Curved domain discretization with boundary defined by polar equations

Abstract

A domain discretisation procedure for a planar curved domain with boundary in polar equations is presented. The curved domain is split into curved triangles and then to a fine mesh of linear triangles in the interior and curved triangles or linear triangles near to the boundary. Later by inserting midside nodes to these triangles 6-node triangles obtained further each one into four triangles. The mesh conformity is preserved by applying similar procedure to every triangle of the domain. This procedure is applied to discretize the star shaped curved domain or cracked convex curved domains into all triangles and then into all quadrilaterals. Thus we generate a triangular and a quadrangular finite element mesh. The refinements to the mesh are obtained by increasing the number of divisions of the boundary curve. This discretization of curved domains will reduce the computational complications in the evaluation of integrals, which has lot of practical applications.