Numerical homogenization by using the fast multipole boundary element method

The paper concerns the numerical homogenization of non-homogeneous linear-elastic materials by using the fast multipole boundary element method (FMBEM). Application of the FMBEM allows for the analysis of structures with larger number of degrees of freedom (DOF) in comparison to the conventional collocation BEM, which has at least the quadratic complexity. The FMBEM is convenient in the numerical homogenization by modelling of complex representative volume elements. In this article two examples of homogenization are presented. The first one concerns a porous material, and the second one – a composite material. The obtained results are in good agreement with analytical, semi-empirical and empirical models, and also with numerical results presented by other authors.