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

Document Type : Research Article

Authors

• R. Si Hadj Mohand
• Y. Belkacemi
• S. Rechak

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

10.22067/ijnao.2025.93526.1647

Abstract

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 two-dimensional elasticity problems is introduced and verified. This criterion is formulated as an empirical formula, 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 compu-tational overhead in the case of pre-treatment of near-singularities by a semi-analytical technique or a variable transformation technique. 

Keywords

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

Main Subjects

• Modeling and Simulation

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