A Hybrid Mesh DGTD Algorithm Based on Virtual Element for Tetrahedron and Hexahedron

Abstract

In the discontinuous Galerkin time-domain (DGTD) method, tetrahedral meshes are typically used to discretize the computational domain. However, due to their different topological structures, when tetrahedrons or hexahedrons of the same discrete scale are used to divide the same computational domain, there are more tetrahedral mesh units, resulting in higher temporal and spatial complexity. In this article, a hybrid mesh DGTD algorithm based on virtual elements for tetrahedra and hexahedra is proposed to improve the computational efficiency compared with the traditional DGTD method. The fine-structured computational domain and the outer region are computed using tetrahedral and hexahedral meshes, respectively. During calculation, the numerical flux of each interface element requires data from the other subdomain. In this article, virtual elements are established at each subdomain interface to enable the exchange of field values for ease of processing. Edge assignment or field interpolation is applied to sample points to create corresponding virtual units to calculate fringe fields. Finally, the field value of each virtual element is assigned to the corresponding real element for the numerical flux calculation. Numerical results verify the correctness and efficiency of the proposed method.