An arbitrary high-order hexahedrons generation technology for DGTD algorithm

The Hexahedral Discontinuous Galerkin time domain (Hex-DGTD) algorithm required the computational domain divided into a set of nonoverlapping curved hexahedral subdomains. Each subdomain´s Jacobian matrix must be obtained by mapping it into a standard cube. However, general commercial software can only divide computational domain into straight or low order hexahedral meshes, these meshes poorly conform to the geometry and bring in errors in DGTD boundary condition. This article proposed the technique of arbitrary high order curved hexahedral meshes combined with Gordon-Hall method, can conform to the geometry´s boundary accurately, and reduce errors in getting each hexahedron´s Jacobian matrix obviously. Numerical results verified the technique of generating curved hexahedral meshes improve the accuracy of the DGTD algorithm without increase computing resources significantly.