Accelerating the frequency dependent Finite-Difference Time-Domain Method using: the spatial filtering and parallel computing techniques

Abstract

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 Finite-Difference Time-Domain (FDTD) method. The FDTD method uses central-difference 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 Courant-Friedrichs-Lewy (CFL) condition, hence the computational resources demand increases for large-scale electromagnetic problems. The Spatially-Filtered FDTD (SF-FDTD) 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 SF-FDTD method can not model the frequency dependent media hence the Frequency Dependent (FD-FDTD) method is utilised to accurately model frequency dependent media. However, the FD-FDTD 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 (SF-FD-FDTD) method with Debye model. Secondly, the application of three absorbing boundary conditions (Mur, Stretched Mesh HABC, and Complex Frequency Shifted PML) with the SF-FD-FDTD method. Thirdly, the investigations in terms of stability, accuracy, and efficiency of the SF-FD-FDTD 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 SF-FD-FDTD method.

Date of Award	1 Aug 2018
Original language	English
Awarding Institution	The University of Manchester
Supervisor	John Oakley (Supervisor) & Fumie Costen (Supervisor)