Finite element time domain method using hexahedral elements

A fast algorithm based on the finite element time domain method for solving Maxwell equations is described. The approach employs an explicit scheme with lumped mass in time integration to avoid solving the linear equations. We propose a new definition of the lumped mass matrix for hexahedral edge elements and arbitrary shape can be modeled without staircasing. We check the performance of the absorbing boundary using a one dimensional model, calculate the propagation of a plane wave in a plate with an unstructured mesh, and investigate the influence of the edge element distortion. The calculation results show that although the proposed method works well for brick elements in 3D problems and unstructured mesh in 2D, it is not appropriate in unstructured 3D mesh.