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Boundary Elements (boundary + element)
Terms modified by Boundary Elements Selected AbstractsReview modeling the free solution and gel electrophoresis of biopolymers: The bead array-effective medium modelBIOPOLYMERS, Issue 2-3 2007Stuart A. Allison Abstract Free solution and gel electrophoresis is an extremely useful tool in the separation of biopolymers. The complex nature of biopolymers, coupled with the usefulness of electrophoretic methods, has stimulated the development of theoretical modeling over the last 30 years. In this work, these developments are first reviewed with emphasis on Boundary Element and bead methodologies that enable the investigator to design realistic models of biopolymers. In the present work, the bead methodology is generalized to include the presence of a gel through the Effective Medium model. The biopolymer is represented as a bead array. A peptide, for example, made up of N amino acids is modeled as 2N beads. Duplex DNA is modeled as a discrete wormlike chain consisting of touching beads. The technical details of the method are placed in three Appendices. To illustrate the accuracy and effectiveness of the approach, two applications are considered. Model studies on both the free solution mobility of 73 peptides ranging in size from 2 to 42 amino acids, and the mobility of short duplex DNA in dilute agarose gels are discussed. © 2007 Wiley Periodicals, Inc. Biopolymers 87: 102,114, 2007. This article was originally published online as an accepted preprint. The "Published Online" date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com [source] Effective condition number of Trefftz methods for biharmonic equations with crack singularitiesNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2 2009Zi-Cai Li Abstract The paper presents the new stability analysis for the collocation Trefftz method (CTM) for biharmonic equations, based on the new effective condition number Cond_eff. The Trefftz method is a special spectral method with the particular solutions as admissible functions, and it has been widely used in engineering. Three crack models in Li et al. (Eng. Anal. Boundary Elements 2004; 28:79,96; Trefftz and Collocation Methods. WIT Publishers: Southampton, Boston, 2008) are considered, and the bounds of Cond_eff and the traditional condition number Cond are derived, to give the polynomial and the exponential growth rates, respectively. The stability analysis explains well the numerical experiments. Hence, the new Cond_eff is more advantageous than Cond. Besides since the bounds of Cond_eff and Cond involve the estimation of the minimal singular value ,min of the discrete matrix F, and since the estimation of ,min is challenging and difficult, the proof for lower bounds of ,min in this paper is important and intriguing. Copyright © 2008 John Wiley & Sons, Ltd. [source] Modeling of Active Noise and Vibration Control with Finite Elements and Boundary ElementsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Stefan Ringwelski A recently developed coupled finite element-boundary element modeling scheme for the design of active noise and vibration control of multi-coupled structural-acoustic systems is presented. The approach allows the computation of structural vibrations and resulting sound fields. By means of an example, the paper describes the theoretical background of the coupled approach. In order to show the performance of the developed approach, test simulations are carried out in the frequency domain. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Coupling of 3D Boundary Elements with Curved Finite Shell ElementsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Bastian Helldörfer The mixed-dimensional coupling of finite shells and 3D boundary elements is presented. A stiffness formulation for the boundary element domain is generated by the Symmetric Galerkin Boundary Element Method and is assembled to the global finite element system. Multipoint constraints are derived in an integral sense by equating the work at the coupling interface. They are evaluated numerically during the analysis and avoid spurious stress concentrations also for curved interfaces. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Boundary elements for half-space problems via fundamental solutions: A three-dimensional analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001J. Liang Abstract An efficient solution technique is proposed for the three-dimensional boundary element modelling of half-space problems. The proposed technique uses alternative fundamental solutions of the half-space (Mindlin's solutions for isotropic case) and full-space (Kelvin's solutions) problems. Three-dimensional infinite boundary elements are frequently employed when the stresses at the internal points are required to be evaluated. In contrast to the published works, the strongly singular line integrals are avoided in the proposed solution technique, while the discretization of infinite elements is independent of the finite boundary elements. This algorithm also leads to a better numerical accuracy while the computational time is reduced. Illustrative numerical examples for typical isotropic and transversely isotropichalf-space problems demonstrate the potential applications of the proposed formulations. Incidentally, the results of the illustrative examples also provide a parametric study for the imperfect contact problem. Copyright © 2001 John Wiley & Sons, Ltd. [source] Dynamic stiffness of deep foundations with inclined pilesEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 12 2010L. A. Padrón Abstract The influence of inclined piles on the dynamic response of deep foundations and superstructures is still not well understood and needs further research. For this reason, impedance functions of deep foundations with inclined piles, obtained numerically from a boundary element,finite element coupling model, are provided in this paper. More precisely, vertical, horizontal, rocking and horizontal,rocking crossed dynamic stiffness and damping functions of single inclined piles and 2 × 2 and 3 × 3 pile groups with battered elements are presented in a set of plots. The soil is assumed to be a homogeneous viscoelastic isotropic half-space and the piles are modeled as elastic compressible Euler,Bernoulli beams. The results for different pile group configurations, pile,soil stiffness ratios and rake angles are presented. Copyright © 2010 John Wiley & Sons, Ltd. [source] Seismic response of slopes subjected to incident SV wave by an improved boundary element approachINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2007Behrouz Gatmiri Abstract In this paper, an improved boundary element approach for 2D elastodynamics in time-domain is presented. This approach consists in the truncation of time integrations, based on the rapid decrease of the fundamental solutions with time. It is shown that an important reduction of the computation time as well as the storage requirement can be achieved. Moreover, for half-plane problems, the size of boundary element (BE) meshes and the computation time can be significantly reduced. The proposed approach is used to study the seismic response of slopes subjected to incident SV waves. It is found that large amplifications take place on the upper surface close to the slope, while attenuations are produced on the lower surface. The results also show that surface motions become very complex when the incident wavelength is comparable with the size of the slope or when the slope is steep. Copyright © 2006 John Wiley & Sons, Ltd. [source] Evaluation of well performance using the coupling of boundary element with finite element methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2004L. Jeannin Abstract In this paper, we apply an FEM,BEM coupling method in petroleum engineering to evaluate complex wells (or fractures) performance. We use boundary element methods around wells and fractures, and finite elements in the remaining part of the reservoir. Copyright © 2004 John Wiley & Sons, Ltd. [source] Mapped infinite elements for three-dimensional multi-region boundary element analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004W. Moser Abstract A formulation for an infinite boundary element (BE) is presented, which allows the modelling of infinite surfaces. The concept is that the finite surface is mapped to an infinite surface using special mapping functions. Using such mapping functions together with linear and quadratic interpolation for the displacements and the tractions, respectively, the desired decay behaviour can be modelled. The implementation of the proposed infinite elements becomes straightforward, since the Cauchy principal value, as well as the free term, are evaluated for the finite and infinite BEs with exactly the same techniques. The element developed can be used in a multi-region BE analysis of piecewise homogeneous domains, or for domains with joints and faults. The accuracy of the element is tested on some benchmark problems. Finally, a practical application in tunnelling is shown. Copyright © 2004 John Wiley & Sons, Ltd. [source] A coupling of multi-zone curved Galerkin BEM with finite elements for independently modelled sub-domains with non-matching nodes in elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2004S. Ganguly Abstract When the different parts of a structure are modelled independently by BEM or FEM methods, it is sometimes necessary to put the parts together without remeshing of the nodes along the part interfaces. Frequently the nodes do not match along the interface. In this work, the symmetric Galerkin multi-zone curved boundary element is a fully symmetric formulation and is the method used for the boundary element part. For BEM,FEM coupling it is then necessary to interpolate the tractions in-between the non-matching nodes for the FEM part. Finally, the coupling is achieved by transforming the finite element domains to equivalent boundary element domains in a block symmetric formulation. This system is then coupled with a boundary element domain with non-matching nodes in-between. Copyright © 2004 John Wiley & Sons, Ltd. [source] A practical determination strategy of optimal threshold parameter for matrix compression in wavelet BEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003Kazuhiro Koro Abstract A practical strategy is developed to determine the optimal threshold parameter for wavelet-based boundary element (BE) analysis. The optimal parameter is determined so that the amount of storage (and computational work) is minimized without reducing the accuracy of the BE solution. In the present study, the Beylkin-type truncation scheme is used in the matrix assembly. To avoid unnecessary integration concerning the truncated entries of a coefficient matrix, a priori estimation of the matrix entries is introduced and thus the truncated entries are determined twice: before and after matrix assembly. The optimal threshold parameter is set based on the equilibrium of the truncation and discretization errors. These errors are estimated in the residual sense. For Laplace problems the discretization error is, in particular, indicated with the potential's contribution ,c, to the residual norm ,R, used in error estimation for mesh adaptation. Since the normalized residual norm ,c,/,u, (u: the potential components of BE solution) cannot be computed without main BE analysis, the discretization error is estimated by the approximate expression constructed through subsidiary BE calculation with smaller degree of freedom (DOF). The matrix compression using the proposed optimal threshold parameter enables us to generate a sparse matrix with O(N1+,) (0,,<1) non-zero entries. Although the quasi-optimal memory requirements and complexity are not attained, the compression rate of a few per cent can be achieved for N,1000. Copyright © 2003 John Wiley & Sons, Ltd. [source] A new variable-order singular boundary element for two-dimensional stress analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002K. M. Lim Abstract A new variable-order singular boundary element for two-dimensional stress analysis is developed. This element is an extension of the basic three-node quadratic boundary element with the shape functions enriched with variable-order singular displacement and traction fields which are obtained from an asymptotic singularity analysis. Both the variable order of the singularity and the polar profile of the singular fields are incorporated into the singular element to enhance its accuracy. The enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the singular node thereby enabling direct calculation instead of through indirect extrapolation or contour-integral methods. Numerical examples involving crack, notch and corner problems in homogeneous materials and bimaterial systems show the singular element's great versatility and accuracy in solving a wide range of problems with various orders of singularities. The stress intensity factors which are obtained agree very well with those reported in the literature. Copyright © 2002 John Wiley & Sons, Ltd. [source] A subdomain boundary element method for high-Reynolds laminar flow using stream function-vorticity formulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2004Matja Abstract The paper presents a new formulation of the integral boundary element method (BEM) using subdomain technique. A continuous approximation of the function and the function derivative in the direction normal to the boundary element (further ,normal flux') is introduced for solving the general form of a parabolic diffusion-convective equation. Double nodes for normal flux approximation are used. The gradient continuity is required at the interior subdomain corners where compatibility and equilibrium interface conditions are prescribed. The obtained system matrix with more equations than unknowns is solved using the fast iterative linear least squares based solver. The robustness and stability of the developed formulation is shown on the cases of a backward-facing step flow and a square-driven cavity flow up to the Reynolds number value 50 000. Copyright © 2004 John Wiley & Sons, Ltd. [source] Potential flow around obstacles using the scaled boundary finite-element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003Andrew J. Deeks Abstract The scaled boundary finite-element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The method works by weakening the governing differential equations in one co-ordinate direction through the introduction of shape functions, then solving the weakened equations analytically in the other (radial) co-ordinate direction. These co-ordinate directions are defined by the geometry of the domain and a scaling centre. The method can be employed for both bounded and unbounded domains. This paper applies the method to problems of potential flow around streamlined and bluff obstacles in an infinite domain. The method is derived using a weighted residual approach and extended to include the necessary velocity boundary conditions at infinity. The ability of the method to model unbounded problems is demonstrated, together with its ability to model singular points in the near field in the case of bluff obstacles. Flow fields around circular and square cylinders are computed, graphically illustrating the accuracy of the technique, and two further practical examples are also presented. Comparisons are made with boundary element and finite difference solutions. Copyright © 2003 John Wiley & Sons, Ltd. [source] A comparison of boundary element and finite element methods for modeling axisymmetric polymeric drop deformationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2001Russell Hooper Abstract A modified boundary element method (BEM) and the DEVSS-G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start-up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd-B differential model, are considered for the drop phase using both FEM and BEM and for both the drop and matrix phases using FEM. Where possible, results are compared with the linear deformation theory. Consistent predictions are obtained among the BEM, FEM, and linear theory for purely Newtonian systems and between FEM and linear theory for fully viscoelastic systems. FEM and BEM predictions for viscoelastic drops in a Newtonian matrix agree very well at short times but differ at longer times, with worst agreement occurring as critical flow strength is approached. This suggests that the dominant computational advantages held by the BEM over the FEM for this and similar problems may diminish or even disappear when the issue of accuracy is appropriately considered. Fully viscoelastic problems, which are only feasible using the FEM formulation, shed new insight on the role of viscoelasticity of the matrix fluid in drop deformation. Copyright © 2001 John Wiley & Sons, Ltd. [source] Method of lines with boundary elements for 1-D transient diffusion-reaction problemsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2006P.A. Ramachandran Abstract Time-dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi-implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 [source] A cell boundary element method for elliptic problems,NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2005Youngmok Jeon Abstract An elementary analysis on the cell boundary element (CBEM) was given by Jeon and Sheen. In this article we improve the previous results in various aspects. First of all, stability and convergence analysis on the rectangular grids are established. Moreover, error estimates are improved. Our improved analysis was possible by recasting of the CBEM in a Petrov-Galerkin setting. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 [source] Chromatin looping mediates boundary element promoter interactionsBIOESSAYS, Issue 1 2007Susan E. Celniker One facet of the control of gene expression is long-range promoter regulation by distant enhancers. It is an important component of the regulation of genes that control metazoan development and has been appreciated for some time but the molecular mechanisms underlying this regulation have remained poorly understood. A recent study by Cleard and colleagues1 reports the first in vivo evidence of chromatin looping and boundary element promoter interaction. Specifically, they studied the function of a boundary element within the cis -regulatory region of the Abdominal-B (Abd-B) gene of Drosophila melanogaster. BioEssays 29: 7,10, 2007. © 2006 Wiley Periodicals, Inc. [source] Steady-state 3D rolling-contact using boundary elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2007R. Abascal Abstract This work presents a new approach to the steady-state rolling contact problem for 3D elastic bodies. The problem solution is achieved by minimizing a general function representing the equilibrium equation and the rolling-contact restrictions. The boundary element method is used to compute the elastic influence coefficients of the surface points involved in the contact (equilibrium equations); while the contact conditions are represented with the help of projection functions. Finally, the minimization problem is solved by the generalized Newton's method with line search. Classic rolling problems are also solved and commented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Fast single domain,subdomain BEM algorithm for 3D incompressible fluid flow and heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009Jure Ravnik Abstract In this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented. The algorithm solves the velocity,vorticity formulation of the incompressible Navier,Stokes equations in 3D. It is based on a combination of a subdomain boundary element method (BEM) and single domain BEM. The CPU time and storage requirements of the single domain BEM are reduced by implementing a fast multipole expansion method. The Laplace fundamental solution, which is used as a special weighting function in BEM, is expanded in terms of spherical harmonics. The computational domain and its boundary are recursively cut up forming a tree of clusters of boundary elements and domain cells. Data sparse representation is used in parts of the matrix, which correspond to boundary-domain clusters pairs that are admissible for expansion. Significant reduction of the complexity is achieved. The paper presents results of testing of the multipole expansion algorithm by exploring its effect on the accuracy of the solution and its influence on the non-linear convergence properties of the solver. Two 3D benchmark numerical examples are used: the lid-driven cavity and the onset of natural convection in a differentially heated enclosure. Copyright © 2008 John Wiley & Sons, Ltd. [source] Localized remeshing techniques for three-dimensional metal forming simulations with linear tetrahedral elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Il-Heon Son Abstract The localized remeshing technique for three-dimensional metal forming simulations is proposed based on a mixed finite element formulation with linear tetrahedral elements in the present study. The numerical algorithm to generate linear tetrahedral elements is developed for finite element analyses using the advancing front technique with local optimization method which keeps the advancing fronts smooth. The surface mesh generation using mesh manipulations of the boundary elements of the old mesh system was made to improve mesh quality of the boundary surface elements, resulting in reduction of volume change in forming simulations. The mesh quality generated was compared with that obtained from the commercial CAD package for the complex geometry like lumbar. The simulation results of backward extrusion and bevel gear and spider forgings indicate that the currently developed simulation technique with the localized remeshing can be used effectively to simulate the three-dimensional forming processes with a reduced computation time. Copyright © 2006 John Wiley & Sons, Ltd. [source] Efficient non-linear solid,fluid interaction analysis by an iterative BEM/FEM couplingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2005D. Soares Jr Abstract An iterative coupling of finite element and boundary element methods for the time domain modelling of coupled fluid,solid systems is presented. While finite elements are used to model the solid, the adjacent fluid is represented by boundary elements. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local non-linearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the non-linear system. In particular a more efficient and a more stable performance of the new coupling procedure is achieved by a special formulation that allows to use different time steps in each subdomain. Copyright © 2005 John Wiley & Sons, Ltd. [source] A fast boundary cloud method for 3D exterior electrostatic analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Vaishali Shrivastava Abstract An accelerated boundary cloud method (BCM) for boundary-only analysis of 3D electrostatic problems is presented here. BCM uses scattered points unlike the classical boundary element method (BEM) which uses boundary elements to discretize the surface of the conductors. BCM combines the weighted least-squares approach for the construction of approximation functions with a boundary integral formulation for the governing equations. A linear base interpolating polynomial that can vary from cloud to cloud is employed. The boundary integrals are computed by using a cell structure and different schemes have been used to evaluate the weakly singular and non-singular integrals. A singular value decomposition (SVD) based acceleration technique is employed to solve the dense linear system of equations arising in BCM. The performance of BCM is compared with BEM for several 3D examples. Copyright © 2004 John Wiley & Sons, Ltd. [source] Boundary elements for half-space problems via fundamental solutions: A three-dimensional analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001J. Liang Abstract An efficient solution technique is proposed for the three-dimensional boundary element modelling of half-space problems. The proposed technique uses alternative fundamental solutions of the half-space (Mindlin's solutions for isotropic case) and full-space (Kelvin's solutions) problems. Three-dimensional infinite boundary elements are frequently employed when the stresses at the internal points are required to be evaluated. In contrast to the published works, the strongly singular line integrals are avoided in the proposed solution technique, while the discretization of infinite elements is independent of the finite boundary elements. This algorithm also leads to a better numerical accuracy while the computational time is reduced. Illustrative numerical examples for typical isotropic and transversely isotropichalf-space problems demonstrate the potential applications of the proposed formulations. Incidentally, the results of the illustrative examples also provide a parametric study for the imperfect contact problem. Copyright © 2001 John Wiley & Sons, Ltd. [source] Self-regular boundary integral equation formulations for Laplace's equation in 2-DINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2001A. B. Jorge Abstract The purpose of this work is to demonstrate the application of the self-regular formulation strategy using Green's identity (potential-BIE) and its gradient form (flux-BIE) for Laplace's equation. Self-regular formulations lead to highly effective BEM algorithms that utilize standard conforming boundary elements and low-order Gaussian integrations. Both formulations are discussed and implemented for two-dimensional potential problems, and numerical results are presented. Potential results show that the use of quartic interpolations is required for the flux-BIE to show comparable accuracy to the potential-BIE using quadratic interpolations. On the other hand, flux error results in the potential-BIE implementation can be dominated by the numerical integration of the logarithmic kernel of the remaining weakly singular integral. Accuracy of these flux results does not improve beyond a certain level when using standard quadrature together with a special transformation, but when an alternative logarithmic quadrature scheme is used these errors are shown to reduce abruptly, and the flux results converge monotonically to the exact answer. In the flux-BIE implementation, where all integrals are regularized, flux results accuracy improves systematically, even with some oscillations, when refining the mesh or increasing the order of the interpolating function. The flux-BIE approach presents a great numerical sensitivity to the mesh generation scheme and refinement. Accurate results for the potential and the flux were obtained for coarse-graded meshes in which the rate of change of the tangential derivative of the potential was better approximated. This numerical sensitivity and the need for graded meshes were not found in the elasticity problem for which self-regular formulations have also been developed using a similar approach. Logarithmic quadrature to evaluate the weakly singular integral is implemented in the self-regular potential-BIE, showing that the magnitude of the error is dependent only on the standard Gauss integration of the regularized integral, but not on this logarithmic quadrature of the weakly singular integral. The self-regular potential-BIE is compared with the standard (CPV) formulation, showing the equivalence between these formulations. The self-regular BIE formulations and computational algorithms are established as robust alternatives to singular BIE formulations for potential problems. Copyright © 2001 John Wiley & Sons, Ltd. [source] Time-domain BEM solution of convection,diffusion-type MHD equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008N. Bozkaya Abstract The two-dimensional convection,diffusion-type equations are solved by using the boundary element method (BEM) based on the time-dependent fundamental solution. The emphasis is given on the solution of magnetohydrodynamic (MHD) duct flow problems with arbitrary wall conductivity. The boundary and time integrals in the BEM formulation are computed numerically assuming constant variations of the unknowns on both the boundary elements and the time intervals. Then, the solution is advanced to the steady-state iteratively. Thus, it is possible to use quite large time increments and stability problems are not encountered. The time-domain BEM solution procedure is tested on some convection,diffusion problems and the MHD duct flow problem with insulated walls to establish the validity of the approach. The numerical results for these sample problems compare very well to analytical results. Then, the BEM formulation of the MHD duct flow problem with arbitrary wall conductivity is obtained for the first time in such a way that the equations are solved together with the coupled boundary conditions. The use of time-dependent fundamental solution enables us to obtain numerical solutions for this problem for the Hartmann number values up to 300 and for several values of conductivity parameter. Copyright © 2007 John Wiley & Sons, Ltd. [source] A variational approach to boundary elements,two dimensional Helmholtz problemsINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2003Y. Kagawa Abstract The boundary element method is a discretized version of the boundary integral equation method. The variational formulation is presented for the boundary element approach to Helmholtz problems. The numerical calculation of the eigenvalues in association with hollow waveguides demonstrates that the variational approach provides the upper and lower bounds of the eigenvalues. The drawback of the discretized system equation must be solved by a trial and error approach, which is shown to be removed by the introduction of the dual reciprocity method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Fast solvers with block-diagonal preconditioners for linear FEM,BEM couplingNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 5 2009Stefan A. Funken Abstract The purpose of this paper is to present optimal preconditioned iterative methods to solve indefinite linear systems of equations arising from symmetric coupling of finite elements and boundary elements. This is a block-diagonal preconditioner together with a conjugate residual method and a preconditioned inner,outer iteration. We prove the efficiency of these methods by showing that the number of iterations to preserve a given accuracy is bounded independent of the number of unknowns. Numerical examples underline the efficiency of these methods. Copyright © 2008 John Wiley & Sons, Ltd. [source] Method of lines with boundary elements for 1-D transient diffusion-reaction problemsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2006P.A. Ramachandran Abstract Time-dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi-implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 [source] Rigid-plastic hybrid element analyses of the plane strain upsettingNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2002Yong-Ming Guo Abstract A rigid-plastic hybrid element method (HEM) for simulation of metal forming is developed. This method is a mixed approach of the rigid-plastic domain-BEM and the rigid-plastic FEM based on the theory of compressible plasticity. Because the compatibilities of not only velocity but also velocity's derivative between the adjoining boundary elements and finite elements can be met, the velocities and the derivatives of the velocity can be calculated with the same precision for the rigid-plastic HEM. Then, it is considered that the rigid-plastic HEM is a more precise method in formulation than the conventional rigid-plastic FEMs for which the compatibilities of velocity's derivative cannot be met. The plane strain upsetting processes with two friction factors are analyzed by the rigid-plastic HEM in this article. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 726,737, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10031. [source] | ||||||||||||||||