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Boundary-element Method (boundary-element + method)
Selected AbstractsResponse of unbounded soil in scaled boundary finite-element methodEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 1 2002John P. Wolf Abstract The scaled boundary finite-element method is a powerful semi-analytical computational procedure to calculate the dynamic stiffness of the unbounded soil at the structure,soil interface. This permits the analysis of dynamic soil,structure interaction using the substructure method. The response in the neighbouring soil can also be determined analytically. The method is extended to calculate numerically the response throughout the unbounded soil including the far field. The three-dimensional vector-wave equation of elasto-dynamics is addressed. The radiation condition at infinity is satisfied exactly. By solving an eigenvalue problem, the high-frequency limit of the dynamic stiffness is constructed to be positive definite. However, a direct determination using impedances is also possible. Solving two first-order ordinary differential equations numerically permits the radiation condition and the boundary condition of the structure,soil interface to be satisfied sequentially, leading to the displacements in the unbounded soil. A generalization to viscoelastic material using the correspondence principle is straightforward. Alternatively, the displacements can also be calculated analytically in the far field. Good agreement of displacements along the free surface and below a prism foundation embedded in a half-space with the results of the boundary-element method is observed. Copyright © 2001 John Wiley & Sons, Ltd. [source] Semi-analytical far field model for three-dimensional finite-element analysisINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2004James P. Doherty Abstract A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non-linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three-dimensional finite-elements with the recently developed scaled boundary finite-element method. The scaled boundary finite-element method is a semi-analytical technique based on finite-elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co-ordinate direction, but, unlike the boundary-element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three-dimensional finite-element domain with the stiffness matrix of the unbounded scaled boundary finite-element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co-ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd. [source] An appropriate quadrature rule for the analysis of plane crack problems in the boundary-element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2001E. E. Theotokoglou Abstract An hypersingular integral equation of a three-dimensional elastic solid with an embedded planar crack subjected to a uniform stress field at infinity is derived. The solution of the boundary-integral equation is succeeded taking into consideration an appropriate Gauss quadrature rule for finite part integrals which is suitable for the numerical treatment of any plane crack with a smooth-contour shape and permit the fast convergence for the results. The problem of a circular and of an elliptical crack in an infinite body subjected to a uniform stress field at infinity is confronted; and the stress intensity factors are calculated. Copyright © 2001 John Wiley & Sons, Ltd. [source] Quasi-dual reciprocity boundary-element method for incompressible flow: Application to the diffusive,advective equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003C. F. Loeffler Abstract This work presents a new boundary-element method formulation called quasi-dual reciprocity formulation for heat transfer problems, considering diffusive and advective terms. The present approach has some characteristics similar to those of the so-called dual-reciprocity formulation; however, the mathematical developments of the quasi-dual reciprocity approach reduces approximation errors due to global domain interpolation. Some one- and two-dimensional examples are presented, the results being compared against those obtained from analytical and dual-reciprocity formulations. The method convergence is evaluated through analyses where the mesh is successively refined for various Peclet numbers, in order to assess the effect of the advective term. Copyright © 2003 John Wiley & Sons, Ltd. [source] Performance of a parallel implementation of the FMM for electromagnetics applicationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2003G. Sylvand Abstract This paper describes the parallel fast multipole method implemented in EADS integral equations code. We will focus on the electromagnetics applications such as CEM and RCS computation. We solve Maxwell equations in the frequency domain by a finite boundary-element method. The complex dense system of equations obtained cannot be solved using classical methods when the number of unknowns exceeds approximately 105. The use of iterative solvers (such as GMRES) and fast methods (such as the fast multipole method (FMM)) to speed up the matrix,vector product allows us to break this limit. We present the parallel out-of-core implementation of this method developed at CERMICS/INRIA and integrated in EADS industrial software. We were able to solve unprecedented industrial applications containing up to 25 million unknowns. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||