Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed

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

A finite element conjugate gradient FFT method for scattering

Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution

Influence of mechanical strains on electromagnetic signals of a microstrip antenna. FEM/BIM model

A hybrid numerical technique is proposed for a characterization of the radar cross section of a microstrip patch antenna residing in a dielectric filled cavity which is loaded by a sinusoidal mechanical pressure. A new 3D hexahedral finite element is developed in order to take into account the deformed shape of the antenna within the electromagnetic computations. The numerical tool combines the finite element and boundary integral methods to formulate a system for the solution of the fields at the aperture and those inside the cavity. In this work, numerical examples are presented for demonstrating the ability and the validity of the hexahedral element

A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability

A finite element: Boundary integral method for electromagnetic scattering

A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications