Elimination of Numerical Dispersion from Electromagnetic Time Domain Analysis by Using Resource Efficient Finite Element Technique

Time domain analysis of electromagnetic wave propagation is required for design and characterization of many optical and microwave devices. The FDTD method is one of the most widely used time domain methods for analysing electromagnetic scattering and radiation problems. However, due to the use of the Finite Difference grid, this method suffers from higher numerical dispersion and inaccurate discretisation due to staircasing at slanted and curve edges. The Finite Element (FE)-based meshing technique can discretize the computational domain offering a better approximation even when using a small number of elements. Some of the FE-based approaches have considered either an implicit solution, higher order elements, the solution of a large matrix or matrix lumping, all of which require more time and memory to solve the same problem or reduce the accuracy. This paper presents a new FE-based method which uses a perforated mesh system to solve Maxwell's equations with linear elements. The perforated mesh reduces the requirement on memory and computational time to less than half of that compared to other FE-based methods. This paper also shows a very large improvement in the numerical dispersion over the FDTD method when the proposed method is used with an equilateral triangular mesh.