Investigating Finite Volume Time Domain Methods in Computational Electromagnetics

Abstract

In this work, the finite volume time domain semidiscrete formulation, discrete in the space and continuous in the time, is derived starting from the Maxwell's equations. This formulation is used to explain variations in finite volume time domain methods e.g., methods which differ in spatial approximation. The time marching schemes that can be employed to turn these semidiscrete formulations into discrete systems are presented. For a given problem, numerical methods anticipate the convergence of the solutions towards the reference (analytical) solution as the grid is refined. But the convergence rate or order depends on the details of the computational domain. The convergence order for various finite volume time domain methods is presented in different scenarios e.g., a computational domain with curved surface and a singularity in the field due to the geometry. It is a well known fact that the numerical solvers facilitate efficient design of passive microwave components by tendering the scattering parameters. Obtaining the scattering parameters using finite volume time methods is illustrated in this work along with the difficulties involved in the process. The solutions obtained for various applications e.g., a coaxial cable with a very high contrast of materials, are bidden against the solutions obtained from the finite integration technique and the finite element method. The development cycle of a finite volume time domain solver is portrayed. Various modules are explained in detail along with assorted libraries employed in the solver. The computational cost, more specifically the floating point operations for various finite volume time domain methods are limned. This work investigates the surmise of superior capabilities of finite volume time domain methods in the computational electromagnetics rigorously on both structured and unstructured grids.