The paper contains a description of a multiscale algorithm based on the boundary element method (BEM) coupled with a discrete atomistic model. The atomic model uses empirical pair-wise potentials to describe interactions between atoms. The Newton-Raphson method is applied to solve a nanoscale model. The continuum domain is modelled by using BEM. The application of BEM reduces the total number of degrees of freedom in the multiscale model. Some numerical results of simulations

at the nanoscale are shown to examine the presented algorithm.

One of the most effective designs to control the road traffic noise is the T-shaped barrier. The aim of this study was to examine the performance of T-shape noise barriers covered with oblique diffusers using boundary element method. A 2D simulation technique based on the boundary element method (BEM) was used to compute the insertion loss at the center frequency of each one-third octave band. In designed barriers, the top surface of the T-shaped noise barriers was covered with oblique diffusers. The width and height of the barrier stem and the width of its cap were 0.3, 2.7, and 1 m, respectively. Angles of he oblique diffusers were 15, 30, and 45 degrees. The oblique diffusers were placed on the top surface with two designs including same oblique diffusers (SOD) and quadratic residue oblique diffusers (QROD). Barriers considered were made of concrete, an acoustically rigid material. The barrier with characteristics of QROD, forward direction, and sequence of angles (15, 30, and 45 degrees) had the greatest value of the overall A-weighted insertion loss equal to 18.3 to 21.8 dBA at a distance of 20 m with various heights of 0 to 6 m.

The paper presents a tool for accurate evaluation of high field concentrations near singular lines, such as contours of cracks, notches and grains intersections, in 3D problems solved the BEM. Two types of boundary elements, accounting for singularities, are considered: (i) edge elements, which adjoin a singular line, and (ii) intermediate elements, which while not adjoining the line, are still under strong influence of the singularity. An efficient method to evaluate the influence coefficients and the field intensity factors is suggested for the both types of the elements. The method avoids time expensive numerical evaluation of singular and hypersingular integrals over the element surface by reduction to 1D integrals. The method being general, its details are explained by considering a representative examples for elasticity problems for a piece-wise homogeneous medium with cracks, inclusions and pores. Numerical examples for plane elements illustrate the exposition. The method can be extended for curvilinear elements.

In the paper the thermal processes proceeding in the solidifying metal are analyzed. The basic energy equation determining the course of solidification contains the component (source function) controlling the phase change. This component is proportional to the solidification rate ¶ fS/¶ t (fS Î [0, 1], is a temporary and local volumetric fraction of solid state). The value of fS can be found, among others, on the basic of laws determining the nucleation and nuclei growth. This approach leads to the so called micro/macro models (the second generation models). The capacity of internal heat source appearing in the equation concerning the macro scale (solidification and cooling of domain considered) results from the phenomena proceeding in the micro scale (nuclei growth). The function fS can be defined as a product of nuclei density N and single grain volume V (a linear model of crystallization) and this approach is applied in the paper presented. The problem discussed consists in the simultaneous identification of two parameters determining a course of solidification. In particular it is assumed that nuclei density N (micro scale) and volumetric specific heat of metal (macro scale) are unknown. Formulated in this way inverse problem is solved using the least squares criterion and gradient methods. The additional information which allows to identify the unknown parameters results from knowledge of cooling curves at the selected set of points from solidifying metal domain. On the stage of numerical realization the boundary element method is used. In the final part of the paper the examples of computations are presented.

An isogeometric boundary element method is applied to simulate wave scattering problems governed by the Helmholtz equation. The NURBS (non-uniform rational B-splines) widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The singular integrals existing in Burton-Miller formulation are evaluated directly and accurately using Hadamard’s finite part integration. Fast multipole method is applied to accelerate the solution of the system of equations. It is demonstrated that the isogeometric boundary element method based on NURBS performs better than the conventional approach based on Lagrange basis functions in terms of accuracy, and the use of the fast multipole method both retains the accuracy for isogeometric boundary element method and reduces the computational cost.