Isoparametric singularity extraction technique for 3D potential problems in BEM

Kanduč, Tadej (author)

To solve boundary integral equations for potential problems using collocation Boundary Element Method (BEM) on smooth curved 3D geometries, an analytical singularity extraction technique is employed. By adopting the isoparametric approach, curved geometries that are represented by mapped rectangles or triangles from the parametric domain are considered. The singularity extraction on the governing singular integrals can be performed either as an operation of subtraction or division, each having some advantage. A particular series expansion of a singular kernel about a source point is investigated. The series in the parametric coordinates consists of functions of a type $R^px^qy^r$, where $R$ is a square root of a quadratic bivariate homogeneous polynomial with coefficients corresponding to the first fundamental form of a smooth surface, and $p, q, r$ are integers, satisfying $p \le -1$ and $q, r \ge 0$. By extracting more terms from the series expansion of the singular kernel, the smoothness of the regularized kernel at the source point can be increased. Analytical formulae for integrals of such terms are obtained from antiderivatives of $R^px^qy^r$, using recurrence formulae, and by evaluating them at the edges of rectangular or triangular parametric domains. Numerical tests demonstrate that the singularity extraction technique can be a useful prerequisite for a numerical quadrature scheme to obtain high order of convergence for the governing singular integrals in 3D collocation BEM with respect to the number of quadrature nodes or with respect to size of the discretization mesh cells.

• Language: English
• Keywords: analytical integration, singular integral, singularity extraction, boundary element method, isogeometric analysis
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics; FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2022
• Number of pages: 25 str.
• Numbering: Vol. 398, art. 115271
• PID: 20.500.12556/RUL-144095
• UDC: 519.651
• ISSN on article: 0045-7825
• DOI: 10.1016/j.cma.2022.115271
• COBISS.SI-ID: 139374339
• Publication date in RUL: 31.01.2023

Record is a part of a journal

• Title: Computer methods in applied mechanics and engineering
• Shortened title: Comput. methods appl. mech. eng.
• Publisher: Elsevier
• ISSN: 0045-7825
• COBISS.SI-ID: 6695685

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: analitična integracija, singularni integral, ekstrakcija singularnosti, metoda končnih elementov, izogeometrična analiza