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 ...

Boundary integral equations are a classical tool for the analysis of boundary value problems for partial differential equations. The term “ boundary element method” (BEM) denotes any method for the approximate numerical solution of these boundary integral equations. The approximate solution of the boundary value problem obtained by BEM has the distinguishing feature that it is an exact solution...

We consider scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. ...

We present and analyze a coupled finite element-boundary element method for a model in stationary micromagnetics. The finite element part is based on mixed conforming elements. For two- and three-dimensional settings, we show well-posedness of the discrete problem and present an a priori error analysis for the case of lowest order elements.

The purpose of this paper is to present a new fictitious domain approach inspired by the extended finite element method introduced by Moës, Dolbow and Belytschko in [18]. An optimal method is obtained thanks to an additional stabilization technique. Some a priori estimates are established and numerical experiments illustrate different aspects of the method. The presentation is made on a simple ...

This paper presents an overview of crack problems and numerical analysis of piezoelectric materials. Developments in Green‘s function, Crack problem, finite element, and boundary element formulation of piezoelectric materials are described. Finally, a brief summary of the approaches discussed is provided and future trends in this field are identified.

Time-dependent problems modeled by hyperbolic partial differential equations (PDEs) can be reformulated in terms of boundary integral equations (BIEs) and solved via the boundary element method (BEM). In this context, the analysis of damping phenomena that occur in many physics and engineering problems is of particular interest. Starting from a recently developed energetic space-time weak formu...