An investigation of alternating-direction implicit finite-difference time-domain (ADI-FDTD) method in numerical electromagnetics

In this thesis, the alternating-direction implicit method (ADI) is investigated in conjunction with the finite difference time-domain method (FDTD) to allow crossing of the Courant-Friedrich-Levy (CFL) stability criterion while maintaining stability in the FDTD algorithm. The main reason for this is to be able to use a larger numerical time step than that governed by the CFL criterion. The desired effect is a significant reduction in numerical run-times. Although the ADI-FDTD method has been used in the literature, most analysis and application have been performed on simple three-dimensional cavities.This work makes original contribution in two aspects. Firstly, a new modified alternating-direction implicit method for a three-dimensional FDTD algorithm has been successfully developed and implemented in this research. This new method allows correct modelling of a realistic physical structure such as a microstrip patch with the ADI scheme without causing instability even when the CFL criterion is not observed. However, due to the inherent property of this modified ADI-FDTD method, a decreasing reflection coefficient is observed using this scheme.The second and more important contribution this research makes in the field of numerical electromagnetics is the development of a new method of simulating realistic complex structures such as geometries comprising copper patch antennas on a dielectric substrate. With this new method, for the first time, the ADl-FDTD algorithm remains stable while still in violation of the CFL criterion, even when complex structures are being modelled.However, there is a trade-off between accuracy and computational speed in ADI-FDTD and modified ADI-FDTD methods. The larger the numerical time step, the shorter is the simulation run-time but an increase in numerical time step causes a degradation in accuracy of numerical results. Comparison between speed and accuracy is shown in this thesis and it has to be mentioned here that these values are very much dependent on the structure being modelled

Numerical simulation of nanopulse penetration of biological matter using the ADI-FDTD method

Nanopulses are ultra-wide-band (UWB) electromagnetic pulses with pulse duration of only a few nanoseconds and electric field amplitudes greater than 105 V/m. They have been widely used in the development of new technologies in the field of medicine. Therefore, the study of the nanopulse bioeffects is important to ensure the appropriate application with nanopulses in biomedical and biotechnological settings. The conventional finite-difference time-domain (FDTD) method for solving Maxwell\u27s equations has been proven to be an effective method to solve the problems related to electromagnetism. However, its application is restricted by the Courant, Friedrichs, and Lewy (CFL) stability condition that confines the time increment and mesh size in the computation in order to prevent the solution from being divergent. This dissertation develops a new finite difference scheme coupled with the Cole-Cole expression for dielectric coefficients of biological tissues to simulate the electromagnetic fields inside biological tissues when exposed to nanopulses. The scheme is formulated based on the Yee\u27s cell and alternating direction implicit (ADI) technique. The basic idea behind the ADI technique is to break up every time step into two half-time steps. At the first half-step, the finite difference operator on the right-hand side of the Maxwell\u27s equation is implicit only along one coordinate axis direction. At the second half-step, the finite difference operator on the right-hand side of the Maxwell\u27s equation is implicit only along the other coordinate axis direction. As such, only tridiagonal linear systems are solved. In this numerical method, the Cole-Cole expression is approximated by a second-order Taylor series based on the z-transform method. In addition, the perfectly matched layer is employed for the boundary condition, and the total/scattered field technique is employed to generate the plane wave in order to prevent the wave reflection. The scheme is tested by numerical examples with two different biological tissues. For the purpose of comparison, both the proposed ADI-FDTD scheme and the conventional FDTD scheme are employed to the numerical examples. The results show that the proposed ADI-FDTD scheme breaks through the CFL stability condition and provides a stable solution with a larger time step, where the conventional FDTD scheme fails. Results also indicate that the computational time can be reduced with a larger time step

Viability of Numerical Full-Wave Techniques in Telecommunication Channel Modelling

In telecommunication channel modelling the wavelength is small compared to the physical features of interest, therefore deterministic ray tracing techniques provide solutions that are more efficient, faster and still within time constraints than current numerical full-wave techniques. Solving fundamental Maxwell's equations is at the core of computational electrodynamics and best suited for modelling electrical field interactions with physical objects where characteristic dimensions of a computing domain is on the order of a few wavelengths in size. However, extreme communication speeds, wireless access points closer to the user and smaller pico and femto cells will require increased accuracy in predicting and planning wireless signals, testing the accuracy limits of the ray tracing methods. The increased computing capabilities and the demand for better characterization of communication channels that span smaller geographical areas make numerical full-wave techniques attractive alternative even for larger problems. The paper surveys ways of overcoming excessive time requirements of numerical full-wave techniques while providing acceptable channel modelling accuracy for the smallest radio cells and possibly wider. We identify several research paths that could lead to improved channel modelling, including numerical algorithm adaptations for large-scale problems, alternative finite-difference approaches, such as meshless methods, and dedicated parallel hardware, possibly as a realization of a dataflow machine

An Improved 3D Complex-Envelope Four-Stage ADI-FDTD Using The Fundamental Scheme

Three corresponding reference methods are developed. The CE explicit FDTD method is used to solve the problem with a point source and perfect electric conductor (PEC) boundaries. The problem with a point source and absorbing boundary conditions (ABC) is solved by the 3D free-space Green\u27s function in the frequency domain, and then transformed to the time domain using the inverse fast Fourier transform (IFFT). For the problem with a plane wave and ABC, the frequency-domain solution is obtained using the volume integral equations and method of moments (VIE-MOM), and is then transformed into the time-domain solution using the IFFT. Comparison of the numerical results demonstrates the accuracy and computational effectiveness of the 3D CE-4S-FADI-FDTD algorithm

Numerical modelling of photonic crystal based switching devices

In the last few years research has identified Photonic Crystals (PhCs) as promising material that exhibits strong capability of controlling light propagation in a manner not previously possible with conventional optical devices. PhCs, otherwise known as Photonic Bandgap (PBG) material, have one or more frequency bands in which no electromagnetic wave is allowed to propagate inside the PhC. Creating defects into such a periodic structure makes it possible to manipulate the flow of selected light waves within the PhC devices outperforming conventional optical devices. As the fabrication of PhC devices needs a high degree of precision, we have to rely on accurate numerical modelling to characterise these devices. There are several numerical modelling techniques proposed in literature for the purpose of simulating optical devices. Such techniques include the Finite Difference Time Domain (FDTD), the Finite Volume Time Domain (FVTD), and the Multi-Resolution Time Domain (MRTD), and the Finite Element (FE) method among many others. Such numerical techniques vary in their advantages, disadvantages, and trade-offs. Generally, with lower complexity comes lower accuracy, while higher accuracy demands more complexity and resources. The Complex Envelope Alternating Direction Implicit Finite Difference Time Domain (CE-ADI-FDTD) method was further developed and used throughout this thesis as the main numerical modelling technique. The truncating layers used to surround the computational domain were Uniaxial Perfectly Matched Layers (UPML). This thesis also presents a new and robust kind of the UPML by presenting an accurate physical model of discretisation error. iv This thesis has focused on enhancing and developing the performance of PhC devices in order to improve their output. An improved and new design of PhC based Multiplexer/Demultiplexer (MUX/DEMUX) devices is presented. This is achieved using careful geometrical design of microcavities with respect to the coupling length of the propagating wave. The nature of the design means that a microcavity embedded between two waveguides selects a particular wavelength to couple from one waveguide into the adjacent waveguide showing high selectivity. Also, the Terahertz (THz) frequency gap, which suffers from a lack of switching devices, has been thoroughly investigated for the purpose of designing and simulating potential PhC based switching devices that operate in the THz region. The THz PhC based switching devices presented in this thesis are newly designed to function according to the variation of the resonant frequency of a ring resonator embedded between two parallel waveguides. The holes of the structures are filled with polyaniline electrorheological fluids that cause the refractive index of the holes to vary with applied external electric field. Significant improvements on the power efficiency and wavelength directionality have been achieved by introducing defects into the system

Efficient excitation of waveguides in Crank-Nicolson FDTD

In this paper, we present a procedure to calculate the discrete modes propagated with Crank-Nicolson FDTD in metallic waveguides. This procedure enables the correct excitation of this kind of waveguides at any resolution. The problem is reduced to solving an eigenvalue equation, which is performed, both in a closed form, for the usual rectangular waveguide, and numerically in the most general case, validated here with a ridged rectangular waveguide.The work described in this paper and the research leading to these results has received funding from the European Community's Seventh Framework Programme FP7/2007-2013, under grant agreement no 205294 (HIRF SE project), and from the Spanish National Projects TEC2010-20841-C04-04, TEC2007-66698-C04-02, CSD2008- 00068, DEX-530000-2008-105, and the Junta de Andalucia Projects TIC1541 and P09-TIC-5327

Doctor of Philosophy

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