Green’s functions are important mathematical tools in mechanics and in other parts of physics. For instance, the boundary element method needs to know the Green’s function of the problem to compute its numerical solution. However, Green’s functions are only known in a limited number of cases, often under the form of complex analytical expressions. In this article, a new method is proposed to ca...

In this paper we prove an optimal error estimate for the H(curl)-conforming projection based p-interpolation operator introduced in [L. Demkowicz and I. Babuška, p interpolation error estimates for edge finite elements of variable order in two dimensions, SIAM J. Numer. Anal., 41 (2003), pp. 1195–1208]. This result is proved on the reference element (either triangle or square) K for regular vec...

We calculate elastic moduli and viscosities for media containing strongly interacting in-plane shear cracks. The cracks are randomly oriented or aligned, with equal length or a logarithmic size distribution. Our results from both a boundary element and a finite-element method suggest that the average moduli are best approximated by a differential, self-consistent model (DEM). Thus crack-tocrack...

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...

This article deals with the existence of blockwise low-rank approximants — so-called H-matrices — to inverses of FEM matrices in the case of uniformly elliptic operators with L∞-coefficients. Unlike operators arising from boundary element methods for which the H-matrix theory has been extensively developed, the inverses of these operators do not benefit from the smoothness of the kernel functio...

Porous materials have recently been used in absorptive treatments around railway tracks to reduce noise emissions. To investigate the effect of porous materials, a finite element model has been developed. 2D models for porous materials have been considered either as an equivalent fluid or as a poroelastic material based on the Biot theory. The two models have been validated and compared with ea...

Simulation of new generation gas detectors is rendered complicated due to the non-trivial nature of the electric field and simultaneous presence of several length-scales. Computation of the electrostatic field, however, is extremely important since streamers in gas volume and streamers across the dielectric surfaces are known to cause serious damage to Micro Pattern Gas Detectors (MPGD) and are...

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.

This paper presents an overview of micromechanics analysis of piezoelectric composites. Developments in micromechanics algorithms, finite element, and boundary element formulation for predicting effective material properties of piezoelectric composites are described. Finally, a brief summary of the approaches discussed is provided and future trends in this field are identified.