The High-Order Symplectic Finite-Difference Time-Domain Scheme

published_or_final_versio

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

Nonequilibrium flow computations. 1: An analysis of numerical formulations of conservation laws

Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, nonequilibrium flows. Generalizations of the Beam-Warming scheme, Steger-Warming and van Leer Flux-vector splittings, and Roe's approximate Riemann solver are presented for 3-D, time-varying grids. The analysis is based on a thermodynamic model that includes the most general thermal and chemical nonequilibrium flow of an arbitrary gas. Various special cases are also discussed

Nodal discontinuous Galerkin method for high-temperature superconductors modeling based on the H-formulation

There is growing interest in superconducting machinery design in AC regime such as generators, motors, and magnets. High-temperature superconductors are used as tapes or cables for the machine windings. Therefore, AC losses have to be evaluated efficiently for an optimal design. Moreover, non-linearities, arising from the power law characterizing the electrical behaviour of superconductor, have to be also dealt with. The development of efficient numerical methods is therefore critical to model high-temperature superconductors. Although numerous methods have already been proposed, the finite element method applied on the time-dependent curl-curl–based H-formulation remains the mostly used. It uses edge elements of Nedelec to naturally ensure the continuity of the tangential components of H. To take into account non-linearities from superconductors, a linearisation of the superconductors constitutive power law E=ρ(J)J was implemented. Discontinuous Galerkin finite element method provides an interesting alternative to edge elements for the time-dependent H-formulation. Indeed, the curl-curl operator is written as a div operator and the interior penalty approach defines numerical fluxes at the interfaces. Those fluxes will ensure the continuity of the tangential components of H. The resistivity ρ(J) is explicitly evaluated at the previous iteration with such an approach leading to convergence. In this paper, both numerical approaches implementation will be presented. We will also compare the numerical results from those methods applied to 3D modelling of simple superconducting geometries in AC regime. Copyright © 2017 John Wiley & Sons, Ltd

A Least-Squares Finite Element Method for Electromagnetic Scattering Problems

The least-squares finite element method (LSFEM) is applied to electromagnetic scattering and radar cross section (RCS) calculations. In contrast to most existing numerical approaches, in which divergence-free constraints are omitted, the LSFF-M directly incorporates two divergence equations in the discretization process. The importance of including the divergence equations is demonstrated by showing that otherwise spurious solutions with large divergence occur near the scatterers. The LSFEM is based on unstructured grids and possesses full flexibility in handling complex geometry and local refinement Moreover, the LSFEM does not require any special handling, such as upwinding, staggered grids, artificial dissipation, flux-differencing, etc. Implicit time discretization is used and the scheme is unconditionally stable. By using a matrix-free iterative method, the computational cost and memory requirement for the present scheme is competitive with other approaches. The accuracy of the LSFEM is verified by several benchmark test problems