(untitled) (International Journal of Engineering and Computer Science, 2017)
This paper presents a numerical integration formula for the evaluation of ( ) ∬ ( ) where ( ) and is any polygonal domain in . That is a closed domain with boundary composed of N oriented piecewise line segments ( ) with end points ( ), ( ) and ( ) (( ). We join each of these line segments to a reference point ( ) interior to the domain . This creates a coarse mesh of N triangles ( ) in and each of these arbitrary triangles have three straight sides. These arbitrary triangles can be divided into arbitrary triangles ( ,2,3,…. ). by using the triangular mesh generation scheme developed in this paper. We transform each = (say) into a standard 1-square and then into a 2-square which can be integrated by using Gauss Legendre quadraure rules.We obtain enhanced accuracy by division of these arbitrary triangles into four arbitrary triangles (e=1,2,3,4) without refining the already generated triangular mesh.We first derive three different integration formulas for the integral ∬ ( ) where (( ) ) Then we establish the necessary numerical integration formulas which use the well known Gauss Legendre quadrature rules. Proposed numerical integration formula is applied to integrals over triangular and polygonal domains with complicated integrands.