M. S. Bapat¹, Y. J. Liu^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 161-184, 2010, DOI:10.3970/cmes.2010.058.161

Abstract A new definition of the interaction list in the fast multipole method (FMM) is introduced in this paper, which can reduce the moment-to-local (M2L) translations by about 30-40% and therefore improve the efficiency for the FMM. In addition, an adaptive tree structure is investigated, which is potentially more efficient than the oct-tree structure for thin and slender domains as in the case of micro-electro-mechanical systems (MEMS). A combination of the modified interaction list (termed L2 modification in the adaptive fast multipole BEM) and the adaptive tree structure in the fast multipole BEM has been implemented for both 3-D potential and… More >

D. Brunner¹, M. Junge¹, P. Rapp¹, M. Bebendorf², L. Gaul¹

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 131-160, 2010, DOI:10.3970/cmes.2010.058.131

Abstract The simulation of the hydroacoustic sound radiation of ship-like structures has an ever-growing importance due to legal regulations. Using the boundary element method, the overall dimension of the problem is reduced and only integrals over surfaces have to be considered. Additionally, the Sommerfeld radiation condition is automatically satisfied by proper choice of the fundamental solution. However, the resulting matrices are fully populated and the set-up time and memory consumption scale quadratically with respect to the degrees of freedom. Different fast boundary element methods have been introduced for the Helmholtz equation, resulting in a quasilinear complexity. Two of these methods are… More >

M. Schanz¹

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 109-130, 2010, DOI:10.3970/cmes.2010.058.109

Abstract Boundary Element formulations in time domain suffer from two problems. First, for hyperbolic problems not too much fundamental solutions are available and, second, the time stepping procedure is expensive in storage and has stability problems for badly chosen time step sizes. The first problem can be overcome by using the Convolution Quadrature Method (CQM) for time discretisation. This as well improves the stability. However, still the storage requirements are large. A recently published reformulation of the CQM by Banjai and Sauter [Rapid solution of the wave equation in unbounded domains, SIAM J. Numer. Anal., 47, 227-249] reduces the time stepping… More >

N. Simões^1,2, A. Tadeu²

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.3, pp. 221-234, 2005, DOI:10.3970/cmes.2005.009.221

Abstract The use of the Boundary Element Method (BEM) to formulate the 3D transient heat transfer through cylindrical structures with irregular cross-sections, bounded by a homogeneous elastic medium, is described in this paper. In this formulation, both the conduction and the convection phenomena are modeled. This system can be subjected to heat emitted by either point or line sources located somewhere in the media. The solution is first obtained in the frequency domain for a wide range of frequencies and axial wavenumbers. Time domain responses are later calculated by means of (fast) inverse Fourier transforms into space-time. The appropriate fundamental solution… More >

J. Purbolaksono¹, M. H. Aliabadi^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.1, pp. 73-90, 2005, DOI:10.3970/cmes.2005.008.073

Abstract This paper presents the dual boundary integral equations for the buckling analysis of the shear deformable cracked plates. The domain integrals which appear in this formulation are transferred to boundary integrals using the dual reciprocity method. The plate buckling displacement and hypersingular traction integral equations are presented as a standard eigenvalue problem, which would allow direct evaluation of the critical load factor and buckling modes. Several examples with different geometries and boundary conditions are presented to demonstrate the accuracy of the proposed formulation. More >

Y.C. Shiah¹, T.L. Guao¹, C.L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 321-338, 2005, DOI:10.3970/cmes.2005.007.321

Abstract It is well known in elastic stress analysis using the boundary element method (BEM) that an additional volume integral appears in the basic form of the boundary integral equation if thermal effects are considered. In order to restore this general numerical tool as a truly boundary solution technique, it is perhaps most desirable to transform this volume integral exactly into boundary ones. For general 2D anisotropic thermo-elastostatics without heat sources, this was only achieved very recently. The presence of concentrated heat sources in the domain, however, leads to singularities at these points that pose additional difficulties in the volume-to-surface integral… More >

Zai You Yan^1,2, Fang Sen Cui², Kin Chew Hung²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 97-106, 2005, DOI:10.3970/cmes.2005.007.097

Abstract Taking the normal derivative of solid angles on the surface into account, a modified Burton and Miller's formulation is derived. From which, a more reasonable expression of the hypersingular operator is obtained. To overcome the hypersingular integral, the regularization scheme developed recently is employed. Plane acoustic wave scattering from a rigid sphere is computed to show the correctness of the modified formulation with the regularization scheme. In the computation, eight-nodded isoparametric element is applied. More >

Haitao Wang¹, Zhenhan Yao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 85-96, 2005, DOI:10.3970/cmes.2005.007.085

Abstract This paper addresses a new boundary element method (BEM) for the numerical analysis of mechanical properties in 3D particle-reinforced composites. The BEM is accelerated by a new version fast multipole method (FMM) in order to perform large scale simulation of a representative volume element (RVE) containing up to several hundred randomly distributed elastic spherical particles on only one personal computer. The maximum number of degrees of freedom (DOF) reaches more than 300,000. Efficiency of the developed new version fast multipole BEM code is evaluated compared with other conventional solutions for BEM. The effects of micro-structural parameters, namely the particle size,… More >

Yoshihiro Ochiai¹, Vladimir Sladek²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 525-536, 2004, DOI:10.3970/cmes.2004.006.525

Abstract The conventional boundary element method (BEM) uses internal cells for the domain integralsCwhen solving nonlinear problems or problems with domain effects. This paper is concerned with conversion of the domain integral into boundary ones and some non-integral terms in a three-dimensional BIEM, which does not require the use of internal cells. This method uses arbitrary internal points instead of internal cells. The method is based on a three-dimensional interpolation method in this paper by using a polyharmonic function with volume distribution. In view of this interpolation method, the three-dimensional numerical integration is replaced by boundary ones and preceding calculation of… More >

S. Callsen¹, O. von Estorff¹, O. Zaleski²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 421-430, 2004, DOI:10.3970/cmes.2004.006.421

Abstract In standard boundary element formulations, singular integrals need to be solved as soon as the considered sources coincide with the collocation points at the boundary. Using a desingularized boundary element approach, the sources are distributed on a surface outside the acoustic domain which means that they are never located at the boundary. Consequently, all the resulting kernels are nonsingular which reduces the complexity of the numerical treatment of the boundary integral equations considerably. In the current contribution a desingularized formulation is given for both, the direct and the indirect boundary element method used to solve acoustical problems. Three basic examples… More >