A New Approach To Automatic Generation Of All Quadrilateral Meshes Over A Linear Convex Polygon With H-Refinements For Finite Element Analysis

Abstract

This paper presents  an automatic  mesh  generation scheme for a  linear convex  polygonal  domain   in   with boundary composed of piecewise straight lines.We  can   express

=

in which  is a polygonal domain of N oriented edges with end points    and . Where,it is assumed that can be discretised into a set of N triangles,  and we can also divide each triangle    into smaller triangles  so that    which gives us a triangular mesh  with  h-refinement ,when this procedure is repeated for all triangles we obtain a triangular mesh with  h-refinement for a linear convex polygon, further we can discretise each triangle   into three special quadrilaterals a=0,1,2 which are obtained by joining the centroid to the midpoint of its sides and we have created an  all quadrilateral mesh. We choose  = an arbitrary triangle with vertices  in Cartesian space We have furthered refined this mesh two times. We have taken  this further and created   12-new quadrilaterals by joining the centroids of the 3-special quadrilaterals to the midpoints  which can be called as first h-refinement.Then each of these  quadrilateral is divided into four smaller quadrilaterals again by joining the centroids to the mid points of sides which we call as  the second h- refinement.