Finite elements with divergence-free shape function and the application to inhomogeneously-loaded waveguide analysis

A simple mixed triangular edge element is proposed for the finite elements, with which inhomogeneously-loaded and arbitrarily shaped waveguides are analyzed. The shape functions used for approximating the fields are found analytically to be divergence-free. The formulation has been found to encounter spurious-free solutions. As evidence, the non-physical solutions that appeared in the longitudinal component finite element formulation are shown to be absent in the present formulation. A comparison with another mixed element is furnished here in order to demonstrate the advantages provided by the present element </p

Hybrid explicit-implicit FDTD-FEM time-domain solver for electromagnetic problems

The Finite-Difference Time-Domain (FDTD) method and Finite-Element (FEM) method are numerical techniques used for solving Maxwell\u27s electromagnetic equations. FDTD-FEM hybrid methods opt for combining the advantages of both FDTD and FEM. In this dissertation, signal processing techniques were used to analyze the FDTD stability condition. A procedure, which reduces time-sampling error yet preserves the stability of algorithm is proposed. Both explicit and implicit time-stepping schemes were treated in the framework of the developed method. An improved version of the implicit-explicit FEM-FDTD hybrid method was developed. The new method minimizes reflection from the interface between different types of grids. A class of transfer functions with low reflection error for stable hybrid time-stepping was derived. The stability of the method is rigorously proven for a general three-dimensional case

Quantifying numerical dispersion in non-orthogonal FDTD meshes

Numerical electromagnetic models such as FDTD are widely used for the design and analysis of structures, including antennas. Numerical dispersion is one of the main sources of error that degrade the accuracy of the results-for each structure of interest, the users of the model must attempt to generate a mesh that will avoid introducing high levels of dispersion. This is, however, especially difficult for non-orthogonal meshes since little information is available on the dispersion properties of the non-orthogonal FDTD algorithm on complex meshes. For the first time, the dispersion in realistic non-orthogonal FDTD models of microstrip structures is quantified directly through numerical simulations. A test structure is considered, discretised using a number of nonorthogonal mesh configurations, including single and multiple skew angles. A numerical analysis of reflections generated at the transition between two mesh regions with different skew angles is also presented. These results give a practical guide to mesh generation for users of the algorith

FDTD-based full wave co-simulation model for hybrid electromagnetic systems

In high-frequency ranges, the present electronic design automation software has limited capabilities to model electromagnetic (EM) systems where there are strong field effects influencing their characteristics. In this situation, a full-wave simulation tool is desired for the analysis and design of high-speed and non-linear EM systems. It is necessary to explore the interaction between the field and electronic components during a transient process when field effects are more significant. The finite-difference time-domain (FDTD) technique receives growing attention in the area of EM system analysis and simulation due to its simplicity, flexibility and robustness. It is a full-wave simulation method that solves the Maxwell\u27s equations in time domain directly. Decades of research and development and rapid growth in computer capability have built up a firm foundation for FDTD techniques to be applied to many practical problems. Based on FDTD, this dissertation develops a stable CO-simulation method to perform a full-wave simulation of a hybrid EM system consisting of lumped elements and distributed structures. In this method, FDTD is used to solve the EM field problems associated with distributed structures, and a circuit simulator solves the response of lumped elements. A field-circuit model proposed in the dissertation serves as the interface between the two simulation tools. Compared with previous methods, the FDTD method based on this model is much more flexible and stable for linear and nonlinear lumped elements under both small and large signal conditions. Because of its flexibility and robustness, this model is a promising approach to integrate a field solver and a circuit simulator in the simulations of practical EM systems. In order to improve the simulation accuracy, some problems related to FDTD simulation are studied. Based on the numerical dispersion in homogeneous media uniform grids, the FDTD numerical reflection and transmission on the boundary of media, which are discritized by a non-uniform grid, are investigated. This investigation provides for the first time an estimation of FDTD numerical error in inhomogeneous media and non-uniform grids. Perfectly matched layer (PML) was previously utilized the homogeneous media or uniform grids. This dissertation extends the PML boundary conditions to handle the inhomogeneous media and non-uniform grid. Techniques extracting S parameters from FDTD simulation are also discussed. Two and three-dimensional CO-simulation software, written in C++, has be derived, developed and verified in this dissertation. The simulation results agree well with results from other simulation methods, like SPICE, for many test circuits. Taking data sampling and interpolation into account, simulation results generally fit well to measurement and other simulation results for complicated three-dimensional structures. With further improvements of the FDTD technique and circuit simulation, field-circuit CO-simulation model will widen its application to general EM systems

A hp-like discontinuous Galerkin method for solving the 2D time-domain Maxwell's equations on non-conforming locally refined triangular meshes

This work is concerned with the design of a hp-like discontinuous Galerkin (DG) method for solving the 2D time-domain Maxwell's equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements of the mesh, with a leap-frog time integration scheme