The finite element method (FEM) is a domain technique of solving the underlying governing equation in the region. The solution obtained in the total region is ideal to study energy/defect interactions, but the extensive discretization demands vast computer resources. On the other hand, the potential savings in computation resources, due to a limited surface or boundary discretization, is the pr...

A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex not...

The numerical analysis of boundary layer effect is one of the major concerned problems in boundary element method (BEM). The accuracy of this problem depends on the precision of the evaluation of the nearly singular integrals. In the boundary element analysis with direct formulation, the hyper-singular integral will arise from the potential derivative boundary integral equations (BIEs). Thus th...

Only very recently, Sayas [The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM J Numer Anal 2009;47:3451-63] proved that the Johnson-Nédélec one-equation approach from [On the coupling of boundary integral and finite element methods. Math Comput 1980;35:1063-79] provides a stable coupling of finite element method (FEM) and boundary element method (BEM). In our work,...

In this paper, we compare the direct boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) for solving the direct interior Helmholtz problem, in terms of their numerical accuracy and efficiency, as well as their applicability and reliability in the frequency domain. For BEM formulation, there are two possible choices for fundamental solutions, which can lead to ...

Sponsored by the U.S. National Science Foundation, a workshop on the boundary element method (BEM) was held on the campus of the University of Akron during September 1–3, 2010 (NSF, 2010, “Workshop on the Emerging Applications and Future Directions of the Boundary Element Method,” University of Akron, Ohio, September 1–3). This paper was prepared after this workshop by the organizers and partic...

The Boundary Element Method (BEM) has long been considered to be a viable alternative to the Finite Element Method (FEM) for doing engineering analysis. The BEM reduces the dimensions of the problem by one and leads to smaller system of equations. One of the inherent limitations of the BEM has been the long time required for the solution of large problems. This makes the BEM prohibitively expen...

The paper presents the effectiveness of the parametric integral equation system (PIES) in solving 3D boundary problems defined by Navier-Lame equations on the example of the polygonal boundary and in comparison with the boundary element method (BEM). Analysis was performed using the commercial software “BEASY” which bases on the BEM method, whilst in the case of PIES using an authors software. ...

We consider the numerical solution of the wave equation in a two-dimensional domain and start from a boundary integral formulation for its discretization. We employ the convolution quadrature (CQ) for the temporal and a Galerkin boundary element method (BEM) for the spatial discretization. Our main focus is the sparse approximation of the arising sequence of boundary integral operators by panel...