This study introduces a high accuracy and noise-robust numerical method, that is, the regularization B-spline wavelet method (RBSWM), for solving the inverse boundary problem of the Laplace equation with noisy data in an irregular domain. The problem that we consider is directly discretized by the B-spline wavelet scaling functions. To obtain a stable numerical solution of the problem for noisy data

In this paper, we propose a robust framework based on the scaled boundary finite element method to model implicit interfaces in two-dimensional differential equations in nonhomegeneous media. The salient features of the proposed work are: (a) interfaces can be implicitly defined and need not conform to the background mesh; (b) Dirichlet boundary conditions can be imposed directly along the interface;

The acoustic transfer function is a well-known concept for efficient computations of acoustic analysis with various boundary conditions and sound sources. It is first proposed to accelerate the boundary element analysis by interpolating instead of directly assembling influence matrices. To further improve its computational efficiency, a new frequency-interpolation algorithm is proposed by incorporating

This paper introduces the inclusion based boundary element method (iBEM) to calculate the elastic fields and effective modulus of a composite containing particles for both three dimensional (3D) and two dimensional (2D) cases. Considering a finite bounded domain containing many inclusions, the isotropic Green’s function has been used to obtain the elastic field caused by source fields on inclusion

This paper investigates the use of the localized method of fundamental solutions (LMFS) for the numerical solution of general transient convection-diffusion-reaction equation in both two-(2D) and three-dimensional (3D) materials. The method is developed as a generalization of the author's earlier work on Laplace's equation to transient convection-diffusion-reaction equation. The popular Crank-Nicolson

Based on Lagrange interpolation polynomials, the penny-shaped cracks placed on but not limited to flat surface are simulated with a single high order smooth boundary element in the present work. By taking advantage of geometrical features of circular shape such as the symmetry and periodicity, the smoothness within the element is realized by repeated use of real nodes for interpolation in both the

The isogeometric analysis boundary element method (IGABEM) has great potential in the simulation of heat conduction problems due to its exact geometric representation and good approximation properties. In this paper, the radial integration IGABEM (RI-IGABEM) is proposed to solve isotropic heat conduction problems in inhomogeneous media with heat source. Similar to traditional BEM, the domain integrals

In this paper, the exhaustive usage and implementation of Streamline-Upwind/Petrov-Galerkin method combining with Stabilized Pressure Gradient Projection (SUPG/SPGP) for incompressible Navier-Stokes equations are investigated. We validate and explore the behavior of cell-based smoothed finite element method (CS-FEM) and finite element method (FEM) based on SUPG/SPGP on five numerical examples. First

Hybrid-Trefftz finite elements are well suited for modeling the response of materials under highly transient loading. Their approximation bases are built using functions that satisfy exactly the differential equations governing the problem. This option embeds relevant physical information into the approximation basis and removes the well-known sensitivity of the conventional finite elements to high

In this paper, we derive analytical time-dependent Green's functions in a two-dimensional, anisotropic elastic, and infinite solid. It is based on the Stroh formalism combined with application of the Cauchy's residue theorem. Final expressions of the Green's function are in terms of simple finite line integral from 0 to 2π. The time-dependence of the line forces can be impulsive, Heaviside, or within

In this paper, we characterize the logarithmic singularities arising in the method of moments from the Green’s function in integrals over the test domain, and we use two approaches for designing geometrically symmetric quadrature rules to integrate these singular integrands. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy

In this study a formulation based on the meshless method is developed to study the dynamic behavior of 2D-functionally graded nanobeams. The First order shear deformation theory is employed to model the behavior of the functionally graded beam and the small size effect is considered by employing the nonlocal theory of elasticity. The material properties are functionally graded both in the thickness

Frank Rizzo was a pioneer in what he called boundary integral equation methods. With his students and colleagues, he developed theory and algorithms for many problems of engineering interest. In this memorial paper, we review his life and work. A list of his publications is included.

This study presents a combined shape and topology optimization method for designing sound barriers by using the isogeometric boundary element method. The objective function of combined optimization is defined as the sound pressure in reference plane. The sensitivity analysis for the combined optimization is conducted by using either the direct differentiation method or the adjoint variable method.

Radiofrequency ablation (RFA) is a minimally invasive therapy widely used for the treatment of tumours. Mathematical modelling of RFA allows medical practitioners to understand the involved electro-thermal transport, thereby helping to improve the effectiveness of prescribed treatments. To this end, we aimed to deduce and numerically prove an analytical transient-time solution for temperature due to

This paper simulates the three-dimensional transient heat diffusion conduction in a solid medium containing multi-layered cylindrical circular heterogeneities using a coupling formulation between the boundary element method (BEM) and analytical solutions. The analytical solutions are incorporated as Green's functions, thereby making the discretization of the interfaces of the multi-layered system unnecessary;

As a numerical method based on the Galerkin variation, the numerical manifold method (NMM) adopts a dual covering system, which is convenient for constructing high-order manifold elements and performing adaptive analysis. In this paper, the NMM is used to simulate the electromagnetic response based on the structure of the undulating terrain existing in actual geophysical exploration. The relevant system

This paper provides an indirect boundary element method (IBEM) to elaborate elastic wave propagation in a layered anisotropic medium (simplified as transversely isotropic, TI) with three-dimensional (3-D) irregular free surfaces. The present method using a modified dynamic Green's function for point loads acting on an internal inclined plane as its kernel function, which has the merits of handling

Simulating the response of piezoelectric devices requires solving the coupled mechanical and electrical partial differential equations. This short communication documents the first attempt to apply the meshless generalized finite difference method (GFDM) for the electroelastic analysis of piezoelectric structures. In the present method, the entire computational domain is represented by a cloud of scattered

This paper presents a review of recent progress made towards the applications of the meshfree particle methods (MPMs) for solving coupled fluid-structure interaction (FSI) problems. Meshfree methods are categorized based on their mathematical formulation and treatment of computational data points. The advantages and limitations of these methods, particularly related to FSI applications, have been identified

This paper presents an EHD model for SPH based on a charge-conservative approach. Compared with the leaky dielectric model, the EHD model used in this paper was charge conserved, since no term in the charge conservation equation was neglected. An implicit SPH formula for calculating the electric potential from the electrical properties of the previous time step was constructed, based on the electric

In this paper we derive the discretization of the nonlinear Monge-Ampère equation by means of the explicit formulae of the meshless Generalized Finite Difference Method (GFDM) in both two and three dimensional settings (2D and 3D). To do so we implement the Cascadic iterative algorithm. We provide a rigorous proof of the consistency of the GFDM for this elliptic equation and present several examples

According to the complex flow dynamics of droplets impacting on the wall, an integrated smoothed particle hydrodynamics (SPH) method is developed by a series of improved techniques including artificial viscosity, kernel gradient correction (KGC) technique, boundary treatment and so on, combined with the surface tension based on the continuous surface force (CSF) model in this paper. This method is

This study presents a coupling formulation for the mechanical modelling of nonhomogeneous reinforced 3D structural systems. The coupling of dissimilar reinforced materials and components provides efficient designs. Particularly, it enables high stiffness and low weight mechanical components, which are largely desired in several engineering applications. In the present study, the Boundary Element Method

The interface problems are faced with multiple connected domains and consequently, their solutions or derivatives might be discontinuous. This paper proposes the use of collocation based radial basis function partition of unity method (RBF-PUM) for solving two-dimensional elliptic interface problems. The RBF-PUM is a local method that allows overcoming the high computational cost associated with the

To solve various problems in complicated and concave domains by the method of fundamental solutions (MFS), it is required to consider a large number of source and collocation points that increases the computational time of the analysis. This paper suggests a modification to the MFS, which can make it more efficient and reliable for solving applied problems in complicated domains. In the proposed method

The goals of this paper are twofold: selection of pseudo-boundaries for sources nodes in the method of fundamental solutions (MFS), and comparisons of the MFS, the method of particular solutions (MPS) and the MFS-QR of Antunes. To pursue better pseudo-boundaries, we provide new estimates of the condition number (Cond) by the MFS for arbitrary pseudo-boundaries, and propose a new sensitivity index of

In this paper, a new and efficient Dual Boundary Element Method (DBEM) named Dual Boundary-Interface Integral Equation Method (DBIIEM) is presented to solve crack problems in objects composed of arbitrary number of different materials. The conventional DBEM has been widely used in crack analysis and proved to be one of the most effective BEM for solving crack problems, however it cannot be directly

A novel coupled hydro-mechanical non-ordinary state-based peridynamics is proposed to investigate hydro-mechanical problems in fissured porous rocks. The hydraulic bond is introduced to the coupled numerical model to transfer the water flow stored in material points. The flow equations for fissured porous rocks are obtained in the framework of peridynamics. Then, the relationship between peridynamic

When using boundary element analysis for thin walled structures, to ensure the computational accuracy, special considerations on the singular and nearly singular integrals are indispensible. The real issue about the singular and nearly singular integrals is how to remove the near singularity (for singular and nearly singular integrals) and singularity (for singular integrals only). The near singularity

The method of fundamental solutions (MFS) is very effective for analysis of problems with moving domain loads. In this work, the MFS is formulated for solution of two dimensional transient uncoupled thermoelastic problems involving moving point heat sources. At first, the time-dependent temperature field is obtained by solving the transient heat conduction equation involving a moving heat source term

Grouting is a commonly used technique in rock engineering to enhance the joint strength and improve the stability of surrounding rock. Grout penetration characteristic is controlled by grouting parameters and has a significant role on practice. In the study, a numerical manifold method (NMM) for grout penetration process simulation in fractured rock mass is firstly proposed. The fluid flow behaviour

In this research, based on three-dimensional (3D) time domain hybrid Green function method, the time-domain nonlinear initial boundary value problem of a ship motion in waves with forward speed is solved. The 3D Rankine source and 3D time domain free surface Green function are adopted to solve flow fields of the inner and the outer domains respectively. Meantime, the instantaneous wet surface during

Micropolar elasticity belongs to the class of so-called multi-fields problems. The numerical solution of the associated field equations by the pure boundary element method (BEM) is available only for some 2D geometries. A judicious combination of the local point interpolation method with the pure BEM leads to a pure BEM solution procedure of 3D problems. The effectiveness of the approach is demonstrated

Electromagnetic wave scattering from a Perfect Electric Conductor (PEC) strip located at the interface of dielectric-Topological Insulator (TI) medium by using Kobayashi Potential (KP) method for Transverse Magnetic (TM) and Transverse Electric (TE) polarization is represented and discussed. Initially, diffracted fields equations are expressed by integral equations terms that contain unknown weighting

This paper deals with the boundary element (BE) approach to modelling of transcranial electric stimulation as an alternative to the widely used finite element method (FEM). The advantages of the BE approach are listed in the paper and demonstrated on a computational example. The formulation is based on the quasi-static approximation of currents and voltages induced in living tissues while the head

A plane stress model of bond-based Cosserat peridynamics is proposed, of which the constitutive equations of Cosserat continuum are implemented. The rotation of the proposed bond-based Cosserat peridynamic model is independent with the translational displacement, and the couple stress is considered in the material points’ interaction. The proposed model can degenerate into bond-based peridynamics and

The main objective of the current work is to enhance consistency and capabilities of Moving Particle Semi-implicit (MPS) method for simulating a wide range of free-surface flows and convection heat transfer. For this purpose, two novel high-order gradient and Laplacian operators are derived from the Taylor series expansion and are applied for the discretization of governing equations. Furthermore,

Due to extensive applications in engineering practice, analysis of heat transfer in three-dimensional anisotropic composites has remained to be an important research topic. For the analysis, conventional numerical methods face modeling difficulties to different degrees when the thickness of component is very small. For this, modeling thin adhesive/interstitial media is usually ignored in conventional

In this study, we propose a novel approach based on the dual reciprocity boundary element method (DRBEM) to approximate the solutions of various Steklov eigenvalue problems. The method consists in weighting the governing differential equation with the fundamental solutions of the Laplace equation where the definition of interior nodes is not necessary for the solution on the boundary. DRBEM constitutes

When undertaking a numerical solution of Helmholtz problems using the Boundary Element Method (BEM) it is common to employ low-order Lagrange polynomials, or more recently Non-Uniform Rational B-Splines (NURBS), as basis functions. A popular alternative for high frequency problems is to use an enriched basis, such as the plane wave basis used in the Partition of Unity Boundary Element Method (PUBEM)

An isogeometric boundary element method (IGABEM) is proposed for solving the steady-state heat transfer problems with concentrated/surface internal heat sources. The isogeometric boundary element method (IGABEM) possesses the advantages of both the isogeometric analysis (IGA) and the boundary element method (BEM), the non-uniform rational B-spline (NURBS) basis functions used in the (computer-aided

This paper presents applications of boundary element method (BEM) in engineering to numerically analyse the Telegraph equation in two dimensions for two cases. For this purpose, the mathematical model developed is called D-BEM, uses a time independent fundamental solution and the Finite Difference Method is combined to BEM to approximate the derivative time terms and the Gauss Quadrature is used for

The gravity wave interaction with horizontally staggered multiple thin wavy porous barriers is analyzed under the assumption of potential flow theory. The dual boundary element method (DBEM) is used to solve the boundary value problem. The accuracy and reliability of the DBEM solutions are ascertained by comparing with known results in the literature and with an independently developed multi-domain

A novel fast algorithm is proposed to analyze the EM scattering from electrically large conducting targets with varying geometrical shapes. Firstly, the target surface can be constructed with several control points by using the non-uniform rational B-spline surface modeling method. More specifically, the surface integral equation can be rewritten in terms of these control points, which contains the

Taylor Expansion Boundary Element Method(TEBEM) is an accurate numerical scheme for solving waves and floating bodies related potential problems, especially the induced velocity at the sharp corner. However, the TEBEM method introduces too many unknowns, resulting in a decrease in the computational efficiency. In this paper, a less time consuming method with similar numerical accuracy named Partial

Flexoelectricity is an electromechanical coupling occurring in dielectric materials that has recently attracted significant attention. The flexoelectric effect is described by a coupled, higher-order electromechanical set of equations that have typically been solved using a computationally expensive monolithic formulation. In the present work, we propose a staggered, explicit-implicit formulation that

Numerical results for polynomial (p-version) refinement in the three-dimensional boundary element method are presented. Results are based on a weakly singular form of the gradient boundary element formulation in potential theory. The weakly singular formulation facilitates direct application of numerical quadrature, completely removing the need for closed-form integration. The new results, which include

A fully coupled dynamic model is presented in this paper by considering the effect of matric suction, varying parameters in connection with saturation, stratification and transverse isotropy. This model can describe separate flows of two immiscible fluids in layered transversely isotropic unsaturated poroelastic media subjected to harmonically dynamic loads. The ordinary differential matrix equations

Based on the coupled oscillatory characteristic of mode-1 and mode-2 near the interface crack tip, one kind of element for the relative displacements of the upper and lower surfaces of the axisymmetric interface crack is constructed. A universal numerical method for solving hypersingular integral equations of axisymmetric interface circular crack is established. For arbitrary normal and shear axisymmetric

Meshfree methods were introduced twenty-five years ago to overcome a range of issues faced by mesh-based methods, which predominately relate to the issues of mesh-entanglement, which can result in poor accuracy. Although meshfree methods have progressed significantly over these years, the application of these techniques to real-world material forming problems is limited, despite the potential benefits

An efficient localized collocation meshless computational approach is applied to the study of transdermal drug delivery (TDD). To validate the numerical technique, a one-dimensional analytical solution is first derived for the set of coupled differential equations that govern the pharmacokinetic process in the two-compartment compound diffusion model. These equations consist of one partial differential

In this paper, we present a new numerical algorithm combining the dual interpolation boundary face method (DiBFM) with the precise integration method for solving the 2D transient heat conduction problem. In this new combined approach, the transient heat conduction problem is transformed from an initial boundary value problem to an initial value problem through a dual interpolation boundary face approach

In this paper, an assessment of the accuracy performance of a new fundamental solution based element is carried out. Dynamic analysis of shear-deformable plate bending problems is considered. The element stiffness matrix is obtained by modified hybrid displacement variational statement. The mass matrix is computed using the relevant element shape functions. Free and forced vibrations are considered

The dual interpolation boundary face method (DiBFM) proposed recently has been successfully applied to solve various problems in two dimensions. Compared with the conventional boundary element method (BEM), it has been proved that the DiBFM has the advantages of higher accuracy, convergence rate and computational efficiency. In addition, the DiBFM is suitable to unify the conforming and nonconforming

A collocation method with space–time radial polynomials for solving two–dimensional inverse heat conduction problems (IHCPs) is presented. The space–time radial polynomial series function is developed for spatial and temporal discretization of the government equation within the space–time domain. Because boundary and initial data are assigned on the space–time boundaries, the numerical solution of

This work presents a boundary element method formulation for the solution of the anomalous diffusion problem. By keeping the fractional time derivative as it appears in the governing differential equation of the problem, and by employing a Weighted Residuals Method approach with the steady state fundamental solution for anisotropic media playing the role of the weighting function, one obtains the boundary

In this paper, a three-dimensional modified boundary element method (BEM) is proposed to solve the guided wave scattering problem by cavity-type flaws in an infinite plate. The aim of modification is to correct the artificial scattering introduced by inevitable modal truncation at far-field in the traditional BEM model. The far-field wave displacement fields beyond the BEM model are assumed to be the

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