Mixed order Finite Difference Time Domain method using the weighted Laguerre Polynomials on a non uniform mesh

The Finite-Difference Time-Domain (FDTD) method is arguably the most popular technique in the field of computational electromagnetics. Although the FDTD method has existed for nearly 30 years, its popularity continues to grow as computing costs continue to decline. FDTD techniques have emerged as primary means to computationally model many scientific and engineering problems dealing with electromagnetic wave interactions with material structures.;The conventional FDTD method is typically used to solve for Maxwell's equations in the field of electromagnetics. The FDTD method is an explicit time-marching technique with its time step limited by the well-known Courant-Friedrich-Levy (CFL) stability condition. Recently to deal with the CFL criterion the weighted Laguerre Polynomials technique was proposed. This method was shown to be unconditionally stable, but due to its second order spatial approximations it may require a dense grid leading to a relatively large computational time and memory requirements.;In this thesis, the existing FDTD using the weighted Laguerre polynomials technique is improved by employing a combination of second and fourth order spatial approximations, applied on a fine and coarse grid respectively. A non uniform mesh employing a fine grid for regions close to the boundary and a coarse grid for regions away from the boundary is used. Consequently, the proposed method reduces the computational time and memory, without significant loss of accuracy, when compared to the method using only second order spatial approximations.