Applications of Composite Numerical Integrations Using Gauss-Radau and Gauss-Lobatto Quadrature Rules
Keywords:Double integral, Numerical Integration, Quadrilateral and Triangular Finite Element, Gauss-Radau and Gauss-Lobatto quadratures.
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)
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