Convergence of error in FVTD methods on tetrahedral meshes in 3D

In this paper, the finite volume time domain (FVTD) semi-discrete formulation, discrete in the space and continuous in the time, is derived for the electromagnetic field simulation, starting from the Maxwell´s equations. The time marching schemes that can be employed to turn this into discrete system of equations are presented. The discrete formulation is used to explain variations in FVTD methods e.g., methods which differ in spatial approximation. For a given problem, numerical methods anticipate the convergence of the solutions towards the reference (analytical) solution as the grid is refined. The convergence order for various FVTD methods is presented in different scenarios and compared with that of finite integration technique (FIT) and finite element method (FEM).