Engineering Analysis with Boundary Elements [3 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 0955-7997 Published by Elsevier [2575 journals] [SJR: 1.22] [H-I: 39] |
- A meshless interpolating Galerkin boundary node method for Stokes flows
- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Xiaolin Li
Combining an improved interpolating moving least-square (IIMLS) scheme and a variational formulation of boundary integral equations, a symmetric and boundary-only meshless method, which is called the interpolating Galerkin boundary node method (IGBNM), is developed in this paper for 2D and 3D Stokes flow problems. The IIMLS is used to form shape functions with delta function property. So unlike the Galerkin boundary node method (GBNM), the IGBNM is a direct numerical method in which the basic unknown quantity is the real solution of nodal variables. Besides, to obtain uniqueness of unknown boundary functions and to retain symmetry of system matrices, a Lagrange multiplier is introduced and then a variational formulation with side conditions is gained. Consequently, in the IGBNM, boundary conditions can be applied directly and easily, and the resulting system matrices are symmetric. Thus, the IGBNM gives greater computational precision than the GBNM. The numerical formulae are valid for 2D and 3D Stokes flows and also valid for both interior and exterior problems simultaneously. The capability of the IGBNM is illustrated and assessed by some numerical examples.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Comment on “A fully nonlinear implicit model for wave interactions
with submerged structures in forced or free motion” by Guerber et
al. (2012)- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Lixian Wang , Hui Tang
This paper reports a problem in the simulation of transient oscillation of a freely heaving cylinder appearing in Guerber et al. (2012)’s recent paper A fully nonlinear implicit model for wave interactions with submerged structures in forced or free motion. The problem is confirmed through a comparison study using an independent two-dimensional fully nonlinear numerical wave tank. The reason may come from the part solving the acceleration potential. In the end, the influence of this problem to the other results presented in the same paper is assessed.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Three-dimensional heat conduction analysis of inhomogeneous materials by
triple-reciprocity boundary element method- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Yoshihiro Ochiai
Homogeneous heat conduction can be easily analyzed by the boundary element method. However, domain integrals are generally necessary to solve the heat conduction problem in non-homogeneous and functionally gradient materials. This paper shows that the three-dimensional heat conduction problem in non-homogeneous and functionally gradient materials can be solved approximately without the use of a domain integral by the triple-reciprocity boundary element method. In this method, the distribution of domain effects is interpolated using integral equations. A new computer program is developed and applied to several problems.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- The numerical solution of Cahn–Hilliard (CH) equation in one, two
and three-dimensions via globally radial basis functions (GRBFs) and
RBFs-differential quadrature (RBFs-DQ) methods- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Mehdi Dehghan , Vahid Mohammadi
The present paper is devoted to the numerical solution of the Cahn–Hilliard (CH) equation in one, two and three-dimensions. We will apply two different meshless methods based on radial basis functions (RBFs). The first method is globally radial basis functions (GRBFs) and the second method is based on radial basis functions differential quadrature (RBFs-DQ) idea. In RBFs-DQ, the derivative value of function with respect to a point is directly approximated by a linear combination of all functional values in the global domain. The main aim of this method is the determination of weight coefficients. GRBFs replace the function approximation into the partial differential equation directly. Also, the coefficients matrix which arises from GRBFs is very ill-conditioned. The use of RBFs-DQ leads to the improvement of the ill-conditioning of interpolation matrix RBFs. The boundary conditions of the mentioned problem are Neumann. Thus, we use DQ method directly on the boundary conditions, which easily implements RBFs-DQ on the irregular points and regions. Here, we concentrate on Multiquadrics (MQ) as a radial function for approximating the solution of the mentioned equation. As we know this radial function depends on a constant parameter called shape parameter. The RBFs-DQ can be implemented in a parallel environment to reduce the computational time. Moreover, to obtain the error of two techniques with respect to the spatial domain, a predictor–corrector scheme will be applied. Finally, the numerical results show that the proposed methods are appropriate to solve the one, two and three-dimensional Cahn-Hilliard (CH) equations.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- 3D numerical modelling of acoustic horns using the method of fundamental
solutions- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): L. Godinho , P. Amado-Mendes , J. Carbajo , J. Ramis-Soriano
In the present work, a three-dimensional (3D) formulation based on the method of fundamental solutions (MFS) is applied to the study of acoustic horns. The implemented model follows and extends previous works that only considered two-dimensional and axisymmetric horn configurations. The more realistic case of 3D acoustic horns with symmetry regarding two orthogonal planes is addressed. The use of the domain decomposition technique with two interconnected sub-regions along a continuity boundary is proposed, allowing for the computation of the sound pressure generated by an acoustic horn installed on a rigid screen. In order to reduce the model discretization requirements for these cases, Green’s functions derived with the image source methodology are adopted, automatically accounting for the presence of symmetry conditions. A strategy for the calculation of an optimal position of the virtual sources used by the MFS to define the solution is also used, leading to improved reliability and flexibility of the proposed method. The responses obtained by the developed model are compared to reference solutions, computed by well-established models based on the boundary element method. Additionally, numerically calculated acoustic parameters, such as directivity and beamwidth, are compared with those evaluated experimentally.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Adaptive numerical integration in Element-Free Galerkin methods for
elliptic boundary value problems- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Grand Roman Joldes , Adam Wittek , Karol Miller
In this paper we present a new numerical integration scheme for Element-Free Galerkin (EFG) methods used for solving elliptic problems. Integration points are distributed within the problem domain using an adaptive procedure, based on the characteristics of the shape functions. Existing numerical integration schemes for EFG methods do not offer any control over the integration accuracy. We devise a method of distributing the integration points which allows control over the integration accuracy for all elements of the stiffness matrix, while reducing the number of integration points required. The performance of the procedure is demonstrated on test problems in 1D and 2D.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Editorial Board
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: January 2015
- The numerical solution of the two–dimensional sinh-Gordon equation
via three meshless methods- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Mehdi Dehghan , Mostafa Abbaszadeh , Akbar Mohebbi
In this paper three numerical techniques are proposed for solving the nonlinear sinh-Gordon equation. Firstly, we obtain a time discrete scheme then we use the radial basis functions (RBFs) collocation based on Kansa׳s approach, RBF-pseudospectral (PS) technique and moving least squares (MLS) methods to approximate the spatial derivatives. The aim of this paper is to show that the meshless methods based on the RBFs using collocation approach and MLS are suitable for the treatment of the nonlinear partial differential equations and also we compare the mentioned methods in terms of condition number of coefficient matrix and absolute value of error. Also, several test problems are given that show the acceptable accuracy and efficiency of the proposed schemes.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- An adaptive element subdivision method for evaluation of weakly singular
integrals in 3D BEM- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Jianming Zhang , Chenjun Lu , Xiuxiu Zhang , Guizhong Xie , Yunqiao Dong , Yuan Li
A general adaptive element subdivision method is presented for the numerical evaluation of weakly singular integrals in three-dimensional boundary element analyses. In our method, the element is subdivided into a number of patches through a sequence of spheres with decreasing radius. The patches obtained by our method are automatically refined as they approach the source point. Consequently, each patch is “good” in shape and size for standard Gaussian quadrature, and hence high accuracy can be achieved by a small number of Gaussian sample points. Our method is applicable to any shape of element with arbitrary location of the source point inside, at vertices or on edges of the element. Numerical examples are presented for planar and curved surface elements. The results demonstrate that our method can provide much better accuracy and efficiency than the conventional subdivision method.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- The analog equation integral formulation for plane piezoelectric media
- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): George S.A. Fam , Youssef F. Rashed , John T. Katsikadelis
In this paper, the two-dimensional piezoelectricity is modelled using a boundary integral formulation based on its corresponding Analog Equation. The problem is transformed into three uncoupled Poisson׳s equations with unknown fictitious body forces terms. The multiquadric radial basis function is used to approximate the fictitious body forces in the particular solutions. The problem is solved by satisfying the governing differential operator and the boundary conditions. A scaling process is used to enhance the numerical behaviour of the obtained system of equations. The formulation is mathematically simpler than formerly proposed BEM formulations and its validity, applicability and accuracy are demonstrated through various numerical examples.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Complexity and accuracy of the grid-based direct-volume integration BEM
for quasilinear problems- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Yani Deng , Wenjing Ye , L.J. Gray
In order for the boundary element method to be competitive when compared with other methods for solving nonlinear problems, the volume integral must be evaluated accurately and efficiently. The recently proposed cell-based volume integration method evaluates the volume integral on uniform Cartesian cells and therefore avoids volume discretization of the problem domain. However, this method requires the solutions of an additional integral equation; hence its efficiency must be examined. Moreover, the accuracy of the method for the boundary integral analysis of nonlinear problems needs to be studied. In this paper, we present the complexity and accuracy analysis of the BEM coupled with the cell-based volume integration method (herein termed as the grid-based direct-volume integration BEM), for solving quasilinear problems. Various numerical examples are employed to verify the theoretical findings.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Reliability analysis of Reissner plate bending problems by stochastic
spline fictitious boundary element method- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Cheng Su , Jia Xu
In this paper the stochastic spline fictitious boundary element method (SFBEM) is presented for reliability analysis of Reissner plate bending problems in conjunction with the first-order reliability method (FORM). As a modified method for the conventional indirect boundary element method, SFBEM has been proved to be accurate and efficient in deterministic analyses. For the purpose of structural reliability analysis, SFBEM is introduced during the iteration process performed in the FORM to obtain the required values of structural responses and their derivatives with respect to the random variables considered. In particular, the gradient formulation for the Reissner plate bending problem has been derived using SFBEM in the current study. The present approach is validated with several numerical examples and a good agreement with solutions of the Monte Carlo simulation is observed.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- A general algorithm for the numerical evaluation of domain integrals in 3D
boundary element method for transient heat conduction- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Yunqiao Dong , Jianming Zhang , Guizhong Xie , Chenjun Lu , Lei Han , Pan Wang
In this paper, a general algorithm is proposed for evaluating domain integrals in 3D boundary element method. These integrals are involved in the solution of transient heat conduction problems when using a time-dependent boundary integral equation method named as pseudo-initial condition method. Accurate evaluation of domain integrals is of great importance to the successful implementation of this method. However, as the time-dependent kernel in the domain integral is close to singular when small time step is used, a straightforward application of Gaussian quadrature may produce large errors, and thus lead to instability of the analysis. To overcome this drawback, a coordinate transformation coupled with an element subdivision technique is presented. The coordinate transformation makes the integrand of domain integral more smooth; meanwhile, the element subdivision technique considers the relations between the size of the element and the time step. With the proposed method, more Gaussian points are shifted towards the source point, thus more accurate results can be obtained. Numerical examples demonstrate that the calculation accuracy of domain integrals and the stability of analysis for transient heat conduction problems are improved by the proposed algorithm when small time step is used.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Two-step Taylor-characteristic-based MLPG method for fluid flow and heat
transfer applications- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Vali Enjilela , Ali Arefmanesh
A stabilized two-step Taylor-characteristic-based meshless local Petrov–Galerkin (2S-TCBMLPG) method is proposed to solve laminar fluid flow and heat transfer problems using the primitive variables form of the Navier–Stokes equations. In this method, a two-step Taylor-characteristic-based scheme is employed in order to obtain stable solutions for the field variables at high Peclet and Reynolds numbers. The test function in the weighted-residual forms of the governing equations is chosen to be unity, and the field variables are approximated using the moving least-squares (MLS) interpolations. Five test cases, namely, Poiseuille flow between parallel plates, lid-driven cavity flow, Couette flow between two eccentric cylinders, non-isothermal flow past a bundle of tubes, and mixed convection heat transfer in a differentially-heated square cavity, are solved in order to examine the effectiveness of the proposed method. Very good agreements exist between the results obtained using the proposed meshless method with those obtained using the conventional methods for the considered test cases. Close agreements among the appropriate results demonstrates a step forward toward further development of stabilized algorithms for solving the primitive variables form of the Navier–Stokes equations by the MLPG method.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- A boundary element formulation for the heat equation with dissipative and
heat generation terms- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Roberto Pettres , Luiz Alkimin de Lacerda , José Antonio Marques Carrer
This article presents a formulation of the Boundary Element Method (BEM) for the study of heat diffusion in isotropic and homogeneous media. The proposed formulation has a time independent fundamental solution obtained from the two-dimensional Laplace equation. Consequently, the formulation is called D-BEM since it has domain integrals in the basic integral equation. The first order time derivative that appears in the integral equations is approximated by a backward finite difference scheme. Internal dissipative and heat generation terms are considered in the analyses. The results from the numerical model are compared with the available analytical solutions. The correlation estimator R2 is employed to validate the numerical model and to demonstrate the accuracy of the proposed formulation.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Neumann problems of Laplace׳s equation in circular domains with
circular holes by methods of field equations- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Ming-Gong Lee , Zi-Cai Li , Hung-Tsai Huang , John Y. Chiang
For Laplace׳s equation in circular domains with circular holes, the null field method (NFM) is proposed by Chen with his groups. In NFM, the fundamental solutions (FS) with the exterior field nodes to the solution domain are used in the Green formulas, where the FS are replaced by the infinite expansion series. The explicit algebraic equations are derived and reported in Li et al. (2012) [20]. The explicit algebraic equations are essential not only to practical computation, but also to the algorithm analysis, such as algorithm singularity, error and stability analysis. So far, the study of the NFM is confined to the Dirichlet problems (i.e., the Dirichlet boundary value problems) by the first kind NFM. This paper is devoted mainly to the Neumann problems (i.e., the Neumann boundary value problems) of Laplace׳s equation by the second kind NFM. When the field nodes are pulled to the domain boundary, this special (i.e., the optimal) NFM is equivalent to the interior field method (IFM) (Huang et al., 2013) [16]. In fact, the IFM results from the Trefftz method, where the interior field solutions are chosen to satisfy the Neumann boundary conditions. For simplicity, we call the IFM and the specific NFM as the method of field equations (MFEs). For the Neumann problems, there do not exist the degenerate scale problems, but the pseudo-singularity may be encountered if the numbers of the unknown coefficients and the collocation equations are exactly the same. To bypass this pseudo-singularity, the overdetermined system and the truncated singular value decomposition (TSVD) are solicited, to restore good stability. Interestingly, the first kind MFE can also be used for the Neumann problems. Numerical experiments with comparisons are carried out by two kinds of MFEs. The stability is made for two kinds of MFEs, and a theoretical argument is provided to verify the effectiveness of the overdetermined system. In summary, two kinds of MFEs are effective for solving the Neumann problems, and their numerical performances are excellent.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- RBF-based meshless method for large deflection of elastic thin plates on
nonlinear foundations- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Mohammed M. Hussein Al-Tholaia , Husain Jubran Al-Gahtani
A simple, yet efficient method for the analysis of thin plates resting on nonlinear foundations and undergoing large deflection is presented. The method is based on collocation with the multiquadric radial basis function. In order to address the in-plane edge conditions, two formulations, namely w–F and u–v–w are considered for the movable and immovable edge conditions, respectively. The resulted coupled nonlinear equations for the two cases are solved using an incremental-iterative procedure. Three foundation models are considered, namely Winkler, nonlinear Winkler and Pasternak. The accuracy and efficiency of the method is verified through several numerical examples.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Bending of a porous piezoelectric cylinder under a thermal load
- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): J. Sladek , V. Sladek , P. Stanak , S. Hrcek
A meshless method based on the local Petrov–Galerkin approach is proposed to analyze bending of a porous piezoelectric cylinder under thermal loading. Constitutive equations for porous piezoelectric materials possess a coupling between mechanical displacements and electric intensity vectors for solid and fluid phases. The influence of thermal expansion coefficients in solid and fluid phases on the plate deflection and on the induced electric potential is investigated via the local integral equation method developed in this paper. The spatial variation of displacements and electric potentials for both phases is approximated by the moving least-squares (MLS) scheme. The heat conduction equation is considered as uncoupled with respect to the mechanical and electrical fields.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- An algorithm with m-step residual history for solving linear equations:
Data interpolation by a multi-shape-factors RBF- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Chein-Shan Liu
We expand the current descent direction in terms of the current residual vector and the previous m-step residual vectors to solve n-dimensional linear equations. The m+1 expansion coefficients with m ≪ n are determined explicitly through the solutions of two optimization problems, such that the resulting double optimal m-step algorithm (DOMSA) in the present paper is very time saving. The DOMSA is proven absolutely convergent step-by-step, and the estimations of residual errors are provided. We propose a new concept of multi-shape factors used in the RBF data interpolation, whose linear equations can be effectively solved by the DOMSA.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Numerical study of the characteristics of wave–wave interactions in
a multiphase wave field- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): Ruey-Syan Shih , Wen-Kai Weng
This paper presents a numerical study of wave–wave interactions in multiphase wave fields using the boundary element method (BEM). Variations in wave height distributions, spatial velocities, and particle trajectories in multi-component wave generation were investigated using a 2D numerical wave tank, which models the interaction between an incoming wave and a reflected wave. This study examined wave–wave interactions in various wave cases, and explored the interactions and variations of velocity fields in various wave periods, in particular, waves with greater discrepancies. Surf beats in the surf zone are the main cause of the cross-shore motion, and induce the generation of high-frequency energy, which is transferred to high-frequency harmonic waves. This study modeled oscillations caused by surf beats and back swash, generated by high-frequency, multi-phase reflected waves, to investigate the deformation of wave profiles, velocity fields, and the movement of particle path-lines. The results revealed that incident waves are affected by high-frequency reversed waves that propagate against them from the other side of the flume, reducing average wave height in the whole area, but become less affected with increasing diversity between the two wave frequencies and/or wave height.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Multi-scale modelling for bending analysis of heterogeneous plates by
coupling BEM and FEM- Abstract: Publication date: February 2015
Source:Engineering Analysis with Boundary Elements, Volume 51
Author(s): G.R. Fernandes , J.J.C. Pituba , E.A de Souza Neto
A multi-scale modelling for analyzing the bending problem of plates composed of heterogeneous materials is presented. The macro-continuum is modelled by a non-linear formulation of the boundary element method (BEM) taking into account the consistent tangent operator (CTO). The micro-scale is represented by the RVE (representative volume element) being its equilibrium problem solved by a finite element formulation that takes into account the Hill-Mandel Principle of Macro-Homogeneity while the volume averaging hypothesis of the strain and stress tensors is used to make the micro-to-macro transition. Three different boundary conditions are imposed over the RVE: (i) linear displacements, (ii) periodic displacement fluctuation and (iii) uniform boundary tractions. The material behaviour is governed by the Von Mises elasto-plastic criterion although the proposed multi-scale model can be used with any other non-linear model. Numerical examples are presented to illustrate the main features and scope of the proposed formulation.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: February 2015
- Cracked plate analysis with the dual boundary element method and
Williams׳ eigenexpansion- Abstract: Publication date: March 2015
Source:Engineering Analysis with Boundary Elements, Volume 52
Author(s): J. Caicedo , A. Portela
This paper provides a numerical verification that the singular term of Williams׳ series eigenexpansion can be used as a singular solution, valid in the neighborhood of each crack tip, in a single-region dual boundary element analysis of two-dimensional piece-wise flat multi-cracked plates, either with edge or internal cracks, in mixed-mode deformation, as an intermediate and necessary research step towards the implementation of the singularity subtraction technique. The dual equations are the displacement and traction boundary integral equations which allow the solution of general mixed-mode crack problems in a single-region boundary-element analysis. The singularity subtraction technique is a regularization procedure that uses a singular particular solution of the crack problem to introduce the stress intensity factors as additional primary unknowns in the dual boundary element method. Its implementation depends on the availability of closed-form singular solutions relative to a single-region of a general multi-cracked plate. In this paper, Williams׳ series eigenexpansion, which is valid for a semi-infinite edge crack, is used to compute the stress intensity factors, for both cases of edge and internal cracks, for each deformation mode. The singular term of the expansion is used as a singular particular solution in the neighborhood of each edge and internal crack tip. Collocation of this term, at a single internal point near the crack tip, is carried out to compute the stress intensity factors in post-processing. Several cracked plates were analyzed with this technique in order to assess the validity of using the singular term of Williams׳ series eigenexpansion for the regularization of the elastic field in a single-region dual boundary element analysis of a general piece-wise multi-cracked plate. The results obtained in this work are in perfect agreement with those obtained with the dual boundary element method, through the J-integral technique, and other published results for both cases of the edge and internal piecewise-flat cracks. Hence, it can be concluded that, in the singularity subtraction technique of the dual boundary element analysis of general edge and internal piecewise-flat multi-cracked plates under mixed-mode deformation, the singular term of Williams׳ series can be used as a closed-form particular solution, valid in the neighborhood of each crack tip.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: March 2015
- A meshless improved boundary distributed source method for two-phase flow
monitoring using electrical resistance tomography- Abstract: Publication date: March 2015
Source:Engineering Analysis with Boundary Elements, Volume 52
Author(s): Anil Kumar Khambampati , Yeon-Gun Lee , Kyung Youn Kim , Dong Wook Jerng , Sin Kim
This paper presents a meshless method based on the improved boundary distributed source method (IBDS) to monitor two-phase flow in pipes using electrical resistance tomography (ERT). The conductivity of background liquid is assumed to be known a priori while the shape and location of the voids are the unknowns to be determined. The forward problem of ERT is solved using meshless IBDS method and the voids location and shape are reconstructed using Levenberg–Marquardt method. IBDS method is purely meshless and places its source and field points on the same physical boundary unlike conventional method of fundamental solution approach. Moreover, the elements of system matrix corresponding to Neumann and Dirichlet boundary conditions are evaluated analytically; therefore the IBDS method is computationally efficient that gives an accurate and stable solution. Numerical and experimental results with single and multiple voids are shown and the performance of IBDS method is compared with the boundary element method (BEM) in monitoring two-phase flow.
PubDate: 2014-12-15T04:46:29Z
- Abstract: Publication date: March 2015
- Meshless local Petrov–Galerkin (MLPG) method for three-dimensional
nonlinear wave equations via moving least squares approximation- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): E. Shivanian
This paper proposes an approach based on the Galerkin weak form and moving least squares (MLS) approximation to simulate three space dimensional nonlinear wave equation of the form u tt + α u t + β u = u xx + u yy + u zz + δ g ( u ) u t + f ( x , y , z , t ) , 0 < x , y , z < 1 , t > 0 subject to given appropriate initial and Dirichlet boundary conditions. The main difficulty of methods in fully three-dimensional problems is the large computational costs. In the proposed method, which is a kind of Meshless local Petrov–Galerkin (MLPG) method, meshless Galerkin weak form is applied to the interior nodes while the meshless collocation method is used for the nodes on the boundary, so the Dirichlet boundary condition is imposed directly. In MLPG method, it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes, such as circles or squares in two dimensions and spheres or cubes in three dimensions. The moving least squares approximation is proposed to construct shape functions. A two-step time discretization method is employed to approximate the time derivatives. To treat the nonlinearity, a kind of predictor–corrector scheme combined with one-step time discretization and Crank–Nicolson technique is adopted. Several numerical examples are presented and satisfactory agreements are achieved.
PubDate: 2014-10-08T06:36:07Z
- Abstract: Publication date: January 2015
- A Meshless Symplectic Algorithm for multi-variate Hamiltonian PDEs with
Radial Basis Approximation- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Z. Wu , S. Zhang
Based on radial basis approximation, in this paper we propose two methods to discretize the problem of multi-variate Hamiltonian system. One is discretizing the system and finding out the corresponding discrete Hamiltonian functional, which will be conserved with respect to the time. The other is discretizing the Hamiltonian functional and deriving the corresponding discrete Hamiltonian system. This helps open a new area of research in developing the expected meshless symplectic algorithm for multi-variate Hamiltonian systems with the scattered data points. Theoretical estimates including the truncation error and the global error are given. Numerical experiments verify the theoretical results. As numerical experiments show, the schemes are easy to implement with the scattered knots. Furthermore, the schemes possesss a long-time tracking capability for these Hamiltonian systems.
PubDate: 2014-10-02T05:36:38Z
- Abstract: Publication date: January 2015
- Generalized polyharmonic multiquadrics
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Chia-Cheng Tsai
In this paper, we construct the two- and three-dimensional generalized polyharmonic multiquadrics (GPMQ) of order (K,L), which are the particular solution of the K-th order generalized multiquadrics (GMQ) associated with the L-th order polyharmonic operator for L>0. By observing the first few orders of the GPMQs, we construct methods of undetermined coefficients and determine the unknown coefficients by expanding the GPMQs into Laurent series. The derived GPMQs are hierarchically unique and infinitely differentiable. Then, the GPMQ definitions are extended for L<0 and the solutions are derived by similar methods. Both symbolic and floating-point implementations are performed for automatically obtaining the GPMQs of arbitrary orders, in which the former is explicitly provided and the later enables to implement numerical methods free from bookkeeping. The derived GPMQs are validated by numerical experiments, in which significant improvement on the accuracy can be observed.
PubDate: 2014-10-02T05:36:38Z
- Abstract: Publication date: January 2015
- Yield design of reinforced concrete slabs using a rotation-free meshfree
method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Canh V. Le , Phuc L.H. Ho , Phuong H. Nguyen , Thang Q. Chu
This paper presents a numerical kinematic procedure for yield design of reinforced concrete slabs governed by Nielsen׳s yield criterion that uses a rotation-free meshfree method and second-order cone programming. A moving least squares approximation technique is employed to approximate the transverse displacement field without using rotational degrees of freedom. A curvature smoothing stabilization technique is applied, ensuring that the size of the resulting optimization problem is reduced significantly. The resulting optimization was solved using a highly efficient primal-dual interior point algorithm. Various reinforced concrete slab problems with arbitrary geometries and different boundary conditions were solved to illustrate the efficacy of the proposed numerical procedure.
PubDate: 2014-10-02T05:36:38Z
- Abstract: Publication date: January 2015
- Fast and data sparse time domain BEM for elastodynamics
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Bernhard Kager , Martin Schanz
Wave propagation is of great interest for all fields of science and engineering. Particularly, for the case of semi-infinite and infinite domains, the Boundary Element Method is an appropriate numerical method for the simulation of such problems. The presented formulation establishes a data efficient and fast boundary element formulation for the 3-d elastodynamic problem. Approximations of the inherently present temporal convolution are computed via the Convolution Quadrature Method in a nonstandard manner. Contrary to utilizing Cauchy׳s integral formula, this paper establishes a ‘direct’ convolution weight evaluation. The application of a cubic spline interpolation on these analytic functions and an appropriate clustering strategy, finally, yield a fast and data efficient formulation that is validated with numerical examples.
PubDate: 2014-10-02T05:36:38Z
- Abstract: Publication date: January 2015
- New analytical expressions in radial integration BEM for solving heat
conduction problems with variable coefficients- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Kai Yang , Hai-Feng Peng , Miao Cui , Xiao-Wei Gao
In this paper, a new approach using analytical expressions in the radial integration boundary element method (RIBEM) is presented for solving three kinds of representative variable coefficient heat conduction problems. This approach can improve the computational efficiency considerably and can overcome the time-consuming deficiency of RIBEM in computing involved radial integrals. Also, because it can solve any kinds of variable coefficient heat conduction problems, this approach has a very wide applicability. The fourth-order spline RBF is employed to approximate the unknowns appearing in domain integrals arising from the varying heat conductivity. The radial integration method is utilized to convert domain integrals to the boundary, which results in a pure boundary discretization algorithm. Numerical examples are given to demonstrate the efficiency of the presented approach.
PubDate: 2014-10-02T05:36:38Z
- Abstract: Publication date: January 2015
- An adaptive node regeneration technique for the efficient solution of
elasticity problems using MDLSM method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): S. Nikravesh Kazeroni , M.H. Afshar
An efficient adaptive node regeneration method is proposed in this paper for solving elasticity problems using the mixed discrete least squares meshless (MDLSM) method. The method starts with a point-wise error estimation of the solution produced on an arbitrary initial configuration defined by the user using the MDLSM method. The point-wise error estimate is associated with the support domain of the nodal points and used to calculate the required nodal spacing at each support domain and subsequently generate new nodes at support domain level. A node-removing process is then used to remove some of the nodes created at the overlapping regions of the support domains. To improve the quality of the final configuration, a node-moving procedure based on interpolation of the errors on the original configuration is used to create the final nodal configuration. The proposed method is a single step refinement procedure and is capable of producing nodal configurations of desired accuracy for different problems. The proposed method is used to simulate three benchmark examples from the literature and the results are produced and compared with those of the conventional multi-stage node enrichment method. The results indicate the superior efficiency and effectiveness of the proposed method compared to the available methods.
PubDate: 2014-09-25T04:20:15Z
- Abstract: Publication date: January 2015
- The ACA–BEM approach with a binary-key mosaic partitioning for
modelling multiple bubble dynamics- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Zhiwei Fu , Viktor Popov
The fast algorithm adaptive cross approximation (ACA) is applied to accelerate the solution of the boundary element method (BEM). A new method for mosaic partitioning is proposed as part of the implementation of the ACA algorithm. It is based on a binary key system, which represents a hierarchical cluster tree and helps to identify the hierarchy within the ℋ -matrix generated by the BEM. The employed ACA approach proves efficient even for relatively small problems with the degree of freedom of O(103). As the problem size grows, the superior performance of the fast approach becomes more notable by comparison with that of the conventional boundary element method (CBEM). Modelling of bubble dynamics belongs to the moving boundary problems and can be efficiently analysed by using the BEM. By applying the ACA approach, the dense matrices via the collocation scheme are successfully compressed, and the developed model is capable of investigating the time-dependent evolution process of a relatively large number of bubbles (>100) in an efficient way.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- Numerical solution of three-dimensional Laplacian problems using the
multiple scale Trefftz method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Cheng-Yu Ku , Chung-Lun Kuo , Chia-Ming Fan , Chein-Shan Liu , Pai-Chen Guan
This paper proposes the numerical solution of three-dimensional Laplacian problems based on the multiple scale Trefftz method with the incorporation of the dynamical Jacobian-inverse free method. A numerical solution for three-dimensional Laplacian problems was approximated by superpositioning T-complete functions formulated from 18 independent functions satisfying the governing equation in the cylindrical coordinate system. To mitigate a severely ill-conditioned system of linear equations, this study adopted the newly developed multiple scale Trefftz method and the dynamical Jacobian-inverse free method. Numerical solutions were conducted for problems involving three-dimensional groundwater flow problems enclosed by a cuboid-type domain, a peanut-type domain, a sphere domain, and a cylindrical domain. The results revealed that the proposed method can obtain accurate numerical solutions for three-dimensional Laplacian problems, yielding a superior convergence in numerical stability to that of the conventional Trefftz method.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- An ultra-accurate hybrid smoothed finite element method for piezoelectric
problem- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Eric Li , Z.C. He , L. Chen , Bing Li , Xu Xu , G.R. Liu
An ultra-accurate hybrid smoothed finite element method (HS-FEM) is presented for the analysis of piezoelectric structures, in which the electrostatic equations governing piezoelectric problem are solved numerically with simplest triangular elements in 2D and tetrahedral elements in 3D. In the present method, the strain field is assumed to be the weighted average between compatible strains from finite element method (FEM) and smoothed strains from node-based smoothed finite element method (NS-FEM). Numerical results demonstrate that the proposed method possesses a novel bound solution in terms of strain energy and eigenfrequencies, which is very important for safety and reliability assessments of piezoelectric structural properties. In addition, the numerical results obtained from HS-FEM are much more accurate than the standard finite element method using the same of nodes. Furthermore, the computational efficiency of HS-FEM is much better than the FEM.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- Free vibration analysis of stepped rectangular plates resting on
non-homogeneous elastic foundations- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): M. Huang , T. Sakiyama , H. Matsuda , C. Morita
A Half Boundary Method (HBM) is proposed for analyzing the free vibration problem of rectangular plates with stepped thickness resting on non-homogeneous elastic foundations. The unknown quantities of the method exist only on half of the boundary. The non-homogeneous elastic foundation discussed here consists of two-segment elastic Winkler foundation. The fundamental differential equations are established for the bending problem of the plate on elastic foundations. The Green function, which is obtained by transforming these differential equations into integral equations and using numerical integration, is used to establish the characteristic equation of the free vibration. The effects of the modulus of the foundation, the stepped thickness and aspect ratio on the frequency parameters are considered. By comparing the present numerical results with those previously published, the efficiency and accuracy of the present method are investigated.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- Finding unknown heat source in a nonlinear Cauchy problem by the Lie-group
differential algebraic equations method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Chein-Shan Liu
We consider an inverse heat source problem of a nonlinear heat conduction equation, for recovering an unknown space-dependent heat source under the Cauchy type boundary conditions. With the aid of measured initial temperature and initial heat flux, which are disturbanced by random noise causing measurement error, we develop a Lie-group differential algebraic equations (LGDAE) method to solve the resultant differential algebraic equations. The Lie-group numerical method has a stabilizing effect to retain the solution on the associated manifold, which thus naturally has a regularization effect to overcome the ill-posed property of the nonlinear inverse heat source problem. As a consequence, we can quickly recover the unknown heat source under noisy input data only through a few iterations. The initial data used in the recovery of heat source are assumed to be the analytic continuation ones which are not given arbitrarily. Certainly, the measured initial data belong to this type data.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- A Laplace transform DRBEM with a predictor–corrector scheme for
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Imam Solekhudin , Keng-Cheng Ang
A problem involving time-dependent infiltration from periodic channels with root-water uptake is governed by Richards equation. To study the problem numerically, the governing equation is transformed into a modified Helmholtz equation using the Kirchhoff transformation, dimensionless variables, and Laplace transforms. The modified Helmholtz equation is then solved numerically using a dual reciprocity boundary element method (DRBEM) and a predictor–corrector scheme simultaneously. A numerical inverse Laplace transform is employed to obtain numerical solutions of the problem.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- Application of complex SIE method for the prediction of hydrofracture path
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): A.A. Andreev , A.N. Galybin , O.Y. Izvekov
This study is aimed at application of the method of complex singular integral equation (SIE) to the problem of crack propagation in non-uniform stress field. The paper examines one actual problem of oil and gas production: modeling of the hydrofracture trajectories in a reservoir subjected to non-uniform distributions of pore pressure. A modification of the method of mechanical quadratures is used to solve the SIE to simulate the hydro-fracture trajectory. The modification addresses discontinuities in the loads acting on the hydrofracture and provides quite accurate and fast solutions for the stress intensity factors. The crack path is modeled by a polygonal line such that the orientation of every subsequent leg is chosen by the criterion of maximum tensile stresses at the crack tip calculated for the current configuration. Different interposition the hydrofracture and the injection wells are examined.
PubDate: 2014-09-21T03:35:17Z
- Abstract: Publication date: January 2015
- Multiobjective optimization for node adaptation in the analysis of
composite plates using a meshless collocation method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): C.M.C. Roque , J.F.A. Madeira , A.J.M. Ferreira
The bending of simply supported composite plates is analyzed using a direct collocation meshless numerical method. In order to optimize node distribution the Direct MultiSearch (DMS) for multiobjective optimization method is applied. In addition, the method optimizes the shape parameter in radial basis functions. The optimization algorithm was able to find good solutions for a large variety of nodes distribution.
PubDate: 2014-09-18T03:07:01Z
- Abstract: Publication date: January 2015
- Fully nonlinear wave interaction with freely floating non-wall-sided
structures- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): B.Z. Zhou , G.X. Wu , B. Teng
A fully nonlinear numerical model for a floating body in the open sea has been developed based on velocity potential together with a higher-order boundary element method (BEM). The total wave elevation and the total velocity potential are separated into two parts, based on the incoming wave from infinity and the disturbed potential by the body. The mesh is generated only once at the initial time and the element nodes are rearranged subsequently without changing their connectivity by using a spring analogy method. Through some auxiliary functions, the mutual dependence of fluid/structure motions are decoupled, which allows the body acceleration to be obtained without the knowledge of the pressure distribution. Numerical results are provided for forces and run-ups of a fixed cylinder with flare and the comparison is made with the second order theory in the frequency domain. Simulations are also made for a freely floating body responding to wave excitation. Resonance related to ringing excited by the high order force at the triple wave frequency is discussed. Further results are provided for motions, forces and run-ups of a floating cylinder with flare. Comparison with the results for the fixed body and body in single degree of freedom is made.
PubDate: 2014-09-18T03:07:01Z
- Abstract: Publication date: January 2015
- The general boundary element method for 3D dual-phase lag model of bioheat
transfer- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Ewa Majchrzak , Lukasz Turchan
Heat transfer processes proceeding in the 3D domain of heating tissue are discussed. The problem is described by dual-phase lag equation supplemented by adequate boundary and initial conditions. To solve the problem the general boundary element method is proposed. The examples of computations are presented in the final part of the paper. The efficiency and exactness of the algorithm proposed are discussed and the conclusions are also formulated.
PubDate: 2014-09-10T01:48:39Z
- Abstract: Publication date: January 2015
- Geometrically nonlinear elastodynamic analysis of hyper-elastic neo-Hooken
FG cylinder subjected to shock loading using MLPG method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Mohammad Hossein Ghadiri Rad , Farzad Shahabian , Seyed Mahmoud Hosseini
In this paper, geometrically nonlinear dynamic behavior of FG thick hollow cylinder under axisymmetric mechanical shock loading is investigated using meshless local Petrov–Galerkin (MLPG) method. The FG cylinder is assumed to be made of large deformable materials such as carbon-based polymers. Thus, the neo-Hooken hyper-elastic constitutive model is employed for the problem. The material properties of FG cylinder are varied as nonlinear function of radius in volume fraction forms. Radial point interpolation method is used to approximate the field variables in the local integral equations. Weak formulation on local sub-domains using a Heaviside test function is adopted to get the system of equations. It should be emphasized that the formulations are derived using total Lagrangian approach, which refers all variables to the initial configuration. The iterative Newmark/Newton–Raphson technique is used to solve the equilibrium equations. In order to verify the feasibility and accuracy of the presented method, a thick hollow FG cylinder is linearly analyzed and compared with published data. The dynamic behaviors of displacements and stresses are obtained using nonlinear analysis and discussed in details for various kinds of neo-Hooken FGMs.
PubDate: 2014-09-10T01:48:39Z
- Abstract: Publication date: January 2015
- Direct use of radial basis interpolation functions for modelling source
terms with the boundary element method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Carlos F. Loeffler , Átila L. Cruz , André Bulcão
In this paper a new technique is presented for transforming the domain integral related to the source term that characterizes the Poisson Equation, within the scope of the boundary element method, for two-dimensional problems. Similarly to the Dual Reciprocity Technique, the proposed scheme avoids domain discretization using primitive radial basis functions; however, it transforms the domain integral into a single boundary integral directly. The proposed procedure is simpler, more versatile and some useful and modern techniques related to radial basis function theory can be applied. Numerical tests show the accuracy of the proposed technique for a simple class of complete radial interpolation functions, pointing out the importance of internal poles and the potential of applying fitting interpolation schemes to minimize the computational storage, particularly considering more complex future approaches, in which a mass matrix may be generated. For the analysis of the accuracy and convergence of the proposed method, results are compared with those obtained using Dual Reciprocity, using known analytical solutions for reference.
PubDate: 2014-09-10T01:48:39Z
- Abstract: Publication date: January 2015
- Simulation of semiconductor devices with a local numerical approach
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): G. Kosec , R. Trobec
A numerical solution of the Drift-Diffusion Model for simulation of semiconductor devices based on the local meshless numerical method is presented. Numerical difficulties inherited from convection-dominated processes and high gradients near junctions typically results in oscillations within the solution. The difficulties can be alleviated by artificial dissipation schemes or by other stabilization approaches that often require a complex computation to improve the solution convergence. We applied a simple numerical approach with a local coupling and without special treatments of nonlinearities. The proposed approach is straightforward to implement and is suitable for parallel execution. We demonstrate the efficiency of the proposed methodology on a simulation of PN junction. The results are compared against previously published data with a good agreement achieved. The applicability of the proposed methodology is confirmed with the simulation of extended tests with more complicated geometries and more intense dynamics. The computational efficiency is demonstrated through the measurement of execution time and speedup on shared memory computer architecture.
PubDate: 2014-09-10T01:48:39Z
- Abstract: Publication date: January 2015
- A least squares based meshfree technique for the numerical solution of the
flow of viscoelastic fluids: A node enrichment strategy- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Mohsen Lashkarbolok , Ebrahim Jabbari , Jerry Westerweel
A fully implicit least-squares-based meshfree method is used to solve the governing equations of viscoelastic fluid flow. Here, pressure is connected to the continuity equation by an artificial compressibility technique. A radial point interpolation method is used to construct the meshfree shape functions. The method is used to solve two benchmark problems. Thanks to the flexibility of meshfree methods in domain discretization, a simple node enrichment strategy is used to discrete the problem domain more purposefully. It is shown that the introduced enrichment process have a positive effect on the accuracy of the results.
PubDate: 2014-09-05T00:42:39Z
- Abstract: Publication date: January 2015
- Stress distribution of mine roof with the boundary element method
- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): R. Wu , J.H. Xu , C. Li , Z.L. Wang , S. Qin
Mine roof, is a stiff rock strata, located on the top of coal seam, which can prevent the deformation and control the stability of coal roadway after the coal roadway is tunneled, so mine roof is one of the most important structures in coal mining engineering. In this paper, mine roof is treated as elastic plate, which is studied thoroughly at the theoretical level. Based on the mechanical models of plane and stress analysis for elastic roof, using the boundary integral equation which is obtained by the natural boundary reduction, this paper obtains stress functions of elastic half roof, as well as the analytical and numerical solutions to the each stress field functions. We also analyze the rules of different stress distributions for roof under a concentrated force and a uniform distribution load, the results of calculation show uniformity of the stress distribution. In order to research the mine roof deformation law, Mohr–Coulomb model is established to describe the deformation behavior of roof surrounding rock, FLAC3D is also used to simulate the deformation of roof after the coal roadway is tunneled under different length of coal roadway excavation. The comparison result between BEM solution and FLAC3D simulation shows advantages to solve the problem by boundary element method, and numerical simulation proves the deformation behavior of roof is influenced by the length of coal roadway excavation.
PubDate: 2014-09-05T00:42:39Z
- Abstract: Publication date: January 2015
- A fast directional BEM for large-scale acoustic problems based on the
Burton–Miller formulation- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Yanchuang Cao , Lihua Wen , Jinyou Xiao , Yijun Liu
In this paper, a highly efficient fast boundary element method (BEM) for solving large-scale engineering acoustic problems in a broad frequency range is developed and implemented. The acoustic problems are modeled by the Burton–Miller boundary integral equation (BIE), thus the fictitious frequency issue is completely avoided. The BIE is discretized by using the Nyström method based on the curved quadratic elements, leading to simple numerical implementation (no edge or corner problems) and high accuracy in the BEM analysis. The linear systems are solved iteratively and accelerated by using a newly developed kernel-independent wideband fast directional algorithm (FDA) for fast summation of oscillatory kernels. In addition, the computational efficiency of the FDA is further promoted by exploiting the low-rank features of the translation matrices, resulting in two- to three-fold reduction in the computational time of the multipole-to-local translations. The high accuracy and nearly linear computational complexity of the present method are clearly demonstrated by typical examples. An acoustic scattering problem with dimensionless wave number kD (where k is the wave number and D is the typical length of the obstacle) up to 1000 and the degrees of freedom up to 4 million is successfully solved within 10h on a computer with one core and the memory usage is 24GB.
PubDate: 2014-09-05T00:42:39Z
- Abstract: Publication date: January 2015
- A modified scaled boundary approach in frequency domain with diagonal
coefficient matrices- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Masoud Hajialilue-Bonab , Hamid Reza Tohidvand
In order to solve the scaled boundary differential equation in dynamic stiffness, an initial value is needed. This initial value can be obtained using high frequency asymptotic expansion of dynamic stiffness matrix. Expanded dynamic stiffness matrix of unbounded mediums at high frequency was presented by previous researchers based on the fully populated coefficient matrices. In this paper, lumped coefficient matrices are used to modify the scaled boundary procedure. Some extra computational efforts of the original scaled boundary method can be eliminated using the proposed approach. The scaled boundary spectral element method (SBSEM) is used to achieve lumped coefficient matrices. It is shown that the proposed method leads to correct dynamic stiffness matrix. Therefore, it can be applied to solve scaled boundary differential equation of unbounded mediums, efficiently. A comparison between the results of the modified and the original methods is presented and accuracy of the modified method is investigated.
PubDate: 2014-08-14T23:16:10Z
- Abstract: Publication date: January 2015
- PROMETHEE technique to select the best radial basis functions for solving
the 2-dimensional heat equations based on Hermite interpolation- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Saeed Kazem , Farhad Hadinejad
In this work, we have decided to select the best radial basis functions for solving the 2-dimensional heat equations by applying the multiple criteria decision making (MCDM) techniques. Radial basis functions (RBFs) based on the Hermite interpolation have been utilized to approximate the solution of heat equation by using the collocation method. Seven RBFs, Gaussian (GA), Multiquadrics (MQ), Inverse multiquadrics (IMQ), Inverse quadrics (IQ), third power of Multiquadrics (MQ3), Conical splines (CS) and Thin plate Splines (TPS), have been applied as basis functions as well. In addition, by choosing these functions as alternatives and calculating the error, condition number of interpolation matrix, RAM memory and CPU time, obtained by Maple software, as criteria, rating of cases with the help of PROMETHEE technique has been investigated. In the end, the best function has been selected according to the rankings.
PubDate: 2014-08-14T23:16:10Z
- Abstract: Publication date: January 2015
- On the use of the vertical straight wire model in electromagnetics and
related boundary element solution- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Dragan Poljak , Silvestar Šesnić , Damir Cavka , Khalil El Khamlichi Drissi
The paper deals with an analysis of various EMC problems related to radiation and scattering from wires using a vertical straight wire model based on the corresponding Pocklington integro-differential equation. The rigorous solution of the Pocklington type equation is undertaken via the Galerkin–Bubnov Indirect Boundary Element Method (GB-IBEM). Many illustrative computational examples presented throughout the paper are related to dipole antenna above a lossy half-space, metal rods penetrating the ground, lightning channel and vertical grounding electrode. Obtained numerical results are somewhere compared to NEC or analytical results, respectively.
PubDate: 2014-08-14T23:16:10Z
- Abstract: Publication date: January 2015
- A numerical study of Asian option with radial basis functions based finite
differences method- Abstract: Publication date: January 2015
Source:Engineering Analysis with Boundary Elements, Volume 50
Author(s): Alpesh Kumar , Lok Pati Tripathi , Mohan K. Kadalbajoo
The purpose of this paper is to design and describe the valuation of Asian option by radial basis function approximation. A one state variable partial differential equation which characterizes the price of European type Asian option is discussed. The governing equation is discretized by the θ-method and the option price is approximated by radial basis function based finite difference method. Numerical experiments are performed with European option and Asian option and results are compared with theoretical and numerical results available in the literature. We show numerically that the scheme is second order accurate. Stability of the scheme is also discussed.
PubDate: 2014-08-14T23:16:10Z
- Abstract: Publication date: January 2015