Maxwell's equations are one of the important electromagnetic fundamentals that have motivated electrical, optical and communication technologies. In order to solve Maxwell's equations, many numerical techniques were introduced, each one has its own advantages and limitations. One of the robust, accurate and widely used numerical techniques is the FiniteDifference TimeDomain (FDTD) method. The FDTD method uses centraldifference approximation to discretise the partial differential form of Maxwell's equations in both space and time, and Yee's algorithm to obtain the solutions. To guarantee stable and accurate solution of the partial form of Maxwell's equations, the time increment of the FDTD method must be upper bounded by the CourantFriedrichsLewy (CFL) condition, hence the computational resources demand increases for largescale electromagnetic problems. The SpatiallyFiltered FDTD (SFFDTD) method is utilised to maintain stability when the CFL condition is altered. In other words, the time increment can be conditionally set larger than the CFL limit by filtering the unwanted high spatial frequency components in the spatial frequency domain to maintain stability. The SFFDTD method can not model the frequency dependent media hence the Frequency Dependent (FDFDTD) method is utilised to accurately model frequency dependent media. However, the FDFDTD method requires a high amount of computational resources for modelling 3D scenarios due to the limitation of the CFL condition. The contributions in this thesis are addressed as following. Firstly, the implementation of 1D, 2D, and 3D spatially filtered frequency dependent FDTD (SFFDFDTD) method with Debye model. Secondly, the application of three absorbing boundary conditions (Mur, Stretched Mesh HABC, and Complex Frequency Shifted PML) with the SFFDFDTD method. Thirdly, the investigations in terms of stability, accuracy, and efficiency of the SFFDFDTD method with each absorbing boundary condition. Fourthly, the extension of late time instability of the Huygens subgridding method (HSG) by implementing a spatial filtering algorithm with the 1D and 2D HSG method. Fifthly, the application of the shared memory architecture with OpenMP to accelerate the 2D SFFDFDTD method.
Date of Award  1 Aug 2018 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  John Oakley (Supervisor) & Fumie Costen (Supervisor) 

Accelerating the frequency dependent FiniteDifference TimeDomain Method using: the spatial filtering and parallel computing techniques
AlKhayyat, A. N. M. T. (Author). 1 Aug 2018
Student thesis: Phd