Abstract
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.