(untitled) (International Journal of Engineering and Computer Science, 2015)
A new method is presented for subdividing a large class of solid objects into topologically simple subregions suitable for automatic finite element meshing with pentagonal elements. It is known that one can improve the accuracy of the finite element solution by uniformly refining a triangulation or uniformly refining a quadrangulation. Recently a refinement scheme of pentagonal partition was introduced in [31,32,33]. It is demonstrated that the numerical solution based on the pentagonal refinement scheme outperforms the solutions based on the traditional triangulation refinement scheme as well as quadrangulation refinement scheme. It is natural to ask if one can create a hexagonal refinement or general polygonal refinement schemes with a hope to offer even further improvement. It is shown in literature that one cannot refine a hexagon using hexagons of smaller size. In general, one can only refine an n-gon by n-gons of smaller size if n ≤ 5. Furthermore, we introduce a refinement scheme of a general polygon based on the pentagon scheme. This paper first presents a pentagonalization (or pentagonal conversion) scheme that can create a pentagonal mesh from any arbitrary mesh structure. We also introduce a pentagonal preservation scheme that can create a pentagonal mesh from any pentagonal mesh. This paper then presents a new numerical integration technique proposed earlier by the first author and co-workers, known as boundary integration method [34-40] is now applied to arbitrary polygonal domains using pentagonal finite element mesh. Numerical results presented for a few benchmark problems in the context of pentagonal domains with composite numerical integration scheme over triangular finite elements show that the proposed method yields accurate results even for low order Gauss Legendre Quadrature rules. Our numerical results suggest that the refinement scheme for pentagons and polygons may lead to higher accuracy than the uniform refinement of triangulations and quadrangulations.