UoM administered thesis: Phd

  • Authors:
  • Hayder Al-Tameemi


Maxwell's equations describe the propagation of electromagnetic fields, and can be solved with the help of a numerical method in order to simulate the electromag- netic behaviour in a wide range of propagation media. The Finite-Difference Time Domain method (FDTD) is one of the algorithms widely-used to solve Maxwell's equations. The Debye model is integrated with the classical FDTD method to simulate frequency-dependent media more accurately than with classical FDTD. A drawback of the FDTD method becomes apparent when the entire FDTD space is refined globally, which requires both the spatial and temporal steps to have a high resolution. The refinement of the entire FDTD space increases the computation requirements. Subgridding techniques are introduced to increase the computational efficiency of the FDTD method, by dividing the computation space into one or more sub-spaces, which are known as subgrids. The main grid has a coarse mesh, while the subgrid has the fine mesh. The Huygens subgrid- ding method (HSG) relies on the connection between the main grid and subgrid by means of Huygens surfaces. A simplification to the HSG is introduced in 3D using the classical FDTD method. In this thesis, the simplified HSG is denoted as the one-sheet HSG. Implementa- tion of the method is performed using the Frequency-Dependent FDTD method in 1D, 2D, and 3D. This work shows that the one-sheet HSG has singular fields at the edges of perfect electric or magnetic conductors, which reduces the accuracy of the method when compared with the conventional HSG. It is shown that the singularity problem appears only in 2D and 3D implementations. The problem can be easily overcome in 2D, but not in 3D. Three combinations of the one-sheet HSG are possible in 3D, and one has a higher accuracy than the others, when compared with the conventional HSG. The one-sheet HSG comes with a reduc- tion in the accuracy, but uses the computation resources more efficiently than the conventional HSG. An algorithm is implemented to accelerate the one-sheet HSG using high-performance computing techniques. My contribution is, detect- ing the problem of singularity of the fields in the 2D of the one-sheet HSG in both TM z and TE z modes, finding a solution to the problem in the 2D one-sheet HSG, detecting the problem of singularity fields in 3D, identifying three possi- ble implementation combinations of the one-sheet HSG in 3D, pointing out the implementation with the higher accuracy among the three, and implementing an algorithm to accelerate the one-sheet HSG using High Performance Computing.


Original languageEnglish
Awarding Institution
Award date31 Dec 2017