**Engineering Analysis with Boundary Elements**[3 followers] Follow

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*It can contain Open Access articles*)

ISSN (Print) 0955-7997

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**Elsevier**[2556 journals] [SJR: 1.22] [H-I: 39]

**A new BE formulation coupled to the FEM for simulating vertical pile**

groups**Abstract:**Publication date: April 2014

Source:Engineering Analysis with Boundary Elements, Volume 41

Author(s): Dimas Betioli Ribeiro , João Batista de Paiva

The aim of this work is to obtain a numerical tool for pile–soil interaction analysis. The soil is modeled as an infinite domain in radial directions. The piles, considered cylindrical, are modeled with the finite element method (FEM), using one-dimensional elements. Displacements and tractions along the shaft are approximated by polynomial functions. The soil is modeled using the boundary element method (BEM) with Kelvin fundamental solutions. Infinite boundary elements (IBEs) are employed for the far field simulation, allowing computational cost reduction without compromising the accuracy. The IBE formulation is based on a triangular boundary element with linear shape functions instead of the commonly used quadrilateral IBEs. By coupling the FEM–BEM formulations, a single system of equations which represents the complete pile–soil interaction problem is obtained.

**PubDate:**2014-01-24T01:34:18Z

**An improved element-free Galerkin method for numerical modeling of the**

biological population problems**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): L.W. Zhang , Y.J. Deng , K.M. Liew

A numerical study is performed for degenerate parabolic equations arising from the spatial diffusion of biological populations based on the improved element-free Galerkin (IEFG) method. Using the IEFG technique, a discrete equation system for the biological problem is derived via the Galerkin procedure, and the penalty method is employed to impose the essential boundary conditions. In this study, the applicability of the IEFG method for biological population problems is examined through a number of numerical examples. In general, the initial and boundary conditions of the biological population problems are time dependent; therefore, it is necessary to carry out convergence studies by varying the number of nodes and time steps in order to establish the convergent solutions. The IEFG solutions obtained for the examples are compared with the results reported in the extant literature and they found to be in close agreement.

**PubDate:**2014-01-24T01:34:18Z

**An Approach Based on Generalized Functions to Regularize Divergent**

Integrals**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): V.V. Zozulya

This article addresses weakly singular, hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used for 3-D potential theory problem solutions. An approach based on the theory of distributions and the application of the second Green theorem has been explored for the calculation of such divergent integrals. The divergent integrals have been transformed to a form that allows easy and uniform calculation of weakly singular and hypersingular integrals. For flat boundary elements (BE), piecewise constants and piecewise linear approximations, only regular integrals over the contour of the BE have to be evaluated. Furthermore, all calculations can be done analytically, so no numerical integration is required. In the case of 3-D, rectangular and triangular BE have been considered. The behavior of divergent integrals has been studied in the context that the collocation point moves to the contour of the BE.

**PubDate:**2014-01-24T01:34:18Z

**BEM numerical simulation of coupled heat and moisture flow through a**

porous solid**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): L. Škerget , A. Tadeu

The problem of unsteady coupled moisture and heat energy transport through a porous solid is studied numerically using singular boundary integral representation of the governing equations. The integral equations are discretized using mixed-boundary elements and a multidomain method also known as the macro-elements technique. Two discretization models over time are presented, i.e. constant and linear interpolation in time. Numerical simulations were performed for the benchmark problems of moisture uptake within a semi-infinite region and for the drying out of a layer. Non-uniform grids of increasing mesh density were employed to ensure accurate solutions. Satisfactory agreement is obtained with benchmark results, especially when using the linear in time numerical model.

**PubDate:**2014-01-12T01:34:28Z

**A cell-based smoothed radial point interpolation method (CS-RPIM) for heat**

transfer analysis**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): X.Y. Cui , S.Z. Feng , G.Y. Li

A cell-based smoothed radial point interpolation method (CS-RPIM) is further extended to solve 2D and 3D heat transfer problems. For this method, the problem domain is first discretized using triangular elements or tetrahedral elements, and each element is further divided into several smoothing cells. Then, the field functions are approximated using RPIM shape functions. Finally, the CS-RPIM utilizes the smoothed Galerkin weak form to obtain the discretized system equations in these smoothing cells. Several numerical examples with different kinds of boundary conditions are investigated to verify the validity of the present method. It has been found that the CS-RPIM can achieve better accuracy and higher convergence rate, when dealing with the 2D and 3D heat transfer analysis.

**PubDate:**2014-01-12T01:34:28Z

**Numerical computation for backward time-fractional diffusion equation****Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): F.F. Dou , Y.C. Hon

Based on kernel-based approximation technique, we devise in this paper an efficient and accurate numerical scheme for solving a backward problem of time-fractional diffusion equation (BTFDE). The kernels used in the approximation are the fundamental solutions of the time-fractional diffusion equation which can be expressed in terms of the M-Wright functions. To stably and accurately solve the resultant highly ill-conditioned system of equations, we successfully combine the standard Tikhonov regularization technique and the L-curve method to obtain an optimal choice of the regularization parameter and the location of source points. Several 1D and 2D numerical examples are constructed to demonstrate the superior accuracy and efficiency of the proposed method for solving both the classical backward heat conduction problem (BHCP) and the BTFDE.

**PubDate:**2014-01-12T01:34:28Z

**The method of approximate particular solutions for solving anisotropic**

elliptic problems**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): Huiqing Zhu

In this paper, we study the method of approximate particular solutions for solving anisotropic elliptic-type problems. A special norm associated with the anisotropic differential operator is introduced for the design of anisotropic radial basis functions. Particular solutions of anisotropic radial basis function can be found by the same procedure as that of regular radial basis functions under Laplace operator. Consequently, the method of approximate particular solutions can be extended to anisotropic elliptic-type problems. Numerical results are presented for a number of two-dimensional anisotropic diffusion problems. It shows that this method permits the choice of collocation points independent of the magnitude of anisotropy.

**PubDate:**2014-01-08T01:34:36Z

**Stable numerical solution to a Cauchy problem for a time fractional**

diffusion equation**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): T. Wei , Z.Q. Zhang

In this paper, we consider a Cauchy problem of one-dimensional time fractional diffusion equation for determining the Cauchy data at x=1 from the Cauchy data at x=0. Based on the separation of variables and Duhamel's principle, we transform the Cauchy problem into a first kind Volterra integral equation with the Neumann data as an unknown function and then show the ill-posedness of problem. Further, we use a boundary element method combined with a generalized Tikhonov regularization to solve the first kind integral equation. The generalized cross validation choice rule is applied to find a suitable regularization parameter. Three numerical examples are provided to show the effectiveness and robustness of the proposed method.

**PubDate:**2014-01-08T01:34:36Z

**Editorial Board****Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

**PubDate:**2014-01-08T01:34:36Z

**The equal spacing of N points on a sphere with application to**

partition-of-unity wave diffraction problems**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): M.J. Peake , J. Trevelyan , G. Coates

This paper addresses applications involving the selection of a set of points on a sphere, in which the uniformity of spacing can be of importance in enhancing the computational performance and/or the accuracy of some simulation. For the authors, the motivation for this work arises from the need to specify wave directions in a partition-of-unity approach for numerical analysis of wave diffraction problems. A new spacing method is presented, based on a physical analogy in which an arbitrary number of charged particles are held in static equilibrium on a spherical surface. The new method, referred to in this paper as the Coulomb force method, offers an improvement over simpler methods, e.g., latitude/longitude and discretised cube methods, in terms of both the uniformity of spacing and the arbitrary nature of the number of points N that can be considered. A simple extension to the algorithm allows points to be biased towards a direction of choice. Numerical results of a wave scattering problem solved with a partition-of-unity boundary element method demonstrate the benefits of the algorithm.

**PubDate:**2014-01-04T01:34:16Z

**Crack-tip amplification and shielding by micro-cracks in piezoelectric**

solids – Part II: Dynamic case**Abstract:**Publication date: Available online 2 January 2014

Source:Engineering Analysis with Boundary Elements

Author(s): Jun Lei , Chuanzeng Zhang , Felipe Garcia-Sanchez

The crack-tip dynamic amplification and shielding by micro-cracks in an unbounded, two-dimensional, homogeneous and linear piezoelectric solid are studied in this paper using a time-domain boundary element method (BEM). The BEM is based on the time-domain hypersingular traction boundary integral equations (BIEs). A quadrature formula for the temporal discretization is adopted to approximate the convolution integrals and a collocation method for the spatial discretization. Quadratic quarter-point elements are implemented at all crack-tips. A novel definition of the dynamic amplification ratios of the dynamic field intensity factors and the mechanical strain or electrical energy release rate is introduced. Then the influences of various loading conditions, the location and orientation of the micro-cracks on the dynamic amplification ratios are investigated. Compared with the corresponding static amplification ratios as presented in Part I, some interesting and useful findings are presented together with a simple method which is very feasible for engineering applications.

**PubDate:**2014-01-04T01:34:16Z

**Investigation of finite/infinite unidirectional elastic phononic plates by**

BEM**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): Haifeng Gao , Toshiro Matsumoto , Toru Takahashi , Hiroshi Isakari

The investigation of finite/infinite unidirectional elastic phononic plates is carried out by using the boundary element method (BEM). The transmissions of elastic waves in finite structures are calculated by solving a size-reduced system matrix, in which the transfer matrix formulated by BEM is used repeatedly and the unknown quantities on the free boundaries of cells are removed. For the infinite structures, the Bloch theorem is applied to the unit cell that has traction free boundaries, and the dispersion relation is plotted by extracting the eigenfrequencies of the nonlinear Bloch eigenvalue problem using a contour integral method. Furthermore, the eigenfrequencies of the finite structure are extracted by applying the contour integral method to the sized reduced system matrix, and a banded distribution of the eigenfrequencies is found. The correlation between the band structures of the infinite structures and the elastic wave transmission of the corresponding finite structures are presented. The frequency-banded nature exhibited by the finite structures shows a good agreement with the band structure of the corresponding infinite structures.

**PubDate:**2013-12-31T01:35:28Z

**Analyzing three-dimensional viscoelasticity problems via the improved**

element-free Galerkin (IEFG) method**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): M.J. Peng , R.X. Li , Y.M. Cheng

Based on the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method for three-dimensional viscoelasticity problems is presented in this paper. The improved moving least-squares (IMLS) approximation is employed to form the shape function, the Galerkin weak form is employed to obtain the equations system, and the penalty method is used to impose the essential boundary conditions. A differential constitutive relationship is assumed to describe the viscoelasticity behavior, and the traditional Newton–Raphson iteration procedure is selected for the time discretization. Then the formulae of the IEFG method for three-dimensional viscoelasticity problems are obtained. Three numerical examples are given to demonstrate the validity and efficiency of the method in this paper. And the scaling parameter, number of nodes and the time step length are considered for the convergence study. Compared with the element-free Galerkin method, the computational efficiency is improved markedly by using the IEFG method.

**PubDate:**2013-12-31T01:35:28Z

**Comparison of meshless local weak and strong forms based on particular**

solutions for a non-classical 2-D diffusion model**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): Saeid Abbasbandy , Hadi Roohani Ghehsareh , Mohammed S. Alhuthali , Hamed H. Alsulami

In the current work, a new aspect of the weak form meshless local Petrov–Galerkin method (MLPG), which is based on the particular solution is presented and well-used to numerical investigation of the two-dimensional diffusion equation with non-classical boundary condition. Two-dimensional diffusion equation with non-classical boundary condition is a challenged and complicated model in science and engineering. Also the method of approximate particular solutions (MAPS), which is based on the strong formulation is employed and performed to deal with the given non-classical problem. In both techniques an efficient technique based on the Tikhonov regularization technique with GCV function method is employed to solve the resulting ill-conditioned linear system. The obtained numerical results are presented and compared together through the tables and figures to demonstrate the validity and efficiency of the presented methods. Moreover the accuracy of the results is compared with the results reported in the literature.

**PubDate:**2013-12-27T10:33:01Z

**Localized method of approximate particular solutions with Cole–Hopf**

transformation for multi-dimensional Burgers equations**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): C.Y. Lin , M.H. Gu , D.L. Young , C.S. Chen

The Burgers equations depict propagating wave with quadratic nonlinearity, it can be used to describe nonlinear wave propagation and shock wave, where the nonlinear characteristics cause difficulties for numerical analysis. Although the solution approximation can be executed through iterative methods, direct methods with finite sequence of operation in time can solve the nonlinearity more efficiently. The resolution for nonlinearity of Burgers equations can be resolved by the Cole–Hopf transformation. This article applies the Cole–Hopf transformation to transform the system of Burgers equations into a partial differential equation satisfying the diffusion equation, and uses a combination of finite difference and the localized method of approximate particular solution (FD-LMAPS) for temporal and spatial discretization, respectively. The Burgers equations with behaviors of propagating wave, diffusive N-wave or within multi-dimensional irregular domain have been verified in this paper. Effectiveness of the FD-LMAPS has also been further examined in some experiments, and all the numerical solutions prove that the FD-LMAPS is a promising numerical tool for solving the multi-dimensional Burgers equations.

**PubDate:**2013-12-27T10:33:01Z

**Discussion on “Two-dimensional elastodynamics by the time-domain**

boundary element method: Lagrange interpolation strategy in time

integration” by Carrer J A M et al.**Abstract:**Publication date: Available online 26 December 2013

Source:Engineering Analysis with Boundary Elements

Author(s): Duofa Ji , Weidong Lei , Qingxin Li

The purpose is to discuss the potential flaws in the elastodynamic boundary integral equation with the authors to the mentioned paper.

**PubDate:**2013-12-27T10:33:01Z

**Green's functions and boundary element analysis for bimaterials with soft**

and stiff planar interfaces under plane elastostatic deformations**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): E.L. Chen , W.T. Ang

Plane elastostatic Green's functions satisfying relevant conditions on soft and stiff planar interfaces between two dissimilar anisotropic half spaces under elastostatic deformations are explicitly derived with the aid of the Fourier integral transformation technique. Green's functions are applied to obtain special boundary integral equations for the deformation of a bimaterial with an imperfect planar interface that is either soft or stiff. The boundary integral equations do not contain any integral over the imperfect interface. They are used to obtain a boundary element procedure for determining the displacements and stresses in the bimaterial. The numerical procedure does not require the interface to be discretized into elements.

**PubDate:**2013-12-23T01:34:29Z

**Analysis of piezoelectric plates with a hole using nature boundary**

integral equation and domain decomposition**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): Xing-Yuan Miao , Guo-Qing Li

In this paper, the plane problems of piezoelectricity are studied by using nature boundary integral equation and domain decomposition. A general displacement solution in terms of three potential functions is adopted to solve exterior boundary value problems of piezoelectricity, and three mapping relations corresponding to three potential functions are proposed for domain decomposition. By symbolic matrix inversion and derivation calculus, each potential function is governed by harmonic second-order partial differential equation in transformed domain with prescribed boundary condition. Therefore, three classic harmonic problems equivalent to the original plane piezoelectricity are established. Two cases of boundary conditions are considered, in which the displacement and electric potential are prescribed or the traction and electric displacement are given on the boundary. All problems considered are equivalent to three independent harmonic problems, which are solved by using nature boundary integration method proposed by Feng and Yu. A piezoelectric plate with a circular hole is analyzed as numerical examples. The results show that the proposed method is valid for the piezoelectric plates with holes. The proposed method has potential applications to analyze multi-field coupling problems.

**PubDate:**2013-12-23T01:34:29Z

**The pre/post equilibrated conditioning methods to solve Cauchy problems****Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): Chein-Shan Liu

In the present paper, the inverse Cauchy problems of Laplace equation and biharmonic equation are transformed, by using the method of fundamental solutions (MFS) and the Trefftz method (TM), to the systems of linear equations for determining the expansion coefficients. Then, we propose three different conditioners together with the conjugate gradient method (CGM) to solve the resultant ill-posed linear systems. They are the post-conditioning CGM and the pre-conditioning CGM based on the idea of equilibrated norm for the conditioned matrices, as well as a minimum-distance conditioner. These algorithms are convergent fast and accurate by solving the inverse Cauchy problems under random noise.

**PubDate:**2013-12-23T01:34:29Z

**Numerical solution of the two-phase incompressible Navier–Stokes**

equations using a GPU-accelerated meshless method**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): Jesse M. Kelly , Eduardo A. Divo , Alain J. Kassab

This paper presents the development and implementation of a Meshless two-phase incompressible fluid flow solver and its acceleration using the graphics processing unit (GPU). The solver is formulated as a Localized Radial-Basis Function Collocation Meshless Method and the interface of the two-phase flow is captured using an implementation of the Level-Set method. The Compute Unified Device Architecture (CUDA) language for general-purpose computing on the GPU is used to accelerate the solver. Through the combined use of the LRC Meshless method and GPU acceleration this paper seeks to address the issue of robustness and speed in computational fluid dynamics. Traditional mesh-based methods require extensive and time-consuming user input for the generation and verification of a computational mesh. The LRC meshless method seeks to mitigate this issue through the use of a set of scattered points that need not meet stringent geometric requirements like those required by finite-volume and finite-element methods, such as connectivity and poligonalization. The method is shown to render very accurate and stable solutions and the implementation of the solver on the GPU is shown to accelerate the solution by several orders.

**PubDate:**2013-12-23T01:34:29Z

**A cell-based smoothed finite element method using three-node shear-locking**

free Mindlin plate element (CS-FEM-MIN3) for dynamic response of laminated

composite plates on viscoelastic foundation**Abstract:**Publication date: Available online 17 December 2013

Source:Engineering Analysis with Boundary Elements

Author(s): H. Luong-Van , T. Nguyen-Thoi , G.R. Liu , P. Phung-Van

A cell-based smoothed finite element method using three-node Mindlin plate element (CS-FEM-MIN3) based on the first-order shear deformation theory (FSDT) was recently proposed for static and dynamic analyses of Mindlin plates. In this paper, the CS-FEM-MIN3 is extended and incorporated with damping-spring systems for dynamic responses of sandwich and laminated composite plates resting on viscoelastic foundation subjected to a moving mass. The plate-foundation system is modeled as a discretization of three-node triangular plate elements supported by discrete springs and dashpots at the nodal points representing the viscoelastic foundation. The position of the moving mass with specified velocity on triangular elements at any time is defined, and then the moving mass is transformed into loads at nodes of elements. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of others available numerical results. A parametric examination is also conducted to determine the effects of various parameters on the dynamic response of the plates on the viscoelastic foundation subjected to a moving mass.

**PubDate:**2013-12-19T01:34:22Z

**The simulation of laminated glass beam impact problem by developing**

fracture model of spherical DEM**Abstract:**Publication date: Available online 14 December 2013

Source:Engineering Analysis with Boundary Elements

Author(s): Wei Gao , Mengyan Zang

A fracture model suitable to spherical discrete element method (DEM) is presented based on the concept of the cohesive model. In this fracture model, there are three types of interaction between discrete elements, namely connection, cohesion and contact. When fracture criterion is met, the type of interaction between the corresponding discrete elements translates from connection to cohesion. The cohesive traction is obtained from the opening displacement of the elements according to the cohesive model. In order to analyze laminated glass impact problem, the combined DE/FE method is employed, as DEM is suitable to simulate glass while FEM is applicable to model the polyvinyl butyral (PVB) film and impact body. The algorithms of the fracture model are implemented into the in-house developed code, named CDFP. This developed code is applied to simulate the fracture process of automobile laminated glass beam subjected to impact and the results are compared with those obtained by experiment.

**PubDate:**2013-12-19T01:34:22Z

**Boundary element method for vibration analysis of two-dimensional**

anisotropic elastic solids containing holes, cracks or interfaces**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): Y.C. Chen , Chyanbin Hwu

By using the anisotropic elastostatic fundamental solutions and employing the dual reciprocity method, a special boundary element method (BEM) was developed in this paper to perform elastodynamic analysis of anisotropic elastic plates containing holes, cracks or interfaces. The system of ordinary differential equations obtained for the vibration transient analysis was solved using the Houlbolt's algorithm and modal superposition method. These equations were reduced to the standard eigenproblem for free vibration, and a purely algebraic system of equations for steady-state forced vibration. Since the fundamental solutions used in the present BEM satisfy the boundary conditions set on the holes, cracks, or interfaces, no meshes are needed along these boundaries. With this special feature, the numerical examples presented in this paper show that to get an accurate result much fewer elements were used in the present BEM comparing with those in the traditional BEM or finite element method.

**PubDate:**2013-12-15T13:30:53Z

**Application of meshfree methods for solving the inverse one-dimensional**

Stefan problem**Abstract:**Publication date: March 2014

Source:Engineering Analysis with Boundary Elements, Volume 40

Author(s): Kamal Rashedi , Hojatollah Adibi , Jamal Amani Rad , Kourosh Parand

This work is motivated by studies of numerical simulation for solving the inverse one and two-phase Stefan problem. The aim is devoted to employ two special interpolation techniques to obtain space-time approximate solution for temperature distribution on irregular domains, as well as for the reconstruction of the functions describing the temperature and the heat flux on the fixed boundary x=0 when the position of the moving interface is given as extra specification. The advantage of applying the methods is producing the shape functions which provide the important delta function property to ensure that the essential conditions are fulfilled. Due to ill-posedness of the problem, the process is intractable numerically, so special optimization technique is used to obtain the regularized solution. Numerical results for the typical benchmark test examples, which have the input measured data perturbed by increasing amounts of noise and continuity to the input data in the presence of additive noise, are obtained, which present the efficiency of the proposed method.

**PubDate:**2013-12-15T13:30:53Z

**Null-field integral approach for the piezoelectricity problems with**

multiple elliptical inhomogeneities**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): Ying-Te Lee , Jeng-Tzong Chen , Shyh-Rong Kuo

Based on the successful experience of solving anti-plane problems containing multiple elliptical inclusions, we extend to deal with the piezoelectricity problems containing arbitrary elliptical inhomogeneities. In order to fully capture the elliptical geometry, the keypoint of the addition theorem in terms of the elliptical coordinates is utilized to expand the fundamental solution to the degenerate kernel and boundary densities are simulated by the eigenfunction expansion. Only boundary nodes are required instead of boundary elements. Therefore, the proposed approach belongs to one kind of meshless and semi-analytical methods. Besides, the error stems from the number of truncation terms of the eigenfunction expansion and the convergence rate of exponential order is better than the linear order of the conventional boundary element method. It is worth noting that there are Jacobian terms in the degenerate kernel, boundary density and contour integral. However, they would cancel each other out in the process of the boundary contour integral. As the result, the orthogonal property of eigenfunction is preserved and the boundary integral can be easily calculated. For verifying the validity of the present method, the problem of an elliptical inhomogeneity in an infinite piezoelectric material subject to anti-plane shear and in-plane electric field is considered to compare with the analytical solution in the literature. Besides, two circular inhomogenieties can be seen as a special case to compare with the available data by approximating the major and minor axes. Finally, the problem of two elliptical inhomogeneities in an infinite piezoelectric material is also provided in this paper.

**PubDate:**2013-12-07T01:34:34Z

**Blood perfusion estimation in heterogeneous tissue using BEM based**

algorithm**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): J. Iljaž , L. Škerget

The estimation of space-dependent perfusion coefficient in homogeneous and non-homogeneous tissue has been investigated. While initial and Dirichlet boundary conditions are known, additional heat-flux measurement data is needed to render a unique solution. A numerical approach based on Boundary Element Method (BEM) combined with two different optimization routines and first-order Tikhonov regularization using L-Curve method has been developed. Efficiency of the algorithm, effect of initial guess, noise, perfusion distribution and non-homogeneous tissue on retrieving the perfusion coefficient has been studied on two test examples using exact as well as noisy data. Results show very good agreement with the true perfusion function under exact and low-noisy data, using Levenberg–Marquardt (LM) method combined with first-order regularization process. If the true perfusion function first-derivative is large, the function can be successfully retrieved only in the region near the boundary measurement, which is especially noticeable for a non-monotonic function in non-homogeneous tissue. This study represents the base for further research on the field of successful non-invasive blood perfusion determination in non-homogeneous tissue.

**PubDate:**2013-12-03T01:34:50Z

**A weighted nodal-radial point interpolation meshless method for 2D solid**

problems**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): Yang Cao , Lin-Quan Yao , Shi-Chao Yi

In this paper, a novel weighted nodal-radial point interpolation meshless (WN-RPIM) method is proposed for 2D solid problems. In the new approach, the moment matrices are performed only at the nodes to get nodal coefficients. At each computational point (node or integration point), the shape functions are obtained by weighting the nodal coefficients whose nodes are located in its support domain. The shape functions obtained by the new scheme preserve the Kronecker delta function property under certain conditions. This conclusion can be extended for the weighted nodal-interpolating moving least squares approximation studied in Most and Bucher [New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares. Eng Anal Bound Elem 2008;32:461–470]. Besides, the new method is much less time consuming than the RPIM method, since the number of nodes is generally much smaller than that of the integration points. Some numerical examples are illustrated to show the effectiveness of the proposed method. Some parameters that influence the performance of the proposed method are also investigated.

**PubDate:**2013-12-03T01:34:50Z

**An image denoising approach based on a meshfree method and the domain**

decomposition technique**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): Maryam Kamranian , Mehdi Dehghan , Mehdi Tatari

In this paper the meshfree finite point method (FPM) with domain decomposition is investigated for solving a nonlinear PDE to denoise digital images. The obtained algorithm is parallel and ideal for parallel computers. We use the scheme of Catté et al. [9] and we believe that this method could be successfully implemented for other noise removal schemes. The finite point method is a meshfree method based on the point collocation of moving least squares approximation. This method is easily applicable to nonlinear problems due to the lack of dependence on a mesh or integration procedure. Also computer experiments indicate the efficiency of the proposed method.

**PubDate:**2013-12-03T01:34:50Z

**A novel three-dimensional element free Galerkin (EFG) code for simulating**

two-phase fluid flow in porous materials**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): Soodeh Samimi , Ali Pak

In the past few decades, numerical simulation of multiphase flow systems has received increasing attention because of its importance in various fields of science and engineering. In this paper, a three-dimensional numerical model is developed for the analysis of simultaneous flow of two fluids through porous media. The numerical approach is fairly new based on the element-free Galerkin (EFG) method. The EFG is a type of mesh-less method which has rarely been used in the field of flow in porous media. The weak forms of the governing partial differential equations are derived by applying the weighted residual method and Galerkin technique. The penalty method is utilized for imposition of the essential boundary conditions. To create the discrete equation system, the EFG shape functions are used for spatial discretization of pore fluid pressures and a fully implicit scheme is employed for temporal discretization. The obtained numerical results indicate that the EFG method has the capability to substitute the classical FE and FD approaches from the accuracy point of view, provided that the efficiency of the EFG is improved. The developed EFG code can be used as a robust numerical tool for simulating two-phase flow processes in the subsurface layers in various engineering disciplines.

**PubDate:**2013-11-29T01:32:37Z

**Convolution quadrature time-domain boundary element method for 2-D and 3-D**

elastodynamic analyses in general anisotropic elastic solids**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): Akira Furukawa , Takahiro Saitoh , Sohichi Hirose

This paper presents a convolution quadrature time-domain boundary element method for 2-D and 3-D elastic wave propagation in general anisotropic solids. A boundary element method (BEM) has been developed as an effective and accurate numerical approach for wave propagation problems. However, a conventional time-domain BEM has a critical disadvantage; it produces unstable numerical solutions for a small time increment. To overcome this disadvantage, in this paper, a convolution quadrature method (CQM) is applied to the time-discretization of boundary integral equations in 2-D and 3-D general anisotropic solids. As numerical examples, the problems of elastic wave scattering by a cavity are solved to validate the present method.

**PubDate:**2013-11-29T01:32:37Z

**Velocity–vorticity RANS turbulence modeling by boundary element**

method**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): Janez Lupše , Leopold Škerget , Jure Ravnik

Turbulent flow over various geometries is studied numerically. Incompressible set of Navier–Stokes equations is considered and solved by boundary domain integral method (BDIM). Governing equations are written in velocity–vorticity form. Turbulence models used are based on eddy-viscosity hypothesis. Integral form of equations, discretization and the solution algorithm are presented. The algorithm is tested with two separate test cases. The first is the turbulent channel flow for two different Reynolds numbers: Re τ = 180 and Re τ = 395 . Results show very good agreement with corresponding DNS data. The second test case is the flow over backward facing step for Reynolds number Re h = 5000 , which shows good agreement with literature data on mean reattachment length.

**PubDate:**2013-11-25T01:34:31Z

**Radial integration BEM for one-phase solidification problems****Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): Bo Yu , Wei-An Yao , Xiao-Wei Gao , Sheng Zhang

In this paper, a new boundary element analysis approach is presented for solving one-phase solidification and freezing problems based on the radial integration method. Green's function for the Laplace equation is adopted in deriving basic integral equations for time-dependent problems with constant heat conductivities and, as a result, a domain integral is involved in the derived integral equations. Based on the finite difference technique, an implicit time marching solution scheme is developed for solving the time-dependent system of equations. Front-tracking method is used to simulate the motion of the phase boundary. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the radial integration BEM. To validate the proposed method, two typical examples are given. Satisfactory results are obtained in comparison with semi-analytical solutions.

**PubDate:**2013-11-25T01:34:31Z

**Editorial Board****Abstract:**Publication date: January 2014

Source:Engineering Analysis with Boundary Elements, Volume 38

**PubDate:**2013-11-25T01:34:31Z

**Solution of two-dimensional modified anomalous fractional sub-diffusion**

equation via radial basis functions (RBF) meshless method**Abstract:**Publication date: January 2014

Source:Engineering Analysis with Boundary Elements, Volume 38

Author(s): Akbar Mohebbi , Mostafa Abbaszadeh , Mehdi Dehghan

This paper is devoted to the radial basis functions (RBFs) meshless approach for the solution of two-dimensional modified anomalous fractional sub-diffusion equation. The fractional derivative of equation is described in the Riemann–Liouville sense. In this method we discretize the time fractional derivatives of mentioned equation by integrating both sides of it, then we will use the Kansa approach to approximate the spatial derivatives. We prove the stability and convergence of time-discretized scheme using energy method. The main aim of this paper is to show that the meshless method based on the radial basis functions and collocation approach is also suitable for the treatment of the fractional partial differential equations. Numerical results obtained from solving this problem on the rectangular, circular and triangular domains demonstrate the theoretical results and efficiency of the proposed scheme.

**PubDate:**2013-11-17T01:34:28Z

**The study of the potential flow past a submerged hydrofoil by the complex**

boundary element method**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): Adrian Carabineanu

We study the free-boundary linearized problem of the two-dimensional steady potential flow past a submerged hydrofoil. The integral representation obtained herein for the complex velocity involves only finite contours. The corresponding integral equation may be solved for any streamlined hydrofoil by means of the complex boundary element method. We calculate the free surface elevation, the velocity field, the pressure coefficients, the lift and the drag for the Kármán–Trefftz and Joukowsky hydrofoils and for the circular obstacle. A comparison between some numerical and analytical results shows a very good agreement.

**PubDate:**2013-11-17T01:34:28Z

**Estimating the optimum number of boundary elements by error estimation in**

a defined auxiliary problem**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): K.H. Chen , J.T. Chen

In this paper, we develop a new estimation technique to estimate the numerical error of the boundary element method (BEM). The discretization error of the BEM can be evaluated without having analytical solution. An auxiliary problem is defined to substitute for the original problem. In the auxiliary problem, the governing equation (GE), domain shape and boundary condition (BC) type are the same as the original problem. By using the linear combination of the complementary solutions set of GE, the analytical solution of the auxiliary problem, which is named quasi-analytical solution is defined. The quasi-analytical solution satisfies the GE and is similar to the real analytical solution of the original problem. By implementing the BEM to solve the auxiliary problem and comparing with the analytical solution, the error magnitude is estimated, which is approximate to the real error. The curve of the R.M.S. error versus different number of elements can be obtained. As a result, we can estimate the optimal number of elements in BEM. Several numerical examples are taken to demonstrate the accuracy of the proposed error estimation technique.

**PubDate:**2013-11-17T01:34:28Z

**Node adaptation for global collocation with radial basis functions using**

direct multisearch for multiobjective optimization**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): C.M.C. Roque , J.F.A. Madeira , A.J.M. Ferreira

Meshless methods are used for their capability of producing excellent solutions without requiring a mesh, avoiding mesh related problems encountered in other numerical methods, such as finite elements. However, node placement is still an open question, specially in strong form collocation meshless methods. The number of used nodes can have a big influence on matrix size and therefore produce ill-conditioned matrices. In order to optimize node position and number, a direct multisearch technique for multiobjective optimization is used to optimize node distribution in the global collocation method using radial basis functions. The optimization method is applied to the bending of isotropic simply supported plates. Using as a starting condition a uniformly distributed grid, results show that the method is capable of reducing the number of nodes in the grid without compromising the accuracy of the solution.

**PubDate:**2013-11-17T01:34:28Z

**Slow convergence of the BEM with constant elements in solving beam bending**

problems**Abstract:**Publication date: February 2014

Source:Engineering Analysis with Boundary Elements, Volume 39

Author(s): Y.J. Liu , Y.X. Li

Constant elements offer many advantages as compared with other higher-order elements in the boundary element method (BEM). With the use of constant elements, integrals in the BEM can be calculated accurately with analytical integrations and no corner problems need to be addressed. These features can make fast solution methods for the BEM (such as the fast multipole, adaptive cross approximation, and pre-corrected fast Fourier transform methods) especially efficient in computation. However, it is well known that the collocation BEM with constant elements is not adequate for solving beam bending problems due to the slow convergence or lack of convergence in the BEM solutions. In this study, we quantify this assertion using simple beam models and applying the fast multipole BEM code so that a large number of elements can be used. It is found that the BEM solutions do converge numerically to analytical solutions. However, the convergence rate is very slow, in the order of h to the power of 0.55–0.63, where h is the element size. Some possible reasons for the slow convergence are discussed in this paper.

**PubDate:**2013-11-17T01:34:28Z

**Efficiency improvement of the polar coordinate transformation for**

evaluating BEM singular integrals on curved elements**Abstract:**Publication date: January 2014

Source:Engineering Analysis with Boundary Elements, Volume 38

Author(s): Junjie Rong , Lihua Wen , Jinyou Xiao

The polar coordinate transformation (PCT) method has been extensively used to treat various singular integrals in the boundary element method (BEM). However, the resultant integrands tend to become nearly singular when (1) the aspect ratio of the element is large or (2) the field point is closed to the element boundary. In this paper, the first problem is circumvented by using a conformal transformation so that the geometry of the curved physical element is preserved in the transformed domain. The second problem is alleviated by using a sigmoidal transformation, which makes the quadrature points more concentrated around the near singularity. By combining the proposed two transformations with the Guiggiani method in Guiggiani et al. (1992) [8], one obtains an efficient and robust numerical method for computing the weakly, strongly and hyper-singular integrals in high-order BEM. Numerical integration results show that, compared with the original PCT, the present method can reduce the number of quadrature points considerably, for given accuracy. For further verification, the method is incorporated into a 2-order Nystrom BEM code for solving acoustic Burton–Miller boundary integral equation. It is shown that the method can retain the convergence rate of the BEM with much less quadrature points than the existing PCT.

**PubDate:**2013-11-13T01:34:54Z

**Fracture modeling of isotropic functionally graded materials by the**

numerical manifold method**Abstract:**Publication date: January 2014

Source:Engineering Analysis with Boundary Elements, Volume 38

Author(s): H.H. Zhang , G.W. Ma

Two-dimensional stationary cracks in isotropic functionally graded materials (FGMs) are studied by the numerical manifold method (NMM). The near-tip behavior of a crack in FGMs is manifested by a special choice of cover functions, and the displacement jump across a crack face is naturally represented taking the benefit of the NMM. The stress intensity factors (SIFs) are computed by the equivalent domain form of the interaction integral using the nonequilibrium auxiliary fields. Typical examples involving single- and multi-branched crack are conducted to verify the accuracy of the proposed method. Problems are tackled with the uniform mathematical cover system independent of the physical boundaries and the calculated SIFs match well with the existing reference solutions.

**PubDate:**2013-11-09T01:39:05Z

**ZZ-Type a posteriori error estimators for adaptive boundary element**

methods on a curve**Abstract:**Publication date: January 2014

Source:Engineering Analysis with Boundary Elements, Volume 38

Author(s): Michael Feischl , Thomas Führer , Michael Karkulik , Dirk Praetorius

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments.

**PubDate:**2013-11-09T01:39:05Z

**On the solution of exterior plane problems by the boundary element method:**

A physical point of view**Abstract:**Publication date: January 2014

Source:Engineering Analysis with Boundary Elements, Volume 38

Author(s): G. Bonnet , A. Corfdir , M.T. Nguyen

The paper is devoted to the solution of Laplace equation by the boundary element method. The coupling between a finite element solution inside a bounded domain and a boundary integral formulation for an exterior infinite domain can be performed by producing a “stiffness” or “impedance matrix”. It is shown in a first step that the use of classical Green's functions for plane domains can lead to impedance matrices which are not satisfying, being singular or not positive-definite. Avoiding the degenerate scale problem is classically overcome by adding to Green's function a constant which is large compared to the size of the domain. However, it is shown that this constant affects the solution of exterior problems in the case of non-null resultant of the normal gradient at the boundary. It becomes therefore important to define this constant related to a characteristic length introduced into Green's function. Using a “‘slender body theory” allows to show that for long cylindrical domains with a given cross section, the characteristic length is shown as being asymptotically equal to the length of the cylindrical domain. Comparing numerical or analytical 3D and 2D solutions on circular cylindrical domains confirms this result for circular cylinders.

**PubDate:**2013-11-09T01:39:05Z

**Editorial Board****Abstract:**Publication date: December 2013

Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 12

**PubDate:**2013-11-09T01:39:05Z

**The FEM–BIM approach using a mixed hexahedral finite element to**

model the electromagnetic and mechanical behavior of radiative microstrip

antennas**Abstract:**Publication date: January 2014

Source:Engineering Analysis with Boundary Elements, Volume 38

Author(s): N. Adnet , I. Bruant , F. Pablo , L. Proslier

This work is focused on the prediction of the impact of microstrip radiative antenna distortions on electromagnetic fields. In this way, a recent numerical tool, able to model the electromagnetic and mechanical behavior of a microstrip antenna, has been developed. Considering a weak coupling between electromagnetism and mechanical behavior, the mechanical equations are first solved. Then, from the mechanical strains results for the antenna, the electromagnetic fields are computed. To solve both problems, a 3D hexahedral finite element is used to discretize the structure, having both nodal mechanical and edges electromagnetic degrees of freedom. The weak electromagnetic formulation inducing integrals on an open infinite domain, a Boundary Integral Method (BIM) is used and applied to the strained structure. Three examples are considered. The simulations show that mechanical distortions can have major influence on the electromagnetic behavior of antennas.

**PubDate:**2013-11-09T01:39:05Z

**Numerical solution of fractional telegraph equation by using radial basis**

functions**Abstract:**Publication date: January 2014

Source:Engineering Analysis with Boundary Elements, Volume 38

Author(s): Vahid Reza Hosseini , Wen Chen , Zakieh Avazzadeh

In this paper, we implement the radial basis functions for solving a classical type of time-fractional telegraph equation defined by Caputo sense for ( 1 < α ≤ 2 ) . The presented method which is coupled of the radial basis functions and finite difference scheme achieves the semi-discrete solution. We investigate the stability, convergence and theoretical analysis of the scheme which verify the validity of the proposed method. Numerical results show the simplicity and accuracy of the presented method.

**PubDate:**2013-11-09T01:39:05Z

**Analysis of frictional contact problems for functionally graded materials**

using BEM**Abstract:**Publication date: January 2014

Source:Engineering Analysis with Boundary Elements, Volume 38

Author(s): Halit Gun , Xiao-Wei Gao

In this paper, a quadratic boundary element formulation for continuously non-homogeneous, isotropic and linear elastic functionally graded material contact problems with friction is presented. To evaluate domain related integrals, the radial integration method (RIM) based on the use of the approximating the normalized displacements in the domain integrals by a series of prescribed radial basis functions (RBF), leading a meshless scheme, is employed. An exponential variation with spatial coordinates is assumed for Young's modulus of the functionally graded materials (FGM), while Poisson's ratio is assumed to be constant. Under the contact conditions, including infinite friction, frictionless and Coulomb friction, different systems of equations for each body in contact are united. Numerical examples including non-confirming contact are given.

**PubDate:**2013-11-01T01:34:54Z

**Extended displacement discontinuity method for nonlinear analysis of**

penny-shaped cracks in three-dimensional piezoelectric media**Abstract:**Publication date: January 2014

Source:Engineering Analysis with Boundary Elements, Volume 38

Author(s): CuiYing Fan , ZhengHua Guo , HuaYang Dang , MingHao Zhao

The polarization saturation (PS) model and the dielectric breakdown (DB) model are both used, under the electrically impermeable crack assumption, to analyze penny-shaped cracks in the isotropic plane of three-dimensional (3D) infinite piezoelectric solids. Using the extended displacement discontinuity integral equation method, we obtained analytical solutions for the size of the electric yielding zone, the extended displacement discontinuities, the extended field intensity factor and the J-integral. Integrating the Green function for the point extended displacement discontinuity provided constant element fundamental solutions. These solutions correspond to an annular crack element applied with uniformly distributed extended displacement discontinuities in the transversely isotropic plane of a 3D piezoelectric medium. Using the obtained Green functions, the extended displacement discontinuity boundary element method was developed to analyze the PS model and DB model for penny-shaped cracks. The numerical method was validated by the analytical solution. Both the analytical results and numerical results show that the PS and the DB models give equivalent solutions for nonlinear fracture analysis of 3D piezoelectric materials, even though they are based on two physically different grounds.

**PubDate:**2013-11-01T01:34:54Z

**The improved element-free Galerkin method for two-dimensional**

elastodynamics problems**Abstract:**Publication date: December 2013

Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 12

Author(s): Zan Zhang , S.Y. Hao , K.M. Liew , Y.M. Cheng

In this paper, we derive an improved element-free Galerkin (IEFG) method for two-dimensional linear elastodynamics by employing the improved moving least-squares (IMLS) approximation. In comparison with the conventional moving least-squares (MLS) approximation function, the algebraic equation system in IMLS approximation is well-conditioned. It can be solved without having to derive the inverse matrix. Thus the IEFG method may result in a higher computing speed. In the IEFG method for two-dimensional linear elastodynamics, we employed the Galerkin weak form to derive the discretized system equations, and the Newmark time integration method for the time history analyses. In the modeling process, the penalty method is used to impose the essential boundary conditions to obtain the corresponding formulae of the IEFG method for two-dimensional elastodynamics. The numerical studies illustrated that the IEFG method is efficient by comparing it with the analytical method and the finite element method.

**PubDate:**2013-10-16T00:35:39Z

**Crack-tip amplification and shielding by micro-cracks in piezoelectric**

solids – Part I: Static case**Abstract:**Publication date: December 2013

Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 12

Author(s): Jun Lei , Hongyan Wang , Chuanzeng Zhang , Felipe Garcia-Sanchez

Analysis of the crack-tip amplification and shielding by micro-cracks in an unbounded two-dimensional piezoelectric solid is presented in this paper. A boundary element method (BEM) based on the hypersingular traction boundary integral equations (BIEs) is developed for this purpose. Integrals with hypersingular kernels are analytically transformed into weakly singular and regular integrals. A collocation method is applied for the spatial discretization. Quadratic quarter-point elements are implemented at all crack-tips. The amplification ratios of the field intensity factors and mechanical strain or electrical energy release rate are defined to show the crack-tip amplification and shielding. Numerical results are compared with the analytical results for isotropic materials to verify the present BEM. The influences of various loading conditions, the location and orientation angles of micro-cracks on the amplification ratios are investigated. The contours of the amplification ratios for an arbitrarily located micro-crack are also presented to show the crack-tip amplification and shielding effects.

**PubDate:**2013-10-16T00:35:39Z

**Application of variational mesh generation approach for selecting centers**

of radial basis functions collocation method**Abstract:**Publication date: December 2013

Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 12

Author(s): M. Barfeie , Ali R. Soheili , Maryam Arab Ameri

In this paper, a two-dimensional variational mesh generation method is applied to obtain adaptive centers for radial basis functions (RBFs). At first, a set of uniform centers is distributed in the domain, then mesh generation differential equations are used to move the centers to region with high gradients. An iterative algorithm is introduced to solve steady-state mesh generation differential equations with RBFs. Functions with steep variation in the domains are used to validate the adaptive centers generation method. In addition to the centers adaption process is applied to solve elliptic partial differential equations via RBFs collocation method. Numerical results of Helmholtz differential equation show a clear reduction in the error, when the adaptive centers are used for RBFs.

**PubDate:**2013-10-12T00:34:49Z