In this work, a novel automated higher-order (HO) unstructured tetrahedral mesh generators for three dimensional geometries are proposed. The proposed mesh generators, HOmesh3d for the regular geometries and CurvedHOmesh3d for spherical geometries are based on the very powerful mesh generator distmeshnd in MATLAB, developed by Persson. The developed MATLAB 3D mesh generation code CurvedHOmesh3d focus on the curved surface using the relations of the nodes acquired from the subparametric mapping by parabolic arcs. The input requirement for these codes is the same as that of distmeshnd and the required order of the tetrahedral elements. As output, an HO tetrahedral mesh with coordinates of each node, element connectivity matrix, boundary edges, and boundary nodes are generated. The effectiveness of CurvedHOmesh3d is enhanced by utilizing HO curved tetrahedral elements along the curved surface and regular HO tetrahedral elements within the interior of the problem domain. For curved geometries, this meshing approach can be very effectively employed with curved finite elements. The suggested mesh generator could be efficiently used for 3D finite element applications as it produces high-quality meshes with minimal curvature loss. This mesh could therefore be of very effective use for the solution of partial differential equations emerging in mechanical and aerospace engineering using the finite element method.

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