The finite difference time domain (FDTD) method is commonly used for numerical simulations of the electromagnetic wave propagation in time domain. The FDTD method is easy to implement and the computational results are highly relevant to the analytical solution, so that the FDTD method is applied to variety application problems. However, the computational efficiency of the FDTD method is constrained by the upper limit of the temporal discretisation. The Courant Friedrich Lewy (CFL) stability condition limits the time step for the computation of the FDTD method, so that if the spatial discretisation of the computation is set to be small in order to obtain high accurate results, the size of the temporal discretisation need to be satisfy the CFL stability condition. The locally one dimensional FDTD (LOD-FDTD) method is unconditionally stable. The time step and the spatial step can be independently chosen for the computation of the LOD-FDTD method. The arithmetic operations of the LOD-FDTD method is fewer than that of the other implicit FDTD method, such as the Crank Nicolson FDTD (CN-FDTD) method and the alternating direction implicit FDTD (ADI-FDTD) method. Although the implementation of the LOD-FDTD method is simpler than that of the ADI-FDTD method,the numerical error in the computational results of the LOD-FDTD method is equivalent to that in the computational results of the ADI-FDTD method. In this thesis, a new three dimensional (3D) frequency dependent (FD) LOD-FDTD method is proposed. The one pole Debye model is incorporated into the 3D-FD-LOD-FDTD method in order to deal with practical applications. The proposed method is implemented in Fortran 90 and parallelised with OpenMP. A simulation model of the human phantom is developed in the 3D-FD-LOD-FDTD method with fine structures and frequency dependent dielectric properties of the human tissues, and numerical simulation of electromagnetic wave propagation inside the human head is shown.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:607426 |
| Date | January 2014 |
| Creators | Hemmi, Tadashi |
| Contributors | Costen, Fumie; Mihajlovic, Milan |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/locally-one-dimensional-finite-difference-time-domain-method-with-frequency-dependent-media-for-three-dimensional-biomedical-applications(f5fc769a-7dc4-4cce-80f0-755054cb4bab).html |
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