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Engineering Analysis with Boundary Elements

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ISSN (Print) 0955-7997
Published by Elsevier

[2564 journals]

BEM analysis of laterally loaded piles in multi-layered transversely isotropic soils
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): Zhi Yong Ai , Dong Liang Feng , Yi Chong Cheng
  This paper presents a theory for the static analysis of laterally loaded piles embedded in multi-layered transversely isotropic soils. Boundary element method (BEM) is applied to the pile–soil model where the floating pile is modeled as a Bernoulli–Euler beam using the finite difference method and the layered soil is represented utilizing a decoupled analytical layer-element solution as a kernel function for its high accuracy and efficiency. Several numerical examples presented reveal that the pile behavior is affected synthetically by both transverse isotropy and stratified character of soil and the pile's size and physical properties.
  
  PubDate: 2013-05-23T00:33:21Z
Solution for Eshelby's elastic inclusions in a finite plate using boundary integral equation method
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): Y.Z. Chen
  This paper provides a solution for Eshelby's elastic inclusions in a finite plate based on the complex variable boundary integral equation (CVBIE) method. In the formulation, an inclusion with Eshelby's eigenstrains is embedded in an elliptic plate, and the exterior boundary is applied by some static loading. Two BIEs are suggested in the present study. One of BIEs is used for the finite inclusion region, and the other is used for region bounded by interface and the exterior boundary. After the discretization of BIEs, a numerical solution is suggested. In the solution, an inverse matrix technique is suggested which can eliminate one unknown vector in advance. Three numerical examples under different generalized loadings are provided. Interaction between the prescribed eigenstrains and the static loading along the exterior boundary is studied in detail.
  
  PubDate: 2013-05-23T00:33:21Z
Study on harbor resonance and focusing by using the null-field BIEM
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): Jeng-Tzong Chen , Jia-Wei Lee , Chine-Feng Wu , Ying-Te Lee
  In this paper, the resonance of a circular harbor is studied by using the semi-analytical approach. The method is based on the null-field boundary integral equation method in conjunction with degenerate kernels and the Fourier series. The problem is decomposed into two regions by employing the concept of taking free body. One is a circular harbor, and the other is a problem of half-open sea with a coastline subject to the impermeable (Neumann) boundary condition. It is interesting to find that the SH wave impinging on the hill can be formulated by the same mathematical model. After finding the analogy between the harbor resonance and hill scattering, focusing of the water wave inside the harbor as well as focusing in the hill scattering are also examined. Finally, two numerical examples, circular harbor problems of 60° and 180° opening entrance, are both used to verify the validity of the present formulation.
  
  PubDate: 2013-05-23T00:33:21Z
Editorial Board
- Abstract: Publication date: June 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 6
  
  PubDate: 2013-05-23T00:33:21Z
Radial integration boundary element method for acoustic eigenvalue problems
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): Shen Qu , Sheng Li , Hao-Ran Chen , Zhan Qu
  In this paper, the radial integration boundary element method is developed to solve acoustic eigenvalue problems for the sake of eliminating the frequency dependency of the coefficient matrices in traditional boundary element method. The radial integration method is presented to transform domain integrals to boundary integrals. In this case, the unknown acoustic variable contained in domain integrals is approximated with the use of compactly supported radial basis functions and the combination of radial basis functions and global functions. As a domain integrals transformation method, the radial integration method is based on pure mathematical treatments and eliminates the dependence on particular solutions of the dual reciprocity method and the particular integral method. Eventually, the acoustic eigenvalue analysis procedure based on the radial integration method resorts to a generalized eigenvalue problem rather than an enhanced determinant search method or a standard eigenvalue analysis with matrices of large size, just like the multiple reciprocity method. Several numerical examples are presented to demonstrate the validity and accuracy of the proposed approach.
  
  PubDate: 2013-05-23T00:33:21Z
A wavenumber domain boundary element method model for the simulation of vibration isolation by periodic pile rows
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): Xu Zhang , Jian-Fei Lu
  The wavenumber domain boundary element method (WDBEM) for the interaction between the half-space soil and periodic structures is important for the design of various periodic structures in civil engineering. In this study, a WDBEM model for the half-space soil and periodic pile rows is developed and used in the analysis of the vibration isolation via pile rows. To establish the model, the rigid-body-motion method for the estimation of the Cauchy type singular integrals involved in the WDBEM is established for the first time. In the proposed model, the half-space soil and periodic pile rows are treated as elastic media. Employing the spatial domain boundary integral equations for the half-space soil and pile rows as well as the sequence Fourier transform method, the wavenumber domain boundary integral equations for the soil and pile rows are derived. By using the obtained wavenumber domain boundary integral equations, WDBEM formulations for the half-space soil and periodic pile rows are established. Using the WDBEM formulations as well as the continuity conditions at the pile–soil interfaces, a coupled WDBEM model for the pile–soil system is derived. With the proposed WDBEM model, the influences of the pile length and the shear modulus of the half-space soil on the vibration isolation effect of pile rows are examined. Presented numerical results show that the isolation vibration effect of pile rows is enhanced considerably with increasing length of the piles. Besides, the isolation vibration effect of pile rows is weakened considerably with increasing shear modulus of the half-space soil. Moreover, as expected, multiple pile rows usually produce a better isolation vibration effect than a single pile row.
  
  PubDate: 2013-05-23T00:33:21Z
Frequency domain analysis of interacting acoustic–elastodynamic models taking into account optimized iterative coupling of different numerical methods
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): L. Godinho , D. Soares Jr.
  In this work, interacting acoustic–elastodynamic models are analyzed by means of an optimized iterative coupling algorithm. In this iterative coupling procedure, each acoustic/elastodynamic sub-domain of the model is solved independently, and the variables at the common interfaces of the sub-domains are successively renewed, until convergence is achieved. A relaxation parameter is introduced in order to ensure and/or speed up the convergence of the iterative analysis, and an expression to compute optimal values for the relaxation parameter is presented. Several numerical methods are considered to discretize the acoustic and elastodynamic sub-domains of the coupled model, and the performance of these different methodologies, in the coupled analysis, is discussed. In this context, the boundary element method and the method of fundamental solutions are applied to model the acoustic sub-domains, whereas the finite element method, the collocation method and the meshless local Petrov–Galerkin method are applied to model the elastodynamic sub-domains. Independent discretizations of the acoustic/elastodynamic sub-domains are allowed, being no matching nodes required along the common interfaces. At the end of the paper, numerical examples are presented, illustrating the performance and potentialities of the adopted procedures.
  
  PubDate: 2013-05-23T00:33:21Z
Conservative multiquadric quasi-interpolation method for Hamiltonian wave equations
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): Zongmin Wu , Shengliang Zhang
  Hamiltonian PDEs have some invariant quantities such as energy and momentum, etc., which should be well conserved with the numerical integration. In this paper we concentrate on the nonlinear wave equation. We study how a space discretization by using multiquadric quasi-interpolation method makes the space discretized system also possess some invariants which are good approximation of the continuous energy. Then, appropriate symplectic scheme is employed for the integration of the semi-discretized system. Theoretical results show that the proposed method has not only high order accuracy but also good properties of long-time tracking capability. Some numerical examples are presented to demonstrate the effectiveness of the proposed method.
  
  PubDate: 2013-05-23T00:33:21Z
Local Kronecker delta property of the MLS approximation and feasibility of directly imposing the essential boundary conditions for the EFG method
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): Xiaodong Wang , Jie Ouyang , Zhao Feng
  The element-free Galerkin (EFG) method is a promising method for solving many engineering problems. Because the shape functions of the EFG method obtained by the moving least-squares (MLS) approximation, generally, do not satisfy the Kronecker delta property, special techniques are required to impose the essential boundary conditions. In this paper, it is proved that the MLS shape functions satisfy the Kronecker delta property when the number of nodes in the support domain is equal to the number of the basis functions. According to this, a local Kronecker delta property, which is satisfying the Kronecker delta property only at boundary nodes, can be obtained in one- and two-dimension. This local Kronecker delta property is an inherent property of the one-dimensional MLS shape functions and can be obtained for the two-dimensional MLS shape functions by reducing the influence domain of each boundary node to weaken the influence between them. The local Kronecker delta property provides the feasibility of directly imposing the essential boundary conditions for the EFG method. Four numerical examples are computed to verify this feasibility. The coincidence of the numerical results obtained by the direct method and Lagrange multiplier method shows the feasibility of the direct method.
  
  PubDate: 2013-05-23T00:33:21Z
The MFS–MPS for two-dimensional steady-state thermoelasticity problems
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): Liviu Marin , Andreas Karageorghis
  We consider the numerical approximation of the boundary and internal thermoelastic fields in the case of two-dimensional isotropic linear thermoelastic solids by combining the method of fundamental solutions (MFS) with the method of particular solutions (MPS). A particular solution of the non-homogeneous equations of equilibrium associated with a planar isotropic linear thermoelastic material is derived from the MFS approximation of the boundary value problem for the heat conduction equation. Moreover, such a particular solution enables one to easily develop analytical solutions corresponding to any two-dimensional domain occupied by an isotropic linear thermoelastic solid. The accuracy and convergence of the proposed MFS–MPS procedure are validated by considering three numerical examples.
  
  PubDate: 2013-05-23T00:33:21Z
An improved boundary distributed source method for two-dimensional Laplace equations
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): Sin Kim
  In this work, the boundary distributed source (BDS) method [EABE 34(11): 914-919] based on the method of fundamental solutions (MFS) is considered for the solution of two-dimensional Laplace equations. The BDS is a truly mesh-free method and quite easy to implement since the source points and field points are collocated on the domain boundary while the conventional MFS requires a fictitious boundary where the source points locate. The main idea of the BDS is that to avoid the singularities of the fundamental solutions the concentrated point sources in the conventional MFS are replaced by distributed sources over circles centered at the source points. In the original BDS, all elements of the system matrix can be derived analytically in a very simple form for the Dirichlet boundary conditions and off-diagonal elements for the Neumann boundary conditions, while the diagonal elements for the Neumann boundary conditions can be obtained indirectly from the constant potential field. This work suggests a simple way to determine the diagonal elements for the Neumann boundary conditions by invoking that the boundary integration of the normal gradient of the potential should vanish. Several numerical examples are addressed to show the feasibility and the accuracy of the proposed method.
  
  PubDate: 2013-05-23T00:33:21Z
Cascadic meshfree method for the elliptic Monge–Ampère equation
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): Zhiyong Liu , Yinnian He
  The elliptic Monge–Ampère equation is a fully nonlinear partial differential equation, which originated in geometric surface theory and has been widely applied in dynamic meteorology, elasticity, geometric optics, image processing and others. The numerical solution of the elliptic Monge–Ampère equation has been a subject of increasing interest recently. In this paper, we design a cascadic algorithm which is meshfree. We first generate hierarchical scattered data sets. Then on each successive refinement levels, the Monge–Ampère equation can be solved by Kansa's method. We call this method as cascadic meshfree method (CMF). Different from cascadic multigrid method, CMF avoids tedious interpolation and is more easy for implementation and coding. Finally, numerical experiments confirm the efficiency and robustness of CMF method.
  
  PubDate: 2013-05-23T00:33:21Z
Numerical study of the three-dimensional wave equation using the mesh-free kp-Ritz method
- Abstract: Publication date: July–August 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issues 7–8
  Author(s): K.M. Liew , R.J. Cheng
  This paper deals with numerical modeling of three-dimensional linear wave propagation based on the mesh-free kp-Ritz method. The mesh-free kernel particle estimate is employed to approximate the 3D displacement field. A system of discrete equations is obtained through application of the Ritz minimization procedure to the energy expressions. Convergence analysis and error estimates of the kp-Ritz method for three-dimensional wave equation are also presented in the paper. From the error analysis, we found that the error bound between the numerical and the exact solution is directly related to the radii of weight functions and the time step length. Effectiveness of the kp-Ritz method for three-dimensional wave equation is investigated by three numerical examples.
  
  PubDate: 2013-05-15T00:35:31Z
A fast multipole boundary element method for solving the thin plate bending problem
- Abstract: Publication date: June 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 6
  Author(s): S. Huang , Y.J. Liu
  A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex notation of the kernel functions, expansions and translations in the fast multipole BEM are presented. Finally, a few numerical examples are presented to show the accuracy and efficiency of the fast multipole BEM in solving thin plate bending problems. The bending rigidity of a perforated plate is evaluated using the developed code. It is shown that the fast multipole BEM can be applied to solve plate bending problems with good accuracy. Possible improvements in the efficiency of the method are discussed.
  
  PubDate: 2013-05-11T00:33:51Z
Structural response of oscillating foil in water
- Abstract: Publication date: June 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 6
  Author(s): M. La Mantia , P. Dabnichki
  Harmonic oscillations of NACA 0012 airfoils in water are numerically simulated to assess the corresponding structural loads due to the generated forces. An appropriately devised procedure estimates the unsteady effect caused by the foil acceleration, i.e. the added mass effect. This is found to play a very important role as the resulting inertia forces are largely enhanced in the range of analysed parameters. The influence of the wing mass is investigated and it is found that light wings generate forces larger than those generated by heavy wings, as light wings accelerate more than heavy wings. The resulting bending stresses and unsteady deflections are calculated by modelling the wings as elastic cantilevers with uniform distributed loads. The maximum unsteady deflection is found to be about 1% of the wing span, that is, the fluid–structure interaction problem can be considered decoupled in the present analysis. It is also shown that heavy, rigid wings appear to be more suitable for the swimming mode corresponding to steady cruise, as the applied stresses result smaller than those obtained for light, flexible wings. The added mass effect could instead be exploited when required, by using lighter propulsors, which generate larger forces.
  
  PubDate: 2013-05-11T00:33:51Z
Determination of a time-dependent heat source from nonlocal boundary conditions
- Abstract: Publication date: June 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 6
  Author(s): A. Hazanee , D. Lesnic
  In this paper, we investigate the inverse heat source problem of finding the time-dependent source function together with the temperature. Three general nonlocal conditions are considered for the boundary and overdetermination conditions resulting in six different cases. The boundary element method combined with Tikhonov regularization is employed in order to obtain an accurate and stable numerical solution.
  
  PubDate: 2013-05-07T00:34:48Z
Analysis of cylindrical shell panels. A meshless solution
- Abstract: Publication date: June 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 6
  Author(s): Aristophanes J. Yiotis , John T. Katsikadelis
  The Meshless Analog Equation Method, a purely meshless method, is applied to the static analysis of cylindrical shell panels. The method is based on the concept of the analog equation of Katsikadelis, which converts the three governing partial differential equations in terms of displacements into three substitute equations, two of second order and one fourth order, under fictitious sources. The fictitious sources are represented by series of radial basis functions of multiquadric type. Thus the substitute equations can be directly integrated. This integration allows the representation of the sought solution by new radial basis functions, which approximate accurately not only the displacements but also their derivatives involved in the governing equations. This permits a strong formulation of the problem. Thus, inserting the approximate solution in the differential equations and in the associated boundary conditions and collocating at a predefined set of mesh-free nodal points, a system of linear equations is obtained, which gives the expansion coefficients of radial basis functions series that represent the solution. The minimization of the total potential of the shell results in the optimal choice of the shape parameter of the radial basis functions. The method is illustrated by analyzing several shell panels. The studied examples demonstrate the efficiency and the accuracy of the presented method.
  
  PubDate: 2013-05-07T00:34:48Z
Iterative estimation of eigenmodes for acoustic cavities
- Abstract: Publication date: June 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 6
  Author(s): Alexandre Leblanc , Antoine Lavie
  In this paper, a stochastic estimation method of the number of eigenvalues of nonlinear eigenproblem (initially proposed by Maeda et al., JSIAM Letters 3, 61-64, (2011)) is employed iteratively in order to identify eigenvalues of acoustic cavities. Applied to several discretization formulations of the Helmholtz equation, the proposed approach handles complex acoustic cavities. Specific developments are carried out concerning the approximation of the stochastic estimator for the solved kernels. The method's accuracy is illustrated with academic nonlinear eigenproblems with various boundary conditions. In particular, a sphere problem with constant surface impedance is solved and validated by comparison with results issued from a finite element method software.
  
  PubDate: 2013-05-07T00:34:48Z
Eigenvalue analysis for acoustic problem in 3D by boundary element method with the block Sakurai–Sugiura method
- Abstract: Publication date: June 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 6
  Author(s): Haifeng Gao , Toshiro Matsumoto , Toru Takahashi , Hiroshi Isakari
  This paper presents accurate numerical solutions for nonlinear eigenvalue analysis of three-dimensional acoustic cavities by boundary element method (BEM). To solve the nonlinear eigenvalue problem (NEP) formulated by BEM, we employ a contour integral method, called block Sakurai–Sugiura (SS) method, by which the NEP is converted to a standard linear eigenvalue problem and the dimension of eigenspace is reduced. The block version adopted in present work can also extract eigenvalues whose multiplicity is larger than one, but for the complex connected region which includes a internal closed boundary, the methodology yields fictitious eigenvalues. The application of the technique is demonstrated through the eigenvalue calculation of sphere with unique homogenous boundary conditions, cube with mixed boundary conditions and a complex connected region formed by cubic boundary and spherical boundary, however, the fictitious eigenvalues can be identified by Burton–Miller's method. These numerical results are supported by appropriate convergence study and comparisons with close form.
  
  PubDate: 2013-05-03T00:38:32Z
The shape parameter in the Gaussian function II
- Abstract: Publication date: Available online 1 May 2013
  Source:Engineering Analysis with Boundary Elements
  Author(s): Lin-Tian Luh
  This is a continuation of our former study, Luh [1], of the shape parameter β contained in Gaussian e − β x 2 , x ∈ R n . Instead of using the error bound presented by Madych and Nelson [2], here we adopt an improved error bound constructed by Luh to evaluate the influence of β on error estimates. This results in a new set of criteria for the optimal choice of β and much sharper error estimates for Gaussian interpolation. What is important is that the notorious ill-conditioning of Gaussian interpolation can be greatly relieved because in this approach the fill distance need not be very small.
  
  PubDate: 2013-05-03T00:38:32Z
Editorial Board
- Abstract: Publication date: May 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 5
  
  PubDate: 2013-04-29T00:34:24Z
Boundary element model for electrochemical dissolution under externally applied low level stress
- Abstract: Publication date: Available online 28 April 2013
  Source:Engineering Analysis with Boundary Elements
  Author(s): Bruce M. Butler , Manoj B. Chopra , Alain J. Kassab , Vimal Chaitanya
  The effects of low levels of stress on the dissolution rate of type 304 stainless steel in seawater are determined, and these effects are incorporated into a boundary element method (BEM) code which was written to predict long-term changes in geometry, including those due to the stress-modified dissolution rates. Corrosion in the absence of stress effects is thoroughly documented, while the effects of micromechanical damage caused by strains in the plastic region are also well recognized. However, very little is known regarding the effects of low levels of stress (in the elastic region) on the behavior of dissolution rates of metals in general. To quantify this effect, a system consisting of stainless steel in seawater was chosen as the subject of this investigation. An initial set of controlled experiments using nearly pure copper with NHOH electrolyte was used to test the experimental methods developed for this study and to verify the functionality of the numerical code in predicting large changes in geometry due to long duration dissolution. The numerical code is based on the BEM to predict the electrochemical dissolution activity in 2D and in 3D-axisymmetric geometries with nonlinearities in the response to stress and the boundary conditions given by the highly non-linear polarization response of the specimen. A Newton–Raphson iterative procedure is used to solve for equilibrium at each solution step. In the BEM code, a nodal optimization routine dynamically modifies the number of nodes and their location on the boundary, which is required by the large changes in geometry experienced during long duration dissolution. New SE-elements are developed to model sections of the boundary where nodes are dynamically located, defined by a curvilinear fit using orthogonal Chebyshev polynomials through previous nodal locations. The code links stress and potential type corrosion formulations to generate geometrical changes due to stress and corrosion. Polarization curves were measured and input into the BEM code and recession profiles were predicted. Comparison between experiment and predictions reveal that, given the polarization curves measured in the lab, the BEM code predicts accurate recession profiles. Once the laboratory methods and computer program were verified, a second electrochemical system is adopted to study the effects of stress in the linear range upon recession rates. This system consists of type 304 stainless steel in simulated seawater subjected to compressive and tensile stresses up to 20% of yield. Comparison between numerical predictions using polarization curves determined by experiment for the copper/ammonium system reveals that the BEM code developed to model recession of corroding surfaces faithfully reproduces the recession fronts measured in the experiments. Furthermore, it is shown in a series of repeatable laboratory tests, in the stainless-steel/saline system, that stress in the linear range indeed affects the polarization curves for different levels of stress and, furthermore, it is found that the shift in the polarization curve depends on stress rate.
  
  PubDate: 2013-04-29T00:34:24Z
Antenna model of the horizontal grounding electrode for transient impedance calculation: Analytical versus boundary element method
- Abstract: Publication date: June 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 6
  Author(s): Silvestar Šesnić , Dragan Poljak
  The paper deals with a simple and efficient procedure for the calculation of the transient impedance of the horizontal grounding electrode. This work represents an extension of a previous paper, published by the authors, on the antenna modeling of the grounding electrode with corresponding Pocklington integro-differential equation. The governing equation is solved in the frequency domain, both numerically and analytically, thus obtaining the solution for the current induced along the electrode. The numerical solution is undertaken via Galerkin–Bubnov scheme of the Indirect Boundary Element Method. Scattered voltage along the electrode is then calculated using Generalized Telegrapher׳s equation. Time domain scattered voltage is evaluated via the Inverse Fast Fourier Transform. Subsequently, transient impedance is determined as a ratio of time domain voltage and current at the feeding point. Results obtained via different methods seem to agree satisfactorily.
  
  PubDate: 2013-04-29T00:34:24Z
Development of a meshless hybrid boundary node method for Stokes flows
- Abstract: Publication date: June 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 6
  Author(s): Fei Tan , Youliang Zhang , Yinping Li
  The meshless hybrid boundary node method (HBNM) is a promising method for solving boundary value problems, and is further developed and numerically implemented for incompressible 2D and 3D Stokes flows in this paper. In this approach, a new modified variational formulation using a hybrid functional is presented. The formulation is expressed in terms of domain and boundary variables. The moving least-squares (MLS) method is employed to approximate the boundary variables whereas the domain variables are interpolated by the fundamental solutions of Stokes equation, i.e. Stokeslets. The present method only requires scatter nodes on the surface, and is a truly boundary type meshless method as it does not require the ‘boundary element mesh’, either for the purpose of interpolation of the variables or the integration of ‘energy’. Moreover, since the primitive variables, i.e., velocity vector and pressure, are employed in this approach, the problem of finding the velocity is separated from that of finding pressure. Numerical examples are given to illustrate the implementation and performance of the present method. It is shown that the high convergence rates and accuracy can be achieved with a small number of nodes.
  
  PubDate: 2013-04-29T00:34:24Z
A meshfree method for the solution of two-dimensional cubic nonlinear Schrödinger equation
- Abstract: Publication date: June 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 6
  Author(s): S. Abbasbandy , H. Roohani Ghehsareh , I. Hashim
  In this paper, an efficient numerical technique is developed to approximate the solution of two-dimensional cubic nonlinear Schrödinger equations. The method is based on the nonsymmetric radial basis function collocation method (Kansa's method), within an operator Newton algorithm. In the proposed process, three-dimensional radial basis functions (especially, three-dimensional Multiquadrics (MQ) and Inverse multiquadrics (IMQ) functions) are used as the basis functions. For solving the resulting nonlinear system, an algorithm based on the Newton approach is constructed and applied. In the multilevel Newton algorithm, to overcome the instability of the standard methods for solving the resulting ill-conditioned system an interesting and efficient technique based on the Tikhonov regularization technique with GCV function method is used for solving the ill-conditioned system. Finally, the presented method is used for solving some examples of the governing problem. The comparison between the obtained numerical solutions and the exact solutions demonstrates the reliability, accuracy and efficiency of this method.
  
  PubDate: 2013-04-29T00:34:24Z
A Trefftz method in space and time using exponential basis functions: Application to direct and inverse heat conduction problems
- Abstract: Publication date: May 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 5
  Author(s): B. Movahedian , B. Boroomand , S. Soghrati
  In this paper we present a Trefftz method based on using exponential basis functions (EBFs) to solve one (1D) and two (2D) dimensional transient problems. We focus on direct and inverse heat conduction problems, the latter being the more challenging ones, to show the capabilities of the method. A summation of exponential basis functions (EBFs), satisfying the governing equation in time and space, with unknown coefficients is considered for the solution. The unknown coefficients are determined by the satisfaction of the prescribed time dependent boundary and initial conditions through a collocation method. Several 1D and 2D direct and inverse heat conduction problems are solved. Some numerical evidence is provided for the convergence and sensitivity of the method with respect to the noise levels of the measured data and time steps.
  
  PubDate: 2013-04-25T00:35:30Z
An overdetermined B-spline collocation method for Poisson problems on complex domains
- Abstract: Publication date: May 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 5
  Author(s): P. Žitňan
  The aim of this work is to show how the B-spline collocation method may be used for the approximate solution of Poisson problems considered on complex shaped planar domains in a simple and stable way. The most important aspect of this work consists in the use of approximate Fekete points recently developed by Sommariva and Vianello. Numerical experiments concerning the collocation solution of Poisson problems defined on an amoeba-like domain, star shaped domain and a square with eight holes subject to Dirichlet boundary conditions are presented.
  
  PubDate: 2013-04-17T00:36:03Z
An improved meshless method with almost interpolation property for isotropic heat conduction problems
- Abstract: Publication date: May 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 5
  
  In the paper an improved element free Galerkin method is presented for heat conduction problems with heat generation and spatially varying conductivity. In order to improve computational efficiency of meshless method based on Galerkin weak form, the nodal influence domain of meshless method is extended to have arbitrary polygon shape. When the dimensionless size of the nodal influence domain approaches 1, the Gauss quadrature point only contributes to those nodes in whose background cell the Gauss quadrature point is located. Thus, the bandwidth of global stiff matrix decreases obviously and the node search procedure is also avoided. Moreover, the shape functions almost possess the Kronecker delta function property, and essential boundary conditions can be implemented without any difficulties. Numerical results show that arbitrary polygon shape nodal influence domain not only has high computational accuracy, but also enhances computational efficiency of meshless method greatly.
  
  PubDate: 2013-04-13T00:34:36Z
Finite integration method for nonlocal elastic bar under static and dynamic loads
- Abstract: May 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 5
  
  The finite integration method is proposed in this paper to approximate solutions of partial differential equations. The coefficient matrix of this finite integration method is derived and its superior accuracy and efficiency is demonstrated by making comparison with the classical finite difference method. For illustration, the finite integration method is applied to solve a nonlocal elastic straight bar under different loading conditions both for static and dynamic cases in which Laplace transform technique is adopted for the dynamic problems. Several illustrative examples indicate that high accurate numerical solutions are obtained with no extra computational efforts. The method is readily extendable to solve more complicated problems of nonlocal elasticity.
  
  PubDate: 2013-04-05T09:33:56Z
Degenerate scale for the Laplace problem in the half-plane; Approximate logarithmic capacity for two distant boundaries
- Abstract: May 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 5
  
  We study the problem of finding a degenerate scale for Laplace equation in a half-plane. It is shown that if the boundary condition on the line bounding the half-plane is of Dirichlet type, there is no degenerate scale. In the case of a boundary condition of Neumann type, there is a degenerate scale, which is shown to be the same as the one for the symmetrized contour with respect to the boundary line in the full plane. We show next a formula for obtaining the degenerate scale of a domain made of two parts, when the components are far from each other, which allows to obtain the degenerate scale for the symmetrized contour. Finally, we give some examples of evaluation of the degenerate scale both by an approximate formula and by a numeric evaluation using integral methods. These evaluations show that the approximate solution is still valid for small values of the distance between symmetrized contours.
  
  PubDate: 2013-04-01T00:35:10Z
Boundary element simulation of inviscid flow around an oscillatory foil with vortex sheet
- Abstract: May 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 5
  
  The dynamic performance of a rigid foil with harmonic vertical and rotational motions in fluid flow has been studied through velocity potential theory. A boundary element based time stepping scheme is introduced to simulate the flow around the foil and the vortex wake. The body surface condition is satisfied on the exact foil surface and the motion and deformation of the wake sheet shed at the trailing edge is tracked. Kelvin condition is satisfied and a Kutta condition for the unsteady motion is proposed to circumvent the singularity at the trailing edge. Point vortex, which is reduced from wake vortex dipole, is introduced to approximate the vorticity. The performance of foil NACA0012 with harmonic vertical and rotational motions are studied extensively; the propulsion/swimming mode, energy harvesting mode and the flying mode are analysed in detail.
  
  PubDate: 2013-04-01T00:35:10Z
A new infinite boundary element formulation combined to an alternative multi-region technique
- Abstract: May 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 5
  
  The main objective of this work is to obtain an efficient three-dimensional boundary element (BE) formulation for the simulation of layered solids. This formulation is obtained by combining an alternative multi-region technique with an infinite boundary element (IBE) formulation. It is demonstrated that such a combination is straightforward and can be easily programmed. Kelvin fundamental solutions are employed, considering the static analysis of isotropic and linear-elastic domains. Establishing relations between the displacement fundamental solutions of the different domains, the alternative technique used in this paper allows analyzing all domains as a single solid, not requiring equilibrium or compatibility equations. It was shown in a previous paper that this approach leads to a smaller system of equations when compared to the usual multi-region technique and the results obtained are more accurate. The two-dimensionally mapped infinite boundary element (IBE) formulation here used is based on a triangular BE with linear shape functions. One advantage of this formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result. The use of IBEs improves the advantages of the alternative multi-region technique, contributing for the low computational cost and allowing a considerable mesh reduction. Furthermore, the results show good agreement with the ones given in other works, confirming the accuracy of the presented formulation.
  
  PubDate: 2013-04-01T00:35:10Z
Elastodynamic problems by meshless local integral method: Analytical formulation
- Abstract: May 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 5
  
  In this paper, analytical forms of integrals in the meshless local integral equation method in the Laplace space are derived and implemented for elastodynamic problems. The meshless approximation based on the radial basis function (RBF) is employed for implementation of displacements. A weak form of governing equations with a unit test function is transformed into local integral equations. A completed set of the local boundary integrals are obtained in closed form. As the closed form of the local boundary integrals are obtained, there are no domain or boundary integrals to be calculated numerically. Several examples including dynamic fracture mechanics problems are presented to demonstrate the accuracy of the proposed method in comparison with analytical solutions and the boundary element method.
  
  PubDate: 2013-03-28T01:32:05Z
A Kriging interpolation-based boundary face method for 3D potential problems
- Abstract: May 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 5
  
  In this paper, a new implementation of the boundary face method (BFM) is presented and developed for solving 3D potential problems. The BFM is implemented directly based on the boundary representation data structure for geometry modeling to eliminate geometry errors. This study combines the BFM with Kriging interpolation method and the corresponding formulae are derived. The Kriging interpolation is applied instead of the traditional moving least squares (MLS) approximation to overcome the lack of Kronecker delta function property, then essential boundary conditions can be imposed directly and easily. Several numerical examples with different geometry and boundary conditions are presented to illustrate the performance of the present method. The comparisons of accuracy between MLS approximation and Kriging interpolation are studied.
  
  PubDate: 2013-03-28T01:32:05Z
Editorial Board
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  PubDate: 2013-03-24T01:32:51Z
Efficient evaluation of weakly/strongly singular domain integrals in the BEM using a singular nodal integration method
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  In many analyses of engineering problems based on boundary element methods, a large number of regular and/or singular domain integrals must be accurately evaluated over a single domain. Evaluation of such domain integrals is very time-consuming and is frequently the main source of errors and loss of accuracy in the solutions. Previous efforts have been constantly made in order to facilitate or overcome such shortcomings. In this article, we propose novel and efficient approaches in the framework of Cartesian transformation method (CTM) and the radial integration method (RIM) that can be used for fast evaluation of numerous weakly/strongly singular two-dimensional domain integrals over a single domain. The domain integrals essentially are expressed in terms of some coefficient matrices and vectors, most of which are independent of the integrand of the domain integrals and are dependent only on the geometry. Several examples for the evaluation of weakly/strongly singular domain integrals and two examples for the flow field analysis in micro-channels are presented and the accuracy and convergence of the proposed approaches are investigated.
  
  PubDate: 2013-03-16T01:32:40Z
The MLPG analyses of large deflections of magnetoelectroelastic plates
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  The von Karman plate theory of large deformations is applied to express the strains, which are then used in the constitutive equations for magnetoelectroelastic solids. The in-plane electric and magnetic fields can be ignored for plates. A quadratic variation of electric and magnetic potentials along the thickness direction of the plate is assumed. The number of unknown terms in the quadratic approximation is reduced, satisfying the Maxwell equations. Bending moments and shear forces are considered by the Reissner–Mindlin theory, and the original three-dimensional (3D) thick plate problem is reduced to a two-dimensional (2D) one. A meshless local Petrov–Galerkin (MLPG) method is applied to solve the governing equations derived based on the Reissner–Mindlin theory. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the centre of a circle surrounding it. The weak form on small subdomains with a Heaviside step function as the test function is applied to derive the local integral equations. After performing the spatial MLS approximation, a system of algebraic equations for certain nodal unknowns is obtained. Both stationary and time-harmonic loads are then analyzed numerically.
  
  PubDate: 2013-03-16T01:32:40Z
A gradient free integral equation for diffusion–convection equation with variable coefficient and velocity
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  In this paper a boundary-domain integral diffusion–convection equation has been developed for problems of spatially variable velocity field and spatially variable coefficient. The developed equation does not require a calculation of the gradient of the unknown field function, which gives it an advantage over the other known approaches, where the gradient of the unknown field function is needed and needs to be calculated by means of numerical differentiation. The proposed equation has been discretized by two approaches—a standard boundary element method, which features fully populated system matrix and matrices of integrals and a domain decomposition approach, which yields sparse matrices. Both approaches have been tested on several numerical examples, proving the validity of the proposed integral equation and showing good grid convergence properties. Comparison of both approaches shows similar solution accuracy. Due to nature of sparse matrices, CPU time and storage requirements of the domain decomposition are smaller than those of the standard BEM approach.
  
  PubDate: 2013-03-16T01:32:40Z
Identification of elastic orthotropic material parameters by the scaled boundary finite element method
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  This paper focuses on a parameter identification algorithm of two-dimensional orthotropic material bodies. The identification inverse problem is formulated as the minimization of an objective function representing differences between the measured displacements and those calculated by using the scaled boundary finite element method (SBFEM). In this novel semi-analytical method, only the boundary is discretized yielding a large reduction of solution unknowns, but no fundamental solution is required. As sufficiently accurate solutions of direct problems are obtained from the SBFEM, the sensitivity coefficients can be calculated conveniently by the finite difference method. The Levenberg–Marquardt method is employed to solve the nonlinear least squares problem attained from the parameter identification problem. Numerical examples are presented at the end to demonstrate the accuracy and efficiency of the proposed technique.
  
  PubDate: 2013-03-16T01:32:40Z
Optimization, conditioning and accuracy of radial basis function method for partial differential equations with nonlocal boundary conditions—A case of two-dimensional Poisson equation
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  Various real-world processes usually can be described by mathematical models consisted of partial differential equations (PDEs) with nonlocal boundary conditions. Therefore, interest in developing computational methods for the solution of such nonclassical differential problems has been growing fast. We use a meshless method based on radial basis functions (RBF) collocation technique for the solution of two-dimensional Poisson equation with nonlocal boundary conditions. The main attention is paid to the influence of nonlocal conditions on the optimal choice of the RBF shape parameters as well as their influence on the conditioning and accuracy of the method. The results of numerical study are presented and discussed.
  Highlights ► The 2D Poisson equation with nonlocal boundary conditions (NBCs) is solved using RBF method. ► Variability of RBF optimal shape parameters respect to parameters of NBCs is investigated. ► The accuracy of results is quite high if optimal or at least near-optimal shape parameters are used. ► The influence of NBCs on the conditioning and accuracy of the method is analyzed. ► The results of numerical study with several test examples are presented and discussed.
  
  PubDate: 2013-03-16T01:32:40Z
Cauchy problems of Laplace's equation by the methods of fundamental solutions and particular solutions
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  The Cauchy problems of Laplace's equation are ill-posed with severe instability. In this paper, numerical solutions are solicited by the method of fundamental solutions (MFS) and the method of particular solutions (MPS). We focus on the analysis of the MFS, and derive the bounds of errors and condition numbers. The analysis for the MPS can also be obtained similarly. Numerical experiments and comparisons are reported for the Cauchy and Dirichlet problems by the MPS and the MFS. The Cauchy noise data and the regularization are also adopted in numerical experiments. Both the MFS and the MPS are effective to Cauchy problems. The MPS is superior in accuracy and stability; but the MFS owns simplicity of algorithms, and earns flexibility for a wide range of applications, such as Cauchy problems. These conclusions also coincide with [37]. The basic analysis of error and stability is explored in this paper, and applied to the Cauchy data. There are many reports on numerical Cauchy problems, see the survey paper in [12]; most of them are of computational aspects. The strict analysis of this paper may, to a certain degree, fill up the existing gap between theory and computation of Cauchy problems by the MFS and the MPS. Moreover, comprehensive analysis and compatible computation are two major characteristics of this paper, which may enhance the study of numerical Cauchy problems forward to a higher and advanced level.
  
  PubDate: 2013-03-16T01:32:40Z
A 3D hybrid BE–FE solution to the forward problem of electrical impedance tomography
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  This paper presents a three dimensional (3D) hybrid boundary element–finite element (BE–FE) method solution to the electrical impedance tomography (EIT) forward problem. EIT is a method to find the distribution of electrical conductivity within an object through injecting current on surface electrodes placed on the object, and measuring the distribution of potential around the object. Existing 3D models are based on the finite element (FE) method and the boundary element (BE) method. In this paper, a hybrid BE–FE method approach is demonstrated for modeling the forward problem of EIT. Such a hybrid BE–FE technique combines strengths of FE and BE methods by dividing the regions into some homogeneous BE regions and heterogeneous FE regions. To validate numerical results, a homogenous test problem is solved analytically for the electrical potential. A cylindrical model of human thorax is studied. Results obtained for this model from BE, FE, and hybrid BE–FE methods with three different meshes and two different electrode placement strategies are compared.
  
  PubDate: 2013-03-16T01:32:40Z
The boundary element method applied to orthotropic shear deformable plates
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  This work presents a formulation for thick plates following Mindlin theory. The fundamental solution takes into account an assumed displacement distribution on the thickness, and was derived by means of Hormander operator and the Radon transform. To compute the inverse Radon transform of the fundamental solution, some numerical integrals need to be computed. How these integrations are carried out is a key point in the performance of the boundary element code. Two approaches to integrate fundamental solutions are discussed. Integral equations are obtained using Betti's reciprocal theorem. Domain integrals are exactly transformed into boundary integrals by the radial integration technique.
  
  PubDate: 2013-03-16T01:32:40Z
Current distribution in circular planar coil
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  The current distribution over the cross section of a planar circular coil is calculated by a Fredholm integral equation technique. An external applied current source is driving the current. The integral equation technique is applied over a two-dimensional cross section of the coil while considering infinitesimally thin windings. The coil windings are divided into equally sized one-dimensional elements. The resulting algebraic system is solved numerically. For low frequencies, the current distribution follows the 1/r behavior. As the frequency increases, the influence of the proximity effect is taken into account. Different cases are studied examining the intensity of these effects on the current distribution as the number of turns, the width of the windings, and the spacing between the turns are varying.
  
  PubDate: 2013-03-16T01:32:40Z
Leakage through a permeable capillary tube into a poroelastic tumor interstitium
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  Fluid flow through a permeable circular tube embedded in an infinite poroelastic ambient medium is studied as a model of blood flow through the vasculature of a solid tumor. The flow through the interstitium is described by Darcy's law for an isotropic porous medium with a pressure-dependent permeability, the flow along the tube is described by Poiseuille's law, and the extravasation flux across the tube surface is described by Starling's law involving the transmural pressure. Kirchhoff's transformation is applied to derive Laplace's equation for a modified interstitial pressure. Given the arterial, venous, and ambient pressures, the problem is formulated in terms of a coupled system of integral, differential, and algebraic equations for the vascular and interstitial pressures. The overall hydrodynamics is described in terms of hydraulic conductivity coefficients for the arterial, venous, and extravasation flow rates. Solutions obtained by a boundary-element method confirm that interstitium dilatation promotes the rate of extravasation.
  
  PubDate: 2013-03-16T01:32:40Z
Meshless solution of axisymmetric convection–diffusion equation: A comparison between two alternative RBIE implementations
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  The radial basis integral equation (RBIE) method was derived using two different approaches to solve the steady-state axisymmetric convection–diffusion equation. In the first approach (Approach 1), the integral representation of the governing equation was derived using the Laplace fundamental solution in the axisymmetric coordinates. In the second approach (Approach 2), the Laplace fundamental solution in two-dimensional Cartesian coordinates was used at the expense of an additional pseudo-source term in the domain integrals. The domain integrals were dealt with using the cell integration technique. The Approach 1 was found to produce results that were more accurate than the Approach 2. However, the CPU time requirement was higher in the Approach 1 than in the Approach 2.
  
  PubDate: 2013-03-16T01:32:40Z
A coupled BEM-stiffness matrix approach for analysis of shear deformable plates on elastic half space
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  In this paper, a new direct Boundary Element Method (BEM) is presented to solve plates on elastic half space (EHS). The considered BEM is based on the formulation of Vander Weeën for the shear deformable plate bending theory of Reissner. The considered EHS is the infinite EHS of Boussinesq–Mindlin or the finite EHS (with rigid end layer) of Steinbrenner. The multi-layered EHS is also considered. In the present formulation, the soil stiffness matrix is computed. Hence, this stiffness matrix is directly incorporated inside the developed BEM. Several numerical examples are considered and results are compared against previously published analytical and numerical methods to validate the present formulation.
  
  PubDate: 2013-03-16T01:32:40Z
Using the iterated sinh transformation to evaluate two dimensional nearly singular boundary element integrals
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  Recently, sinh transformations have been proposed to evaluate nearly weakly singular integrals which arise in the boundary element method. These transformations have been applied to the evaluation of nearly weakly singular integrals arising in the solution of Laplace's equation in both two and three dimensions and have been shown to evaluate the integrals more accurately than existing techniques. More recently, the sinh transformation was extended in an iterative fashion and shown to evaluate one dimensional nearly strongly singular integrals with a high degree of accuracy. Here the iterated sinh technique is extended to evaluate the two dimensional nearly singular integrals which arise as derivatives of the three dimensional boundary element kernel. The test integrals are evaluated for various basis functions and over flat elements as well as over curved elements forming part of a sphere. It is found that two iterations of the sinh transformation can give relative errors which are one or two orders of magnitude smaller than existing methods when evaluating two dimensional nearly strongly singular integrals, especially with the source point very close to the element of integration. For two dimensional nearly weakly singular integrals it is found that one iteration of the sinh transformation is sufficient.
  
  PubDate: 2013-03-16T01:32:40Z
Boundary node method based on parametric space for 2D elasticity
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  This paper presents a new implementation of the boundary node method (BNM) for 2D elasticity based on the parametric space. The BNM couples the boundary integral equations (BIE) with the moving least square (MLS) approximation, which retains the dimensionality advantage and the meshless attribute. However, the BNM is performed on an approximate geometry by MLS fitting and geometry errors are inevitable. In this paper, the BNM is implemented directly on the boundary representation (B-rep) data structure used in most CAD packages for geometry modeling, which named the boundary line method (BLM). The integration quantities, such as the coordinates of Gauss points, the outward normal and Jacobian are calculated directly from the lines represented in a parametric form which are the same as the real boundary, and thus no errors will be introduced. A new integration scheme has been developed to deal with weakly singular integrals easily. Numerical results presented in this paper show excellent accuracy and high convergence rate.
  
  PubDate: 2013-03-08T01:33:12Z
Stability estimate on meshless unsymmetric collocation method for solving boundary value problems
- Abstract: April 2013
  Publication year: 2013
  Source:Engineering Analysis with Boundary Elements, Volume 37, Issue 4
  
  We investigate in this paper the stability of meshless unsymmetric collocation method by using radial basis functions for solving boundary value problems under Dirichlet, Neumann, or Robin boundary conditions. Using the monotonically decreasing property of the Fourier transforms of RBFs, we prove that the lowest bound of the resultant linear system depends on the separation distance of distinct centers and the decreasing order of the RBFs. Stability estimates can then be obtained for the meshless unsymmetric collocation method. For verification, several numerical examples are constructed to verify the theoretical results.
  
  PubDate: 2013-03-08T01:33:12Z