Applications of Composite Numerical Integrations Using Gauss-Radau and Gauss-Lobatto Quadrature Rules
DOI:
https://doi.org/10.3329/jsr.v2i3.5123Keywords:
Double integral, Numerical Integration, Quadrilateral and Triangular Finite Element, Gauss-Radau and Gauss-Lobatto quadratures.Abstract
In this paper, numerical integrals over an arbitrary triangular region are evaluated exploiting finite element method. The physical region is transformed into a standard triangular finite element using the basis functions in local space. Then the standard triangle is discretized into 4×n2 right isosceles triangles, in which each of these triangles having area 1/2n2, and thus composite numerical integration is employed. In addition, the affine transformation over each discretized triangle and the use of linearity property of integrals are applied. Finally, each isosceles triangle is transformed into a 2-sqare finite element to generate new n2 extended sampling points and corresponding weight coefficients, using n point’s conventional Gauss-Radau and Gauss-Lobatto quadratures, which are applied again to evaluate the double integral. The performance is depicted by means of numerical examples.
Keywords: Double integral; Numerical Integration; Quadrilateral and Triangular Finite Element; Gauss-Radau and Gauss-Lobatto quadratures.
© 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.
DOI: 10.3329/jsr.v2i3.5123 J. Sci. Res. 2 (3), 465-467 (2010)
Downloads
111
83
Downloads
Published
How to Cite
Issue
Section
License
© Journal of Scientific Research
Articles published in the "Journal of Scientific Research" are Open Access articles under a Creative Commons Attribution-ShareAlike 4.0 International license (CC BY-SA 4.0). This license permits use, distribution and reproduction in any medium, provided the original work is properly cited and initial publication in this journal. In addition to that, users must provide a link to the license, indicate if changes are made and distribute using the same license as original if the original content has been remixed, transformed or built upon.