Automated Mesh Generation Using Curved Cubic Triangular Elements for a Circular Domain with a Finite Element Implementation

Abstract We propose a method for automated unstructured mesh generation using curved cubic triangular elements for a circular domain which can be efficiently used for finite element analysis in industrial engineering and applied sciences. This approach uses subparametric transformations with the parabolic arcs to obtain the nodal relations for the curved geometry under consideration. Persson and Strang developed a simple and well-known MATLAB mesh generator distmesh2d with linear triangular elements using signed distance function for the geometric description. The technique used here, to generate cubic (10-noded) triangular elements is based on distmesh2d. This approach can be easily adapted for any curved geometry. For illustration purpose, in this paper finite element method is applied to a Poisson equation over a circular domain. The efficiency of the proposed technique using curved cubic triangular elements is shown in the numerical results which are more accurate compared to linear and straight edged cubic ordered triangular elements for a fixed element size.

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