Polygonal finite element: A comparison of the stiffness matrix integration methods

Renan Lima Thomes and Fernando C.M. Menandro

Applied Mathematics and Computation, 2020, vol. 375, issue C

Abstract: This paper aims to determine which numerical integration method shows the best performance when integrating the polygonal finite element stiffness matrix. Hence, numerical comparisons were made between two existing methods, triangulation and quadrangulation, and two new quadrature rules developed by the authors called Polygonal Gauss–Legendre quadrature (PGL) and Rational Polynomial Gauss quadrature (RPG). In this study, PGL11Polygonal Gauss-Legendre quadrature. points and weights were obtained for polynomials of degree 3, 5, 6, 8 and 9, while RPG22Rational Polynomial Gauss quadrature. rules were calculated for rational polynomials of degree 8/8, 10/8 and 16/16. Briefly, the PGL rule showed the best performance, reducing the execution time in 38.6% at best (compared with the triangulation), also, its implementation is much more straightforward.

Keywords: Polygonal finite element; Numerical integration; Gaussian quadrature; Rational polynomial; Rational function (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:375:y:2020:i:c:s0096300320300588

DOI: 10.1016/j.amc.2020.125089

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