Time-domain Finite Element Method Research Articles

Hybrid method for transient responses of transmission line in an apertured enclosure based on FETD method and transmission line equations

A hybrid method combining the finite-element time-domain (FETD) method and transmission line (TL) equations (FETD-TL) is presented for evaluating the transient responses of a lossy TL in an apertured rectangular enclosure excited by electromagnetic pulses. First, the electric fields in the enclosure without the TL are calculated based on the Bethe's small holes theory and the mirror procedure. Then, the enclosure's electric fields are introduced into the second-order TL equation for current as the equivalent distributed sources. The transient currents induced on the TL are obtained by solving the second-order TL equation for current based on the FETD method with a single iteration variable. Finally, the transient voltages induced on the TL are computed by discretising the first-order TL equation. Compared with the method based on finite-difference time-domain (FDTD) method and TL (FDTD-TL) via several examples, the proposed hybrid method is proved to be correct and effective, which possesses much higher convenience and efficiency than FDTD-TL method in dealing with TL model terminated by complex lumped parametric networks.

Performance change of a semi-submersible production platform system with broken mooring line or riser

Under high sea states, positioning mooring lines or production risers could be led to failure. Such an accident will change the watching circle of the platform or even cause production to shut down. The present paper is aimed at investigating the transient/unsteady response of a semi-submersible platform, tension variation of the remaining lines, and evaluate the risk of risers clashing after mooring lines or risers failure. The fully coupled time-domain analysis is set up for the whole system which including a semi-submersible platform, 12 mooring lines, and 22 production risers. One or several mooring lines and risers are intentionally disconnected from the fairleads at a certain time. Combined environmental loads are selected from irregular waves and the steady current varying from very rough to phenomenal sea conditions. Hydrodynamic response of the semi-submersible with regarding first-order and second-order wave forces is calculated with the combination of three-dimension radiation/diffraction theories and Morison's equation. Nonlinear time-domain finite element methods are employed to analyze the behavior of mooring lines and risers. Results indicated that the platform has a large horizontal offset with the lost positioning forces. This will lead to the successive failure of the neighboring objects. The tension of the rest lines is also increased accordingly. Remaining lines that are closer to the failed lines will have larger tension increase to compensate. A practical methodology for investigating the risk of risers collision is also provided in this paper.

New Mixed SETD and FETD Methods to Overcome the Low-Frequency Breakdown Problems by Tree-Cotree Splitting

Traditional time-domain finite-element and spectral-element methods are known to suffer from the so-called low-frequency breakdown problem, where the system matrix can become ill-conditioned, and results can be unstable for electrically fine structures. In this article, a new mixed spectral-element time-domain (SETD) and finite-element time-domain (FETD) methods are proposed to overcome this low-frequency breakdown problem by constraint equations and tree-cotree splitting. Two forms of gradient matrices or the null space of the stiffness matrix of high-order basis functions are calculated to construct the constraint equations. Then, the constraint equations are directly applied in the time-stepping matrix equation by tree-cotree splitting to improve the properties of system matrices when the implicit Newmark-beta algorithm is adopted in two different forms. In the calculation of the first form of gradient matrix, the electric field is expanded by high-order edge basis functions; in the second form of gradient matrix, high-order edge basis functions associated with cotree edges and nodal basis functions defined on the free nodes are both employed to expand the electric field. Several numerical examples demonstrate that the new mixed SETD and mixed FETD methods can effectively overcome the low-frequency breakdown with high accuracy and without increasing the number of degrees of freedom over the conventional SETD and FETD methods.

Wideband Low-Frequency Design of Inductors and Wireless Power Transfer Coils Using the Mixed Finite-Element Time-Domain Method

Wideband low-frequency designs of inductors and wireless power transfer (WPT) coils are challenging because of the low-frequency breakdown in traditional numerical methods. In this letter, we apply a recently developed mixed finite-element time-domain (mixed FETD) method to overcome such low-frequency breakdown difficulties in designing inductors and WPT coils and verify the feasibility of the mixed FETD method for such models at low frequencies. This letter provides a demonstration for the design of the low-frequency electrically small electromagnetic devices.

Locally implicit time-domain finite element method for sound field analysis including permeable membrane sound absorbers

Locally implicit time-domain finite element method for sound field analysis including permeable membrane sound absorbers

Time Domain Room Acoustic Solver with Fourth-Order Explicit FEM Using Modified Time Integration

This paper presents a proposal of a time domain room acoustic solver using novel fourth-order accurate explicit time domain finite element method (TD-FEM), with demonstration of its applicability for practical room acoustic problems. Although time domain wave acoustic methods have been extremely attractive in recent years as room acoustic design tools, a computationally efficient solver is demanded to reduce their overly large computational costs for practical applications. Earlier, the authors proposed an efficient room acoustic solver using explicit TD-FEM having fourth-order accuracy in both space and time using low-order discretization techniques. Nevertheless, this conventional method only achieves fourth-order accuracy in time when using only square or cubic elements. That achievement markedly impairs the benefits of FEM with geometrical flexibility. As described herein, that difficulty is solved by construction of a specially designed time-integration method for time discretization. The proposed method can use irregularly shaped elements while maintaining fourth-order accuracy in time without additional computational complexity compared to the conventional method. The dispersion and dissipation characteristics of the proposed method are examined respectively both theoretically and numerically. Moreover, the practicality of the method for solving room acoustic problems at kilohertz frequencies is presented via two numerical examples of acoustic simulations in a rectangular sound field including complex sound diffusers and in a complexly shaped concert hall.

The phase change thermoelastic analysis of biological tissue with variable thermal properties during cryosurgery

In this work, the coupling phase change heat transfer process and thermal stress behavior of biological tissue during cryosurgery are studied in the context of a generalized thermoelastic theory. The nonlinear governing equations are constructed while considering the variable thermal properties and solved by a time-domain finite element method based on the effective heat capacity formulation. A 2-D tumor and normal tissue model is adopted for simulating the freezing process in cryosurgery. The effects of temperature-dependent thermal properties and relaxation time on the responses of biological tissue are discussed and illustrated graphically.

Time-domain finite element method to generalized diffusion-elasticity problems with the concentration-dependent elastic constants and the diffusivity

The investigations of mechanical-diffusion coupling are of great importance for the micro-electromechanical devices under non-uniform concentration environment, especially with the development of energy storage technology for a rapid charging system. In recent years there have been many experimental and theoretical studies show that the elastic constants and the diffusivity depend on the concentration of diffusing substances. In view of this, present work aims to study generalized diffusion-elasticity problems considering the concentration-dependent elastic constants and the diffusivity by time-domain finite element method. By using principle of virtual work, the obtained nonlinear finite element equations are solved directly in time domain to minimize precision losses in the application of integrated transformation method, and then the nonlinear solutions can be obtained. As numerical examples, the developed method is used to investigate the transient response of a thick circular plate subjected to the shock loading of the concentration. The results demonstrate that the developed method can faithfully predict the deformation of structure and most importantly the diffusive wave feature in both one-/two-dimensional solids whilst it is commonly difficult to model, especially for two-dimensional case, by using transform method. Parametric studies are performed to evaluate and discuss the effects of concentration-dependent elastic constants and diffusivity on the structural dynamic responses.

Energy-Stable Time-Domain Finite Element Methods for the 3D Nonlinear Maxwell's Equations

In this paper, time-domain finite element methods for the full system of Maxwell's equations with cubic nonlinearities in 3D are presented, including a selection of computational experiments. The new capabilities of these methods are to efficiently model linear and nonlinear effects of the electrical polarization. The novel strategy has been developed to bring under control the discrete nonlinearity model in space and time. It results in energy stable discretizations both at the semi-discrete and the fully discrete levels, with spatial discretization using edge and face elements (Nedelec-Raviart-Thomas formulation). In particular, the proposed time discretization schemes are unconditionally stable with respect to a specially defined nonlinear electromagnetic energy, which is an upper bound of the electromagnetic energy commonly used. The approaches presented prove to be robust and allow the modeling of 3D optical problems that can be directly derived from the full system of Maxwell's nonlinear equations, and allow the treatment of complex nonlinearities and geometries of various physical systems coupled with electromagnetic fields.

An Improved Fast Finite Element Time-Domain Method Based on Compressive Sensing for Cavity Problems

To avoid directly solving linear equations for major time marching in the finite element time-domain (FETD) method, the compressive sensing (CS) theory is introduced to construct an explicit iterative scheme instead of an implicit form. In this method, Whitney elements and a leapfrog model are applied to time-dependent Maxwell curl equations for space and time discretization. After a small number of iterations, steps for linear equations in the initial time, the electric field intensity and magnetic flux density are updated just by the linear combination of results of previous time steps. Furthermore, a restart mechanism is built to control the computational complexity and accuracy over a long simulation time. The effectiveness of the new algorithm is verified by analyzing 3-D resonant cavities.

High-precision Runge-Kutta method for transmission line equation

This paper presents a high-precision Runge-Kutta (RK) method for solving transmission line equations. This method adopts high-order Taylor expansion in space, which improves the approximation accuracy of spatial differentiation. Compared with the traditional finite element time-domain method, when the number of samples per wavelength is the same, RK method has higher precision. At the same time, according to the Taylor model, researchers use RK method to solve transmission line equation in the external field excitation. The correctness and high precision of the RK method are verified by numerical examples of our study.

A Parallel Finite-Element Time-Domain Method for Nonlinear Dispersive Media

In this article, a novel use of graphics processing units (GPUs) is presented for the acceleration of finite-element time-domain (FETD) methods containing electrically complex media. By leveraging the massively parallel architecture of the GPU via NVIDIA's Compute Unified Device Architecture (CUDA) language, the immense computational burden imposed by these materials can be largely alleviated, facilitating their modeling and incorporation into electromagnetic devices and systems. To that end, an analysis of both mixed and vector wave equation-based nonlinear dispersive FETD algorithms is presented in order to both identify computational bottlenecks and determine their amenability to parallelization. Based on this analysis, a parallel elemental matrix-evaluation procedure is proposed, which when coupled to the recently derived Gaussian belief propagation method for matrix assembly and solution, demonstrates a performance increase of up to 200 times as compared with a traditionally serial implementation.

Electromagnetic and Semiconductor Modeling of Scanning Microwave Microscopy Setups

This article presents finite difference time domain (FDTD) and finite element method (FEM) based electromagnetic modeling and simulation of an industrial scanning microwave microscopy (SMM) material measurement setup. These two methods have been employed to cross verify each other for classical electromagnetic simulations of the homogeneous conductive materials under SMM. For the SMM simulations involving semiconductor materials, however, a coupled multiphysics solver is required in addition to the pure electromagnetic analysis. As a solution to this problem, an FEM-based semiconductor Poisson-Drift-Diffusion (PDD) solver and its coupling to transient electromagnetic solver is presented in this article. The considered SMM setup consists of a conductive fine tip suspended at a certain height above the sample. For the validation purposes of electromagnetic solvers, the numerical modeling was based on both the time domain FEM (TD-FEM) and FDTD. Both numerical methods extract the scattering parameters from the computed field of the conductive or dielectric samples. At the second stage of the analysis, the TD-FEM solver is coupled with the time domain PDD semiconductor solver in order to simulate charge transport and explain behavior of the charges in semiconducting domains under electromagnetic illumination similar to SMM setups.

A Time-Domain Multigrid Solver With Higher-Order Born Approximation for Full-Wave Radar Tomography of a Complex-Shaped Target

This article introduces and evaluates numerically a multigrid solver for non-linear tomographic radar imaging. Our goal is to enable the fast and robust inversion of sparse time-domain data with a mathematical full-wave approach utilizing a higher-order Born approximation (BA). Full-wave inversion is computationally expensive, hence techniques to speed up the numerical procedures are needed. To model the wave propagation effectively, we use the finite element time-domain (FETD) method, which is equipped with a multigrid scheme to enable the rapid evaluation of the higher-order BA. As a potential application, we consider the tomography of small solar system bodies (SSSBs) and asteroid interiors particular, the latter of which can contain internal details observable by radar, e.g., layers, voids and cracks. In the numerical experiments, we investigated monostatic, bistatic and multistatic measurement configurations. The results obtained suggest that, with a relevant noise level, the tomographic reconstruction quality can be improved by applying the higher-order BA in comparison to the first-order case, which we interpret as a linearization of the inverse problem. Our open multigrid-FETD solver for Matlab (The Mathworks Inc.) is available online. It applies Matlabs features for graphics computing unit acceleration to enhance computational performance.

No Load Simulation and Downscaled Experiment of UHV Single-Phase Autotransformer Under DC Bias

The time-domain field-circuit coupled finite element method (FEM) is widely used to analyze the DC effects on transformers. However, the long transient process of calculation will encounter difficulties due to the tremendous requirement of computer memory and CPU time, especially when it comes to ultra-high-voltage (UHV) autotransformers, which has a large time constant due to their less resistance and larger inductance. Besides, compared to the AC voltage, the DC voltage is much smaller, miscalculations usually occur as the component of DC bias can be easily neglected in the simulation. In this paper, a time-domain field-circuit coupling FEM combined with the series resistance and voltage compensation method (SRVCM) is proposed, a large resistance is in series in the circuit model to speed up the convergence of transient process and amplify DC component. Afterwards, the voltage supply is increased to compensate for the reduced voltage drop due to series resistance. The excitation waveform and its frequency characteristics of UHV autotransformer under various DC bias are discussed under no-load condition. Its advantages over conventional decrease the numerical miscalculation and the iterations calculation of the transient process. An experimental verification of the proposed method is carried out by a downscaled autotransformer.

A time-domain finite element method for the transient electric field and transient charge density on the dielectric interface

A time-domain finite element method for the transient electric field and transient charge density on the dielectric interface

A numerical study on the transverse seismic response of lined circular tunnels under obliquely incident asynchronous P and SV waves

The numerical analysis of the transverse seismic response of tunnels is an important issue in the design and safety evaluation of tunnel structures, where the spatial variation of earthquake ground motion induced by wave passage effect has been recognized as an important influence factor that cannot be ignored. In this paper, a 2-D transient dynamic finite element modelling technique is applied to investigate the seismic response of two soil-structure interaction systems subjected to obliquely incident plane P and SV waves. Based on the theory of wave input, the incident earthquake motion is modeled as equivalent nodal forces applied on the truncated boundary, and the free field ground response is calculated from the 1-D time-domain finite element method by considering the wave passage effect. The numerical scheme is implemented into the commercial software ABAQUS, and its accuracy is verified by comparing with the analytical solutions of soil-structure interaction problems. Firstly, the verified method is applied to study the transverse seismic response of a circular tunnel embedded in a homogenous elastic half-space under obliquely incident P and SV waves, where the influence of the incident wave type, incident angle, burial depth and tunnel diameter is discussed. Secondly, the response of circular tunnels embedded in a multi-layered non-homogenous elastic foundation is studied, where the influence of tunnel position in the foundation, flexibility ratio between soil and tunnel and stiffness difference of adjacent soil layers in the foundation are extensively investigated. Moreover, comparison is drawn between the tunnel responses in the homogenous and non-homogenous foundation systems, and the importance of conducting asynchronous seismic response analysis of circular tunnels is highlighted.

Dynamic response of soft soils in high-speed rail foundation: in situ measurements and time domain finite element method model

The dynamic response of soil to vibrations induced by moving trains has been widely studied using in situ measurements. However, few in situ tests have been conducted to measure the resulting vibration of foundation soils, especially for the foundation of high-speed rail (HSR) in a soft area. In this study, a number of field experiments were conducted on Shanghai–Hangzhou HSR in a suburb of Shanghai, China. The testing instruments were installed in foundation soils just beneath the HSR track to measure the vibration induced by trains moving at different speeds. Test results show the frequencies of foundation soil vibration are characterized by the train speed and geometrical features of the trains and slab track. In the frequency domain, the dominant frequency bands for vertical acceleration, velocity, and displacement of foundation soil decrease successively. In the time domain, the magnitudes of vibration levels at different locations in a soil foundation decrease gradually with increasing distance from the track. Furthermore, higher train speed can result in higher vibration level. Based on the field conditions, a three-dimensional dynamic finite–infinite element model is developed in the time domain. It shows the model is capable of capturing the primary characteristics of train-induced vibration in the field.

Parallel Simulation of Fully Coupled Electrothermal Processes in Large-Scale Phase-Change Memory Arrays

Numerical simulation of fully coupled electrothermal processes in phase-change memory (PCM) arrays is performed in this article. For realizing the ability in simulating the electrothermal responses of large-scale PCM arrays, an in-house parallel simulator based on domain decomposition method (DDM) and time-domain finite element method (FETD) is developed, with its performance evaluated in terms of accuracy and scalability. Then, thermal crosstalk in the PCM array is investigated using the developed simulator, and a diamond layer is introduced to suppress thermal crosstalk. Furthermore, the scaling effects of PCM arrays on their electrothermal performance are examined. A scheme for multibit PCM design is proposed, and the electrothermal characteristics of proposed 2-bit PCM cells and arrays are studied numerically.

A Convolution-Free Finite-Element Time-Domain Method for the Nonlinear Dispersive Vector Wave Equation

In this article, a finite-element time-domain method is presented for the solution of the second-order vector wave equation (VWE) subject to electrically complex materials, including general combinations of linear dispersion, instantaneous nonlinearity, and dispersive nonlinearity. The presented method is novel in that it offers greater geometric flexibility than existing finite-difference methods, incorporates both instantaneous and dispersive nonlinearity, scales to arbitrary dispersive and nonlinear orders, and is simpler, faster, and requires less computational complexity than existing mixed formulations due to the use of edge elements only.