinear water waves are common physical phenomena in the field of coastal and ocean engineering, which plays a critical role in the investigation of hydrodynamics regarding offshore and deep-water structures. In the present study, a three-dimensional (3D) numerical wave flume (NWF) is constructed to simulate the propagation of nonlinear water waves. On the basis of potential flow theory, the second-order

The recently developed edge-based smoothed finite element method (ES-FEM) is an efficiency method for solving frequency response of structural-acoustic systems with nominally deterministic parameters. In order to further dealing with the unavoidable uncertainties, both the interval perturbation techniques and the subinterval perturbation techniques are introduced and embedded into the hybrid edge-based

We propose a novel approach for two-way coupled simulations of multiphase flows within an Eulerian-Lagrange framework. Lagrangian particles are commonly approximated as point sources of either energy, mass or momentum. To introduce them into the Eulerian computation of the fluid flow, an approximation of the Dirac delta function has to be made. By resorting to the Boundary Element Method (BEM) based

Based on the Erdogan fundamental solutions for infinite cracked plates, a new hybrid boundary node method for linear fracture problems is proposed in this paper. The origin singular intensity factor for the Erdogan fundamental solutions is developed to overcome the singular when the field points are coincided with the source points, and no virtual source points are needed, a new scheme for calculating

A mixed analytical-numerical method is proposed to evaluate the acoustic radiation of a double elastic spherical shell in finite-depth water by combining the analytical method with the numerical Wave Based Method (WBM) [or Wave Superposition Method, WSM]. The effects of reflection from both the free surface and the seabed are considered. The correctness of this method is verified through several numerical

The current paper describes a rapid and impressive numerical technique to simulate the flows with multiple phases and components based upon the Shan-Chen model. The Shan-Chen model is a generalization of the incompressible Navier-Stokes equation with the variable density. The local radial basis function-generated finite difference method or local RBF-FD approach has been developed to solve the considered

In this paper, a localized meshless collocation method, the generalized finite difference method (GFDM), is first applied to calculate the bandgaps of anti-plane transverse elastic waves in 2D solid phononic crystals with square and triangular lattice. The corresponding theoretical consistency analysis of the GFDM is given. The universal algorithm for the uniform/scattered node generation in the GFDM

A boundary element method (BEM) for the solution of lubrication problems on finite bearings is presented. The formulation requires the Reynolds equation to be transformed into a constant coefficient equation. Several film shapes that make the transformation possible are systematically obtained. Noticeably, they cover most practical cases. As an example of application, a numerical solution that only

Finite element-least squares point interpolation method (FE-LSPIM) developed recently shows some excellent features to improve the calculation accuracy of mechanical problems. In this paper, a coupled finite element-least squares point interpolation method/ boundary element method (FE-LSPIM/BEM) is proposed to analyze plate-like structural-acoustic coupled system. Here, the FE-LSPIM is used to model

Consider a two dimensional steady low Reynolds number flow past a circular cylinder. A boundary integral representation that matches an outer Oseen flow and inner Stokes flow is given, and the matching error is shown to be smallest when the outer domain is as close as possible to the body. Also, it is shown that as the Greenâs function is approached, the oseenlet becomes the stokeslet to leading order

In this study, a symmetric method of approximate particular solutions (MAPS) is proposed for solving certain partial differential equations (PDEs). Inspired by the unsymmetric MAPS and symmetric radial basis function collocation method (RBFCM), the symmetric MAPS is developed by using the bi-particular solutions of the multiquadrics (MQ). Similar to the unsymmetric MAPS, the right-hand-side of the

The augmented moving least squares (AMLS) approximation is a meshless scheme to construct continuous functions by using fundamental solutions as basis functions. By incorporating the AMLS approximation into the method of fundamental solutions (MFS), the localized MFS can significantly reduce the computational load and accelerate the solution progress of the MFS. In this paper, error estimates of the

An equivalent linear BEM-FEM model for the approximate analysis of the time harmonic lateral response of piles considering soil degradation along the soil-pile interface is proposed. The non-degraded soil around the foundation is modelled with boundary elements as a continuum, semi-infinite, isotropic, homogeneous or zoned homogeneous, linear, viscoelastic medium. Piles are modelled with finite elements

The paper takes advantage of the digital images exported from the digital visualization models of geotechnical engineering and the meshless method based on Shepard function and Partition of Unity (MSPU) to develop a new solution for the automatic digital-numerical integrated analysis. The proposed method fully utilizes the information of pixels to substitute geometric models with digital images, which

In this paper, a novel space-time generalized finite difference method (GFDM) is proposed for solving transient heat conduction problems by integrating a direct space-time discretization technique into the meshless GFDM. The spatial and temporal dimensions are simultaneously discretized by randomly distributed nodes in the coupled space-time continuum. Transient heat conduction in homogenous and heterogeneous

A full coupled multi-scale modelling using the Boundary Element Method for analysing the 2D problem of stretched plates composed of heterogeneous materials, where dissipative phenomena can be considered, is presented. Both the macro-scale and the micro-scale are modelled by BEM formulations where the consistent tangent operator (CTO) is used to achieve the equilibrium of the iterative procedures. The

This paper proposes the topology optimization for steady-state heat conduction structures by incorporating the meshless-based generalized finite difference method (GFDM) and the solid isotropic microstructures with penalization interpolation model. In the meshless GFDM numerical scheme, the explicit formulae of the partial differential equation are expressed by the Taylor series expansions and the

The main aim of this study is presenting a semi-discretization scheme to find the numerical solution of two dimensional (2D) stochastic time fractional diffusion-wave equation, which obtains from classical 2D diffusion-wave equation by replacing integer time derivative with Caputo fractional time derivative of order α (1 < α ≤ 2) and inserting some stochastic factors. In this scheme, first Crank-Nicolson

In this paper both of the elastic-viscoelastic correspondence principle and time stepping method, which can convert viscoelasticity to elasticity, are employed to the boundary element method (BEM) to solve the contact problems between multiple rigid punches and anisotropic viscoelastic foundation. The one based upon the correspondence principle has the restriction on time-invariant boundaries, and

An easy implemented and effective pure meshfree method is first developed to solve the 1D/2D constant/variable-order time fractional convection-diffusion equation (TF-CDE) on non-regular domain with two boundary conditions in this paper. The proposed method (CSPH-FDM) is derived from that the finite difference scheme (FDM) for Caputo time fractional derivative and a corrected smoothed particle hydrodynamics

In this paper we present an approach which predicts directly without search the optimal choice of the shape parameter c contained in the multiquadrics (−1)⌈β2⌉(c2+∥x∥2)β2,β>0, and the inverse multiquadrics (c2+∥x∥2)β2,β<0. Unlike the simplex scheme where the data points are required to be evenly spaced, as in a recent paper of the author, here we allow them to be arbitrarily scattered in the simplex

A new nested complex source beam (NCSB) method based on the volume-surface integral equation (VSIE) is proposed for fast electromagnetic scattering analysis of composite conducting-dielectric objects. This scheme is based on the nested equivalent structure of the complex source beams to approximate the far-field interactions of both the RWG basis functions and SWG basis functions with an acceptable

This work presents a novel formulation of the Boundary Element Method (BEM) with the Radial Integration Method (RIM) to calculate the critical loads of the plate buckling problem with shear deformation. An alternative formulation is adopted where the effect of the geometric non-linearity is described by using the first derivative of the function for the out-of-plane displacements. The RIM is developed

In this paper, we develop a meshless method by using radial basis functions (RBFs) to solve time domain Maxwell’s equations resulting from simulating wave propagation in electromagnetic wave splitter and rotator devices. To simulate wave propagation in these devices, we introduce a perfectly matched layer (PML) to reduce the unbounded physical domain problem to a bounded domain problem. Using PML leads

We present a B-spline based semi-analytical technique for solving 2D convection-diffusion-reaction equations. The main feature of the presented technique is to separate the satisfaction of the conditions on the boundary and the elliptic partial differential equation inside. To be more precise, we transform the original equation into the problem with homogeneous boundary conditions and seek the approximate

In the paper, an inverse source problem for a 2D nonlinear elliptic partial differential equation is considered. With the over-specified boundary data given on two sides of a rectangle, we do not need the data on bottom and top sides to estimate an unknown 2D source function. As a consequence, we encounter a quite difficult inverse problem for solving the inverse source problem in an environment of

The meshless local technique is employed to simulate potential problems involving material anisotropy and also plane elastostatic equations of anisotropic functionally graded materials (PEE-AFGM). We utilize direct meshless local Petrov Galerkin (DMLPG) technique to discrete the spatial directions. The DMLPG5 (based on weak form) is applied to solve potential problems involving material anisotropy

Wave scattering of plane waves by irregularities in a transversely isotropic (TI) saturated half-space has been rarely studied. Based on Biot's theory, this paper used an indirect boundary element method (IBEM) to solve the two-dimensional (2D) wave scattering of incident plane qP1- and qSV-waves by irregularities in a layered TI saturated half-space. 2D dynamic Green's functions for uniformly distributed

In this paper, three meshless methods are proposed to solve boundary value problems. The special purpose Trefftz function method, the method of fundamental solutions and the symmetry method of fundamental solutions are compared. We considered six numerical examples for harmonic and biharmonic problems as a flow through the cylindrical fibers arranged in a regular square array, deflection of a uniformly