Another general numerical method has recently emerged that provides good computational abilities and has some particular advantages when compared to FEM. The technique known as the boundary element method (BEM) has been widely used by computational mechanics investigators leading to the development of many private and commercial codes. Similar to the finite element method, BEM can analyze many ...

An advanced boundary element method (BEM) with thin-body capabilities was developed recently for the study of interphases in ®ber-reinforced composite materials (Y.J. Liu, N. Xu and J.F. Luo, Modeling of interphases in ®berreinforced composites under transverse loading using the boundary element method, ASME J. Appl. Mech. 67 (2000) 41±49). In this BEM approach, the interphases are modeled as t...

In this paper, a coupled numerical method of the edge-based smoothed finite element (ES-FEM) with the fast multipole BEM (FM-BEM) is proposed to analyze structural acoustic problems. The vibrating structure is modeled using the so-called ES-FEM-DSG3 method, where the 3-node linear triangle plate elements based on the Reissner–Mindlin plate theory with the discrete shear gap (DSG) technique for ...

The most suitable and widely used numerical integration method for boundary integrals in the BEM method is Gauss-Legendre integration. But, this integration method is not appropriate for singular and nearly singular integrations in BEM. In this study, some criteria are introduced for recognizing nearly singular integrals in the integral form of the Laplace equation. At the rst stage, a criterio...

This study is concerned with the numerical approximation of the extended Fisher-Kolmogorov equation with a modified boundary integral method. A key aspect of this formulation is that it relaxes the domain-driven approach of a typical boundary element (BEM) technique. While its discretization keeps faith with the second order accurate BEM formulation, its implementation is element-based. This le...

In this paper, an advanced boundary element method (BEM) with thin-body capabilities is applied to model multiple cells of ®ber-reinforced composites with the consideration of the interphases. E€ects of the multiple-cell models, as compared to the unit-cell model, in determining the e€ective material constants in the transverse plane, are studied. In this BEM approach, the interphases are model...

The boundary element method (BEM) is a useful tool in diffuse optical imaging (DOI) when modelling large optical regions whose parameters are piecewise constant, but are computationally expensive. We present here an acceleration technique, the single-level fast multipole method, for a highly lossy medium. The enhanced practicability of the BEM in DOI is demonstrated through test examples on sin...

Traditional numerical methods for time-harmonic acoustic scattering problems become prohibitively expensive in the high-frequency regime where the scatterer is large compared to the wavelength of the incident wave. In this paper we propose and analyse a hybrid boundary element method (BEM) for a class of non-convex polygonal scatterers. In this method the approximation space is enriched with os...

We consider the Galerkin boundary element method (BEM) for weaklysingular integral equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the unknown Galerkin BEM error. The required assumptions are weak and allow for piecewise smooth parametrizations of the boundary, local mesh-refinement, and related s...

Nowadays, various numerical methods are developed to extend computational fluid dynamics in engineering applications. One of the most useful methods in free surface modeling is Boundary Element Method (BEM). BEM is used to model inviscid fluid flow such as flow around ships. BEM solutions employ surface mesh at all of the boundaries. In order to model the linear free surface, BEM can be modifie...