An adaptive scheme for the efficient evaluation of integrals in two-dimensional boundary element method

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 مرداد 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.93526.1647

نویسندگان

Rahim SI HADJ MOHAND^* ؛ Yacine BELKACEMI؛ Said RECHAK

Laboratory of Green Mechanics and Development (LGMD), Department of mechanical engineering, Ecole Nationale Polytechnique, Algiers, Algeria.

چکیده

An efficient analysis with the boundary element method requires an accurate evaluation of all the boundary integrals. Typically, nonsingular integrals are solved numerically using Gauss quadrature. Therefore, the development of criteria and schemes that determine the appropriate Gauss order while maintaining a balance between accuracy and performance is of great importance.
In the present work, an adaptive integration criterion tailored for 2D elasticity problems is introduced and verified. This criterion is formulated as empirical formulae, incorporating a parameter ranging from zero to unity. This parameter enables control over computational effort, making the criterion very efficient across a wide range of applications, from thick structures to extremely thin ones where near-singularities are pronounced.
The proposed integration criterion is tested on a very thin structure, where it showed a high degree of accuracy and effectiveness in solving problems with a very pronounced boundary layer effect. Additionally, the criterion demonstrated its advantage by reducing and moderating computational overhead in the case of pretreatment of near-singularities by a semi-analytical technique or a variable transformation technique.

کلیدواژه‌ها

Boundary integrals؛ Near-singularity؛ Gauss quadrature؛ Integration criterion؛ Thin structures