A Comparative Study of Three Finite Element-Based Explicit Numerical Schemes for Solving Maxwell's Equations

Three finite element-based explicit numerical algorithms, named the dual-field domain decomposition at the element level (DFDD-ELD), the discontinuous Galerkin time-domain method with upwind fluxes (DGTD-Upwind), and the discontinuous Galerkin time-domain method with central fluxes (DGTD-Central), are investigated and compared in terms of accuracy and efficiency. All three algorithms can perform an efficient domain decomposition and avoid the inversion of a global system matrix, yet the study shows that they differ from each other in terms of accuracy and efficiency. Hybrid implicit-explicit schemes, which can relax the restriction on the time step size imposed by the smallest elements in the computational domain, are also investigated for both DFDD and DGTD and compared in terms of efficiency.