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BEM
Kinds of BEM Terms modified by BEM Selected AbstractsNumerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in single-cell trapsELECTROPHORESIS, Issue 11 2005Carlos Rosales Abstract This paper presents detailed numerical calculations of the dielectrophoretic force in traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that a small number of multipolar terms need to be considered in order to obtain accurate results for spheres, even in the proximity of the electrodes, and that the full MST calculation is only required in the study of nonspherical particles. [source] A predictor,corrector scheme for the optimization of 3D crack front shapesFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 1-2 2005K. KOLK ABSTRACT A predictor,corrector scheme is presented to improve the shape of 3D crack fronts within the 3D simulation of fatigue crack growth. This concept is fully functional for mode-I, and an extension for mixed-mode problems is presented. The whole procedure is embedded in an automatic incremental crack growth algorithm for arbitrary 3D problems with linear elastic material behaviour. The numerical simulation is based on the 3D dual boundary element method (Dual BEM) and on an optimized evaluation of very accurate stress intensity factors (SIFs) and T-stresses. As part of the proposed predictor,corrector scheme, 3D singularities along the crack front especially in the vicinity of the intersection of the crack front and the boundary are considered. The knowledge of these singularities allows the specification of crack front shapes with bounded energy release rate. Numerical examples with complex cross-sections are presented to show the efficiency of the proposed crack growth algorithm. The obtained results are in good agreement with recent experimental results. [source] Will climate change be beneficial or detrimental to the invasive swede midge in North America?GLOBAL CHANGE BIOLOGY, Issue 8 2008Contrasting predictions using climate projections from different general circulation models Abstract Climate change may dramatically affect the distribution and abundance of organisms. With the world's population size expected to increase significantly during the next 100 years, we need to know how climate change might impact our food production systems. In particular, we need estimates of how future climate might alter the distribution of agricultural pests. We used the climate projections from two general circulation models (GCMs) of global climate, the Canadian Centre for Climate Modelling and Analysis GCM (CGCM2) and the Hadley Centre model (HadCM3), for the A2 and B2 scenarios from the Special Report on Emissions Scenarios in conjunction with a previously published bioclimatic envelope model (BEM) to predict the potential changes in distribution and abundance of the swede midge, Contarinia nasturtii, in North America. The BEM in conjunction with either GCM predicted that C. nasturtii would spread from its current initial invasion in southern Ontario and northwestern New York State into the Canadian prairies, northern Canada, and midwestern United States, but the magnitude of risk depended strongly on the GCM and the scenario used. When the CGCM2 projections were used, the BEM predicted an extensive shift in the location of the midges' climatic envelope through most of Ontario, Quebec, and the maritime and prairie provinces by the 2080s. In the United States, C. nasturtii was predicted to spread to all the Great Lake states, into midwestern states as far south as Colorado, and west into Washington State. When the HadCM3 was applied, southern Ontario, Saskatchewan, and Washington State were not as favourable for C. nasturtii by the 2080s. Indeed, when used with the HadCM3 climate projections, the BEM predicted the virtual disappearance of ,very favourable' regions for C. nasturtii. The CGCM2 projections generally caused the BEM to predict a small increase in the mean number of midge generations throughout the course of the century, whereas, the HadCM3 projections resulted in roughly the same mean number of generations but decreased variance. Predictions of the likely potential of C. nasturtii spatial spread are thus strongly dependent on the source of climate projections. This study illustrates the importance of using multiple GCMs in combination with multiple scenarios when studying the potential for spatial spread of an organism in response to climate change. [source] The boundary element method for solving the Laplace equation in two-dimensions with oblique derivative boundary conditionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2007D. Lesnic Abstract In this communication, we extend the Neumann boundary conditions by adding a component containing the tangential derivative, hence producing oblique derivative boundary conditions. A variant of Green's formula is employed to translate the tangential derivative to the fundamental solution in the boundary element method (BEM). The two-dimensional steady-state heat conduction with the imposed oblique boundary condition has been tested in smooth, piecewise smooth and multiply connected domains in which the Laplace equation is the governing equation, producing results at the boundary in excellent agreement with the available analytical solutions. Convergence of the normal and tangential derivatives at the boundary is also achieved. The numerical boundary data are then used to successfully calculate the values of the solution at interior points again. The outlined test cases have been repeated with various boundary element meshes, indicating that the accuracy of the numerical results increases with increasing boundary discretization. Copyright © 2006 John Wiley & Sons, Ltd. [source] Fast multipole boundary element analysis of two-dimensional elastoplastic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2007P. B. Wang Abstract This paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher run-time and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix,vector multiplication are both reduced to O(N), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. [source] Three-dimensional elastoplastic analysis by triple-reciprocity boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2007Yoshihiro Ochiai Abstract In general, internal cells are required to solve elastoplastic problems using a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is ease of data preparation, is lost. Triple-reciprocity BEM can be used to solve two-dimensional elastoplasticity problems with a small plastic deformation. In this study, it is shown that three-dimensional elastoplastic problems can be solved, without the use of internal cells, by the triple-reciprocity BEM. An initial strain formulation is adopted and the initial strain distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solving several problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] Electrostatic BEM for MEMS with thin beamsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2005Zhongping Bao Abstract Micro-electro-mechanical (MEM) and nano-electro-mechanical (NEM) systems sometimes use beam- or plate-shaped conductors that can be very thin,with h/L,,,(10,2,10,3) (in terms of the thickness h and length L of a beam or the side of a square pate). Conventional boundary element method (BEM) analysis of the electric field in a region exterior to such thin conductors can become difficult to carry out accurately and efficiently,especially since MEMS analysis requires computation of charge densities (and then surface tractions) separately on the top and bottom surfaces of such objects. A new boundary integral equation (BIE) is derived in this work that, when used together with the standard BIE with logarithmically singular kernels, results in a powerful technique for the BEM analysis of such problems with thin beams. This new approach, in fact, works best for very thin beams. This thin beam BEM is derived and discussed in this work. Copyright © 2005 John Wiley & Sons, Ltd. [source] Efficiency of boundary element methods for time-dependent convective heat diffusion at high Peclet numbersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2005M. M. Grigoriev Abstract A higher-order boundary element method (BEM) recently developed by the current authors (Comput Methods Appl Mech Eng 2003; 192: 4281,4298; 4299,4312; 4313,4335) for time-dependent convective heat diffusion in two-dimensions appears to be a very attractive tool for efficient simulations of transient linear flows. However, the previous BEM formulation is restricted to relatively small time step sizes (i.e. ,t,4,/V2) owing to the convergence issues of the time series for the kernel representation within a time interval. This paper extends the boundary element formulation in a way to allow time step sizes several orders of magnitude larger than in the previous approach. We consider an example problem of thermal propagation, and investigate the accuracy and efficiency of BEM formulations for Peclet numbers in the range from 103 to 105. Copyright © 2005 John Wiley & Sons, Ltd. [source] Algebraic preconditioning versus direct solvers for dense linear systems as arising in crack propagation problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2005Erik Bängtsson Abstract Preconditioned iterative solution methods are compared with the direct Gaussian elimination method to solve dense linear systems Ax=b which originate from problems, discretized by boundary element method (BEM) techniques. Numerical experiments are presented and compared with the direct solution method available in a commercial BEM package, which show that the preconditioned iterative schemes are highly competitive with respect to both arithmetic operations required and memory demands. Copyright © 2004 John Wiley & Sons, Ltd. [source] Acoustic eigenanalysis for multiply-connected problems using dual BEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2004J. T. Chen Abstract In this paper, the eigenanalysis for the multiply-connected domain problem is studied by using the dual boundary element method. The occurrence and treatment of the spurious eigenvalues for multiply-connected domain problem are reviewed when the complex-valued BEM in used. Three approaches, Burton and Miller method, CHIEF concept and SVD updating techniques, are adopted to suppress the occurrence of spurious eigensolutions. Instead of using the singular and hypersingular formulations, the singularity-free methods, the null-field equation approach and the fictitious BEM, are also utilized to deal with the eigenproblem. Both the eigenvalues and eigenmodes are compared with the analytical solutions and those of FEM for the illustrative examples. Good agreement is made. Copyright © 2004 John Wiley & Sons, Ltd. [source] Transient scattering of plane waves from an inclusion with a unilateral frictional contact interface,a 2D time domain boundary element analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2004Yang-De Feng Abstract This paper is the continuity of our previous work (Commun Numer Meth Engng 2003; 19: 25,36) which applies the 2D time domain boundary element method (BEM) to solve the transient scattering of SH waves by an inclusion with a unilateral frictional contact interface. The case of the plane wave (P and/or SV wave) incidence is studied. Localized slip and separation at the interface caused by strong incident waves are considered. Therefore the interface involves three different kinds of unknown intervals: slip, separation and stick regions. In order to determine the unknown intervals, an iterative technique is developed. As an example, we compute the scattering of P waves by a cylinder of circular cross-section embedded in an infinite solid. Numerical results for the near field solutions are presented. The distortion of the response waves and the variation of the interface states are discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source] Transient scattering of SH waves from an inclusion with a unilateral frictional interface,a 2D time domain boundary element analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2003Yang-De Feng Abstract This paper develops a 2D time domain boundary element method (BEM) to solve the transient SH-wave scattering from an inclusion with a unilateral frictional interface. The incident SH-wave is assumed strong enough to break friction so that localized slip takes place along the interface. The present problem is indeed a non-linear boundary value problem since the mixed boundary conditions involve unknown intervals (the slip and stick zones). In order to determine the intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embedded in an infinite solid. The numerical results of the interface traction and relative slip velocity are presented. Copyright © 2003 John Wiley & Sons, Ltd. [source] Symmetric Galerkin BEM for multi-connected bodiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2001J. J. Pérez-Gavilán In this paper, it is shown that the symmetric Galerkin boundary element formulation cannot be used in its standard form for multiple connected bodies. This is because the traction integral equation used for boundaries with Neuman boundary condition give non-unique solutions. While this fact is well known from the classical theory of integral equations, the problem has not been fully addressed in the literature related to symmetric Galerkin formulations. In this paper, the problem is reviewed and a general way to deal with it is proposed. The details of the numerical implementation are discussed and an example is solved to demonstrate the effectiveness of the proposed solution. Copyright © 2001 John Wiley & Sons, Ltd. [source] BEM-analysis of interaction of elastic waves with unilateral interface crackINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2001Gai Bing-Zheng Abstract In this paper, to solve the problems of the interaction between the unilateral interface cracks and elastic wave, a new numerical method based on boundary element method (BEM) has been proposed. In this method, an iterating,correcting process of the solution in frequency domain and the correction in time domain has been designed to eliminate the mutual interference between the time and frequency domain. As an illustration to the algorithm, an interface crack between two half-planes under the attack of harmonic plane elastic wave has been analysed in detail. The contact configurations and stress field at the crack surface, and dynamic stress intensity factor (DSIF) at the crack tip have been given. Copyright © 2001 John Wiley & Sons, Ltd. [source] Coupling BEM/TBEM and MFS for the simulation of transient conduction heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2010António Tadeu Abstract The coupling between the boundary element method (BEM)/the traction boundary element method (TBEM) and the method of fundamental solutions (MFS) is proposed for the transient analysis of conduction heat transfer in the presence of inclusions, thereby overcoming the limitations posed by each method. The full domain is divided into sub-domains, which are modeled using the BEM/TBEM and the MFS, and the coupling of the sub-domains is achieved by imposing the required boundary conditions. The accuracy of the proposed algorithms, using different combinations of BEM/TBEM and MFS formulations, is checked by comparing the resulting solutions against referenced solutions. The applicability of the proposed methodology is shown by simulating the thermal behavior of a solid ring incorporating a crack or a thin inclusion in its wall. The crack is assumed to have null thickness and does not allow diffusion of energy; hence, the heat fluxes are null along its boundary. The thin inclusion is modeled as filled with thermal insulating material. Copyright © 2010 John Wiley & Sons, Ltd. [source] An advanced boundary element method for solving 2D and 3D static problems in Mindlin's strain-gradient theory of elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010G. F. Karlis Abstract An advanced boundary element method (BEM) for solving two- (2D) and three-dimensional (3D) problems in materials with microstructural effects is presented. The analysis is performed in the context of Mindlin's Form-II gradient elastic theory. The fundamental solution of the equilibrium partial differential equation is explicitly derived. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative, is developed. The global boundary of the analyzed domain is discretized into quadratic line and quadrilateral elements for 2D and 3D problems, respectively. Representative 2D and 3D numerical examples are presented to illustrate the method, demonstrate its accuracy and efficiency and assess the gradient effect on the response. The importance of satisfying the correct boundary conditions in gradient elastic problems is illustrated with the solution of simple 2D problems. Copyright © 2010 John Wiley & Sons, Ltd. [source] Meshless thermo-elastoplastic analysis by triple-reciprocity boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Yoshihiro OchiaiArticle first published online: 18 SEP 200 Abstract In general, internal cells are required to solve thermo-elastoplasticity problems by a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is the easy preparation of data, is lost. A conventional multiple-reciprocity boundary element method (MRBEM) cannot be used to solve elastoplasticity problems, because the distribution of initial strain or stress cannot be determined analytically. In this study, it is shown that without the use of internal cells, two-dimensional thermo-elastoplasticity problems can be solved by a triple-reciprocity BEM using a thin plate spline. Initial strain and stress formulations are adopted and the initial strain or stress distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solve several problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] GPU-accelerated boundary element method for Helmholtz' equation in three dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2009Toru Takahashi Abstract Recently, the application of graphics processing units (GPUs) to scientific computations is attracting a great deal of attention, because GPUs are getting faster and more programmable. In particular, NVIDIA's GPUs called compute unified device architecture enable highly mutlithreaded parallel computing for non-graphic applications. This paper proposes a novel way to accelerate the boundary element method (BEM) for three-dimensional Helmholtz' equation using CUDA. Adopting the techniques for the data caching and the double,single precision floating-point arithmetic, we implemented a GPU-accelerated BEM program for GeForce 8-series GPUs. The program performed 6,23 times faster than a normal BEM program, which was optimized for an Intel's quad-core CPU, for a series of boundary value problems with 8000,128000 unknowns, and it sustained a performance of 167,Gflop/s for the largest problem (1 058 000 unknowns). The accuracy of our BEM program was almost the same as that of the regular BEM program using the double precision floating-point arithmetic. In addition, our BEM was applicable to solve realistic problems. In conclusion, the present GPU-accelerated BEM works rapidly and precisely for solving large-scale boundary value problems for Helmholtz' equation. Copyright © 2009 John Wiley & Sons, Ltd. [source] An energy approach to space,time Galerkin BEM for wave propagation problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2009A. Aimi Abstract In this paper we consider Dirichlet or Neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential. Starting from a natural energy identity, a space,time weak formulation for 1D integral problems is briefly introduced, and continuity and coerciveness properties of the related bilinear form are proved. Then, a theoretical analysis of an extension of the introduced formulation for 2D problems is proposed, pointing out the novelty with respect to existing literature results. At last, various numerical simulations will be presented and discussed, showing unconditional stability of the space,time Galerkin boundary element method applied to the energetic weak problem. Copyright © 2009 John Wiley & Sons, Ltd. [source] Axial symmetric elasticity analysis in non-homogeneous bodies under gravitational load by triple-reciprocity boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009Yoshihiro Ochiai Abstract In general, internal cells are required to solve elasticity problems by involving a gravitational load in non-homogeneous bodies with variable mass density when using a conventional boundary element method (BEM). Then, the effect of mesh reduction is not achieved and one of the main merits of the BEM, which is the simplicity of data preparation, is lost. In this study, it is shown that the domain cells can be avoided by using the triple-reciprocity BEM formulation, where the density of domain integral is expressed in terms of other fields that are represented by boundary densities and/or source densities at isolated interior points. Utilizing the rotational symmetry, the triple-reciprocity BEM formulation is developed for axially symmetric elasticity problems in non-homogeneous bodies under gravitational force. A new computer program was developed and applied to solve several test problems. Copyright © 2008 John Wiley & Sons, Ltd. [source] A hypersingular time-domain BEM for 2D dynamic crack analysis in anisotropic solidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2009M. Wünsche Abstract A hypersingular time-domain boundary element method (BEM) for transient elastodynamic crack analysis in two-dimensional (2D), homogeneous, anisotropic, and linear elastic solids is presented in this paper. Stationary cracks in both infinite and finite anisotropic solids under impact loading are investigated. On the external boundary of the cracked solid the classical displacement boundary integral equations (BIEs) are used, while the hypersingular traction BIEs are applied to the crack-faces. The temporal discretization is performed by a collocation method, while a Galerkin method is implemented for the spatial discretization. Both temporal and spatial integrations are carried out analytically. Special analytical techniques are developed to directly compute strongly singular and hypersingular integrals. Only the line integrals over an unit circle arising in the elastodynamic fundamental solutions need to be computed numerically by standard Gaussian quadrature. An explicit time-stepping scheme is obtained to compute the unknown boundary data including the crack-opening-displacements (CODs). Special crack-tip elements are adopted to ensure a direct and an accurate computation of the elastodynamic stress intensity factors from the CODs. Several numerical examples are given to show the accuracy and the efficiency of the present hypersingular time-domain BEM. Copyright © 2008 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] Charge distribution on thin conducting nanotubes,reduced 3-D modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Hui Chen Abstract The subject of this paper is the calculation of charge distribution on the surfaces of thin conducting nanotubes in electrostatic problems, by the boundary element method (BEM). A line model of a nanotube is proposed here. This model overcomes the problem of dealing with nearly singular matrices that occur when the standard BEM is applied to very thin features (objects or gaps). This new approach is also very efficient. Numerical results are presented for selected examples. Copyright © 2006 John Wiley & Sons, Ltd. [source] A fast multi-level convolution boundary element method for transient diffusion problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005C.-H. Wang Abstract A new algorithm is developed to evaluate the time convolution integrals that are associated with boundary element methods (BEM) for transient diffusion. This approach, which is based upon the multi-level multi-integration concepts of Brandt and Lubrecht, provides a fast, accurate and memory efficient time domain method for this entire class of problems. Conventional BEM approaches result in operation counts of order O(N2) for the discrete time convolution over N time steps. Here we focus on the formulation for linear problems of transient heat diffusion and demonstrate reduced computational complexity to order O(N3/2) for three two-dimensional model problems using the multi-level convolution BEM. Memory requirements are also significantly reduced, while maintaining the same level of accuracy as the conventional time domain BEM approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] Boundary element formulation for 3D transversely isotropic cracked bodiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004M. P. Ariza Abstract The boundary traction integral representation is obtained in elasticity when the classical displacement representation is differentiated and combined according to Hooke's law. The use of both traction and displacement integral representations leads to a mixed (or dual) formulation of the BEM where the discretization effort for crack problems is much smaller than in the classical formulation. A boundary element analysis of three-dimensional fracture mechanics problems of transversely isotropic solids based on the mixed formulation is presented in this paper. The hypersingular and strongly singular kernels appearing in the formulation are regularized by using two terms of the displacement series expansion and one term of the traction expansion, at the collocation point. All the remaining integrals are analytically evaluated or transformed by means of Stokes' theorem into regular or weakly singular integrals, which are numerically computed. The method is general and can be used for elements of any shape including quarter-point crack front elements. No change of co-ordinates is required for the integration. The formulation as presented in this paper is something as clear, general and easy to handle as the classical BE formulation. It is used in combination with three-dimensional quadratic and quarter-point elements to obtain accurate results for several different crack problems. Cracks in boundless and finite transversely isotropic domains are studied. The meshes are simple and include only discretization of the crack and the external boundary. The obtained results are in good agreement with those existing in the literature. Copyright © 2004 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] 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] Transient heat conduction analysis in a piecewise homogeneous domain by a coupled boundary and finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2003I. Guven Abstract A coupled finite element,boundary element analysis method for the solution of transient two-dimensional heat conduction equations involving dissimilar materials and geometric discontinuities is developed. Along the interfaces between different material regions of the domain, temperature continuity and energy balance are enforced directly. Also, a special algorithm is implemented in the boundary element method (BEM) to treat the existence of corners of arbitrary angles along the boundary of the domain. Unknown interface fluxes are expressed in terms of unknown interface temperatures by using the boundary element method for each material region of the domain. Energy balance and temperature continuity are used for the solution of unknown interface temperatures leading to a complete set of boundary conditions in each region, thus allowing the solution of the remaining unknown boundary quantities. The concepts developed for the BEM formulation of a domain with dissimilar regions is employed in the finite element,boundary element coupling procedure. Along the common boundaries of FEM,BEM regions, fluxes from specific BEM regions are expressed in terms of common boundary (interface) temperatures, then integrated and lumped at the nodal points of the common FEM,BEM boundary so that they are treated as boundary conditions in the analysis of finite element method (FEM) regions along the common FEM,BEM boundary. Copyright © 2002 John Wiley & Sons, Ltd. [source] Analytical study and numerical experiments for degenerate scale problems in the boundary element method for two-dimensional elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002J. T. Chen Abstract For a plane elasticity problem, the boundary integral equation approach has been shown to yield a non-unique solution when geometry size is equal to a degenerate scale. In this paper, the degenerate scale problem in the boundary element method (BEM) is analytically studied using the method of stress function. For the elliptic domain problem, the numerical difficulty of the degenerate scale can be solved by using the hypersingular formulation instead of using the singular formulation in the dual BEM. A simple example is shown to demonstrate the failure using the singular integral equations of dual BEM. It is found that the degenerate scale also depends on the Poisson's ratio. By employing the hypersingular formulation in the dual BEM, no degenerate scale occurs since a zero eigenvalue is not embedded in the influence matrix for any case. Copyright © 2002 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||