Arid Zone Journal of Engineering, Technology and Environment, April, 2017; Vol. 13(2):238-251 Copyright © Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria. Print ISSN: 1596-2490, Electronic ISSN: 2545-5818, www.azojete.com.ng 238 IMPLEMENTATION OF UNSPLIT PERFECTLY MATCHED LAYER ABSORBING BOUNDARY CONDITION IN 3 DIMENSIONAL FINITE DIFFERENCE TIME DOMAIN METHOD B. U. Musa (Department of Electrical and Electronics Engineering University of Maiduguri, Maiduguri, Nigeria) E-mail address: musa_bu@yahoo.com Abstract The C++ programming language was used to implement three-dimensional (3-D) finite-difference time-domain (FDTD) technique to simulate radiation of high frequency electromagnetic waves in free space. To achieve any meaningful results the computational domain of interest should have to be truncated in some way and this is achieved by applying absorbing boundary conditions. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used in this work. The discretised equations of the UPML in FDTD time stepping scheme were derived and has been successfully implemented using the computer program. Simulation results showed that the UPML behaves as an absorber. This was confirmed by comparing the results with another boundary condition, the Mur ABC. Keywords: Electromagnetics, 3D Finite Difference Time Domain, 3D Unsplit field perfectly Matched Layer, Absorbing boundary conditions 1. Introduction Electromagnetic fields can be computed either in free space in enclosed space. The behaviour of the electromagnetic fields distributions at the interface between two or more media is completely different from the field distribution away from the interface. For this reason, it is necessary to define the conditions at the interfaces when solving for the electromagnetic fields. The FDTD technique is based on direct solution of Maxwell’s equations in differential form, and for partial differential equations to be well posed; an appropriate number of boundary conditions need to be specified. As described by the uniqueness theorem (Georgapoulos et al, 2002), it is required to specify the tangential components of the electric field  and magnetic field  (or both) over the boundary of a domain to be sufficient for a unique solution. Since the introduction of PML to the electromagnetic community by Berenger in 1994, it has been applied widely to the solution of numerous problems. The area of application is too numerous that it is almost impossible to discuss in a single paper. Another important development in the PML is the extensions to Berenger’s original split field algorithm. One such proposal is that the PML can be realized through an anisotropic medium having complex permittivity and permeability tensors, known as Unsplit Field Perfectly Matched Layer (UPML) Formulation. This strategy was first put forward and discussed by (Sacks et al., 1995) and implemented in the FDTD grid by (Gedney, 1996).The solution of maxwell’s equations in differential form using the FDTD method in three dimensions produces 6 electromagnetic field quantities-  ,   ,  ,  ,   and   . Following the derivation of the 3 electric field quantities in (Taflove and Hagness, 2000), the derivation of the 3 magnetic field quantities is covered in thispaper. These together with the 3 electric field quantities are then implemented in the FDTD