Parametric integral equation system (PIES) for solving problems with inclusions and non-homogeneous domains using Bézier surfaces

Abstract

The paper presents the approach for solving 2D elastic boundary value problems defined in domains with inclusions with different material properties using the parametric integral equation system (PIES). The main feature of the proposed strategy is using Bézier surfaces for global modeling of inclusions. Polygonal inclusions are defined by bilinear surfaces, while others by bicubic surfaces. It is beneficial over other numerical methods (such as FEM and BEM) due to the lack of discretization. Integration over inclusions defined by surfaces is also performed globally without division into subareas. The considered problem is solved iteratively in order to simulate different material properties by applying initial stresses within the inclusion. This way of solving avoids increasing the number of unknowns and can also be used for elasto-plastic problems without significant changes. Some numerical tests are presented, in which the results obtained are compared with those calculated by other numerical methods. This paper is an extended version of author's conference paper [1]. It has been enriched with, among others, the description of modeling more complex inclusions, as well as additional results obtained by PIES compared to other numerical methods.