MATLAB 2D higher-order triangle mesh generator with finite element applications using subparametric transformations. (January 2018) - Smitha, T.V.; Nagaraja, K.V.; Jayan, Sarada
Highlights: A novel higher order (HO) automated unstructured triangular mesh generation is presented with the MATLAB code for regular and curved geometries. The interior nodes and nodes on the boundaries are obtained using subparametric transformations with parabolic arcs especially for curved geometries. Illustrated HO finite element (HOFE) method for some elliptic PDE using the proposed technique. The proposed approach drastically simplifies the computational complexities involved in the FE formulation and thus increasing the efficiency of the HOFE scheme. Numerical examples show the simplicity, efficiency and accuracy of HOFE scheme with the proposed HO automated mesh generation techniques up to 28- noded triangle elements (sextic triangular elements). It is shown that coarse HO meshes of 21 and 28-noded triangle elements outperform the fine linear and quadratic meshes in terms of the accuracy of the numerical results as well as degrees of freedom and number of elements are reduced in the FEA. Abstract: This paper presents a novel automated higher-order (HO) unstructured triangular mesh generation of the two-dimensional domain. The proposed HO scheme uses the nodal relations obtained from subparametric transformations with parabolic arcs, especially for curved geometry. This approach is shown to drastically simplify the computational complexities involved in the HO finite element (HOFE) formulation of any partial differential equation (PDE). The prospective generalised MATLAB 2D mesh generation codes, HOmesh2d for the regular domain and CurvedHOmesh2d for a circular domain are based on the MATLAB mesh generator distmesh of Persson and Strang. As an input, the code takes a signed distance function of the domain geometry and the desired order for the triangular elements and as outputs, the code generates an HO triangular mesh with element connectivity, node coordinates, and boundary data (edges and nodes). The working principle of HOFE scheme, using subparametric transformations with the proposed HO automated mesh generator is explained. The simplicity, efficiency, and accuracy of the HOFE method, with the proposed HO automated mesh generator up to 28-noded triangular elements, are illustrated with elliptic PDE. The proposed techniques are applied to some electromagnetic problems. The use of higher order elements from the proposed mesh generator is shown to increase the accuracy and efficiency of the numerical results. Also, with the proposed HOFE scheme it is verified that HO elements significantly decrease the numbers of degrees of freedom, and elements required to achieve a specific level of accuracy compared to lower order elements. Numerical results show that the HO elements outperform the lower order elements in terms of efficiency and accuracy of the numerical results.