Global finite element time domain analysis of active non-linear microwave circuits

This paper proposes an extension of the unconditionally stable finite-element time-domain (FETD) method for the global electromagnetic analysis of active microwave circuits. This formulation has two advantages. First, the time-step size is no longer governed by the spatial discretization of the mesh, but rather by the Nyquist sampling criterion. Second, the implementation of the truncation by the perfectly matched layers (PML) is straightforward. An anisotropic PML absorbing material is presented for the truncation of FETD lattices. Reflection less than -50 dB is obtained numerically over the entire propagation bandwidth in waveguide and microstrip line. A benchmark test on a microwave amplifier indicates that this extended FETD algorithm is not only superior to finite-difference time-domain-based algorithm in mesh flexibility and simulation accuracy, but also reduces computation time dramatically.

In order to analyze the switching transient electromagnetic fields generated by the aerial busbars in substation, the one-dimensional (1-D) time domain finite element (TDFE) method is presented to analyze the transient wave process in multi-conductor transmission lines (MTLs) with branches. Based on the Pade's approximation and on Prony's method, the iterative equations of the aerial MTLs are reported. Iterative formulae are also presented to determine the boundary conditions at the nodes of the branches in this paper. The proposed method avoids the Gibbs effect of the finite difference time domain (FDTD) method. An aerial busbars model in a 500 kV substation is analyzed when circuit breakers and disconnect switches are closed. The numerical results are in good agreement with those calculated by Bergeron's method and FDTD method.

Finite-difference time-domain (FDTD) methods have long been the most popular solution for transient electromagnetic (TEM) modeling. Compared with FDTD methods, finiteelement time-domain (FETD) methods have the potential to reduce the number of unknowns and the number of time steps. However, with a requirement to solve an irregular and large sparse matrix equation at every time step, it is generally difficult for FETD methods to take advantage of massively parallel computers. In our work, we propose a parallel FETD solution for TEM diffusion phenomena. We design and implement a parallel iterative solver, which includes a preconditioner that is customized for the FETD method to achieve both fast convergence and good scalability. Using a seabed model, our experiments show that our parallel FETD solution provides the same accuracy as the FDTD methods. On the performance side, using 8 CPU cores, the iterative solver part runs 5 times faster than the serial verison, while the preconditioner part runs 3 times faster. In total, our parallel FETD method runs 3.5 times faster than the serial verison when simulating a seabed model with around 100,000 unknowns.

The purpose of this work is to compute the electromagnetic fields generated by lightning return stroke using the TDFE (time domain finite element) method. Using the TL (transmission line) lightning return stroke model, the point-matched TDFE method is used to solve the telegraph equations that represent the line dynamic behavior, and the electromagnetic fields at ground level are computed using the dipole method. The results show the advantages of the TDFE method, where the channel boundary conditions and transmission line parameters are easy to compute using a very small code and processing time.

A new 3-D domain decomposition based hybrid finite-difference time-domain (FDTD)/finite-element time-domain (FETD) method is introduced to facilitate electromagnetic modeling by exploiting both the computational efficiency of FDTD and the meshing flexibility of FETD. The proposed hybrid method allows the FETD mesh and the FDTD grid to be nonconformal based on domain decomposition technique. It implements the hybridization with a buffer zone, which functions as a transition region between FDTD and FETD. The buffer zone helps the proposed hybrid method obviate the interpolation approach for field coupling of the nonconformal mesh and hence overcome the late-time instability issue. The discontinuous Galerkin method is utilized to couple different regions, thus improving the coupling accuracy compared with that using the Dirichlet boundary condition. Moreover, the hybrid method allows further division of the FETD region into multiple subdomains when the degrees of freedom in this region are large. For temporal discretization, a global leapfrog time integration scheme is implemented to sequentially update the fields in the FDTD, buffer, and FETD regions. The numerical results are shown to demonstrate the meshing flexibility and computational efficiency of the proposed hybrid method inherited from FETD and FDTD methods.

A hybrid scheme for time-domain electromagnetic simulations, combining the explicit finite-difference time-domain (FDTD) method and the implicit finite-element time-domain (FETD) method, is developed. In the hybrid method, the FETD part uses the unconditionally stable Crank-Nicholson method; while the standard FDTD part employs staggered Cartesian grid for spatial discretization and the leap-frog scheme for time stepping. Non-conforming meshes are allowed between the FETD and the FDTD sub-domains. The hybrid method takes advantages of the modeling flexibility of the FETD method for complex structures and the efficiency of the FDTD method for simple structures. The hybrid implicit-explicit time stepping scheme allows time steps as long as the stability limit for the FDTD method, which can be much larger than the stability criterion of the explicit FETD scheme with small elements. Numerical examples demonstrate the efficiency of the proposed method.

In this paper, a hybrid algorithm of explicit finite-element time-domain (FETD) and finite-difference time-domain (FDTD) methods with a large time step is proposed. The FETD method based on the unstable modes filtering (UMF-FETD) is adopted in the region involving fine structures while the FDTD method is employed in the other region. The proposed hybrid algorithm reduces the scale of the system matrix in UMF-FETD and guarantees that the whole calculation region adopts the uniform, large time step. The result proves the good ability of the proposed hybrid algorithm.

A finite-element time-domain (FETD) method for solving Maxwell's equations was developed by combining prism-based edge elements with central differencing in the time domain. This method solves for the electric field as a vector function of space and time in finite cylindrical cavity geometries of arbitrary geometry. Two stability analyses of this method are performed using the growth factor technique and the Z-transform. Furthermore, the computational complexity of the present approach is also investigated, This method has been implemented and its validity tested by studying the resonant frequencies of various microwave cavities.

The finite difference time domain method and finite element methods have proven to be highly effective techniques for the full wave analysis of microwave circuits and resonators. The finite difference time domain (FDTD) method is highly efficient, explicit and parallelizable. Finite element methods have been used in the frequency domain and in the time domain using implicit methods. Implicit methods require a solution of a linear system of equations at each time step. For the finite element time domain (FETD) algorithm to be competitive with the FDTD, the number of time iterations required for a simulation must be significantly less. An unconditionally stable FETD algorithm is used. The variational formulation is based on the vector wave equation. Unconditional stability is achieved by using a modified Newmark-Beta time integration technique. In addition, this algorithm is implemented on parallel message passing computers using a finite element tearing and interconnecting scheme. Some numerical examples based on cavity resonator problems are presented to demonstrate the efficiency and accuracy of the method and the parallel efficiency of the algorithm.

In this paper, an efficient algorithm for implementing Crank-Nicolson scheme in the finite-element time-domain (FETD) method is presented. Based on a direct discretization of the first-order coupled Maxwell curl equations, this algorithm employs edge elements (Whitney 1-form) to expand the electric field and face elements (Whitney 2-form) for the magnetic field. Since the curl of an edge-element is the linear combination of those face elements whose faces contain the given edge, only the Maxwell-Ampere equation composes a sparse linear matrix equation for the electric field update; the Maxwell-Faraday equation is explicit. The Crank-Nicolson scheme is implemented leading to an unconditionally stable vector FETD method and the matrix inverse is not required to be computed explicitly. Therefore, only one matrix equation is required to be solved at each time step. Numerical results demonstrate that the proposed method is efficient when compared with the conventional leap-frog mixed FETD method and the Crank-Nicolson FDTD method.

A metal-only reflectarray (MOR) antenna for 77 [GHz] was analyzed with the equivalent surface current sources. The equivalent current sources can be used to produce the incident fields radiated from a feed. When a feed is an open-ended rectangular waveguide (OERW), the calculated antenna gains for the equivalent current sources, point source, and CST Microwave Studio (MWS) are 31.8, 30.0, and 31.6 [dBi], respectively. The simulated results of the equivalent current sources and CST MWS are in good agreement with each other in terms of the antenna gain.

The discrete origin of FETD-Newmark late time instability, and a correction scheme

An efficient field‐to‐line coupling model in the time domain is developed combining the second‐order decoupled multiconductor transmission lines (MTLs) equations and the finite‐element time‐domain (FETD) method for evaluating the electromagnetic (EM) transient response of MTLs over a lossy ground excited by a high‐altitude EM pulse (HEMP). First, the incident HEMP electric fields on the lines are calculated as equivalent distributed sources introduced into the MTLs equations. Then, the discrete FETD equations for the lines against the HEMP, in which the effect of frequency‐dependent parameters caused by the ground impedance is considered, are derived using the FETD method with current as the single iteration variable. Finally, the transient currents induced on the lines are obtained by assembling all the discrete FETD equations into the global FETD equation, and the transient induced voltages on the lines are calculated by discretising the coupled equations with respect to current and voltage. The proposed model is successfully compared with the finite‐difference time‐domain method via several examples. It is then employed to analyse the effect of various parameters on the transient currents including the polarisation and the incident angles of the HEMP, the conductivity, and the relative permittivity of the soil.

Based on high order hierarchical vector function, the finite-element time-domain (FETD) method combined with tearing and interconnecting (TI) algorithm is presented. This method is efficient for time domain analysis of substrate integrated waveguide (SIW) structures, since the SIW structures have a lot of fine via holes. By means of the high order hierarchical vector function, the accuracy and ability of FETD simulation of complicated SIW problems are improved. With the aid of non overlapping domain decomposition tearing and interconnecting algorithm, the ill-conditioned spare linear system obtained by the high order hierarchical vector finite element can be solved with direct methods even if the SIW structures lead to very large linear systems. Simulation results have verified this hybrid algorithm.

Chapter 8 - Finite-Element Time Domain Method