Time-domain Finite Element Method Research Articles

A new time-domain finite element method for simulating surface plasmon polaritons on graphene sheets

In this paper, we develop a new variational form to simulate the propagation of surface plasmon polaritons on graphene sheets. Here the graphene is treated as a thin sheet of current with an effective conductivity, and modeled as a lower-dimensional interface. A novel time-domain finite element method is proposed for solving this graphene model, which coupled an ordinary differential equation on the interface with Maxwell's equations in the physical domain. Discrete stability and error estimate are proved for our proposed method. Numerical results are presented to demonstrate the effectiveness of this graphene model for simulating the surface plasmon polaritons propagating on graphene sheets.

A 3-D Hybrid Maxwell’s Equations Finite-Difference Time-Domain (ME-FDTD)/Wave Equation Finite-Element Time-Domain (WE-FETD) Method

A 3-D Hybrid Maxwell’s Equations Finite-Difference Time-Domain (ME-FDTD)/Wave Equation Finite-Element Time-Domain (WE-FETD) Method

A Spatial Modes Filtering FETD Method With Nonuniform Subgridding Mesh

A spatial modes filtering finite-element time-domain method with nonuniform subgridding mesh (NUSSMF-FETD) is proposed to enhance the modeling flexibility and computation efficiency of electromagnetic simulations with fine structures. Taking the nonuniform rectangular meshes as local refinement elements causes complex edge distributions in subgridding elements, the element and system matrices construction process of nonuniform subgridding FETD (NUS-FETD) is given in detail. Then the NUSSMF-FETD is obtained by introducing the spatial modes filtering (SMF) method. NUS-FETD effectively reduces the unknowns in local refinement regions compared to the uniform subgridding FETD (US-FETD). On this basis, NUSSMF-FETD can expand the time step and also keep computation accurate and efficient. The NUSSMF-FETD based on local eigenvalue solution (LES-NUSSMF-FETD) further reduces the time and memory consumption of system eigenvalue analysis. Numerical results present that the NUSSMF-FETD method has high spatial modeling flexibility and computation efficiency.

Finite-amplitude nonlinear waves in inertial amplification metamaterials: Theoretical and numerical analyses

The motivation of this study is to understand the unique characteristics of finite-amplitude elastic wave propagation in an inertial amplification (IA) system coupled with a Duffing resonator and leverage the unique opportunities offered by the IA mechanism and nonlinearities to achieve the modulation of elastic waves. Based on the assumption of the perturbation method, the effective range of the wave amplitude was investigated, which is usually ignored. Meanwhile, the obvious phenomenon of bandgap transition (between the single resonance bandgap and hybrid bandgap) is observed with varying IA levels. In particular, we demonstrated a new phenomenon of negative wave propagation and an obvious standing-wave mode in this system. Here, an analytical investigation of the amplitude-dependent and IA-dependent nonlinear dispersion is conducted based on the perturbation approach. Numerical simulations using the time-domain finite element method and Gaussian pulse excitation were performed to validate the nonlinear dispersion and negative motion of the wave packet. The research results can be used to tune wave propagation in metamaterials and provide ideas for the design of metamaterials, which can be used in practical circumstances for different energy transfer needs.

Electrothermal analysis of a TEC-less IR microbolometer detector including self-heating and thermal drift

ABSTRACT The article presents the results of modelling and experiments of the self-heating and thermal drift effects of microbolometric sensors of infrared radiation. The developed electrothermal model of the readout electronic circuit generates the power dissipated in the active microbolometer during row-by-row scanning implemented in the focal plane array (FPA) detector. Two approaches to thermal modelling are presented. Both 1D frequency domain and 2D time domain finite element method models allow estimation of the thermal behaviour of an FPA microbolometer. The modelling and presented experiment results lead to the estimation of the deterioration in FPA performance and allow definition of the basic limits of resistive bolometers in operation.

An advanced detection method for unfavorable geological boulder based on electrical source in drill holes under shield machine

Abstract In recent years, due to the increasingly complex terrain, geological conditions, and working environments in engineering, the accuracy requirements in explorations have been continuously growing. In this study, with the goal of high-resolution prospecting for unfavorable geological boulder under a complex detection environment (such as subway shield machine tunnel). A tunnel model with an unfavorable geological boulder was constructed, and a time domain finite element method was adopted for 3D transient electromagnetic forward modeling. To realize high resolution in the positioning of small-scaled boulders, a detection method in complex environments was explored. A hole was drilled from the central point of the tunnel face toward the tunnel construction direction. Then, an electrical source was placed into the hole and array data was collected on the tunnel face. Electromagnetic sounding was achieved through the movement of the source, and the plane positions of the geological bodies were determined through the electromagnetic field distribution characteristics on the tunnel face. It was observed that the Ex and Ey (horizontal components of the electric field) had a higher resolution for a high resistance geological boulder. Therefore, the results indicated that in complex environments, collecting the horizontal components of the electric fields on the tunnel face excited by the electrical source within a drill hole could be a feasible method for fine explorations of a small-scale high resistance boulder.

Shadow effect and source overprint effect of short-offset transient electromagnetic method

AbstractIn artificial-source electromagnetic explorations, the shadow effects and source overprint effects are two of the key factors to affect the detection reliability. Compared with frequency-domain electromagnetic methods, the transient electromagnetic (TEM) shadow effect and source overprint effect are more complex, especially for the short-offset TEM (SOTEM) observed in the near-source region. However, there is less relevant research. Therefore, in this paper, we first realize 3D SOTEM simulations based on the vector time-domain finite element method, then further analyze the generation of SOTEM shadow effect and source overprint effect from view of the diffused electromagnetic fields, as well as their influence on ground horizontal electric field Ex and vertical induced voltage dBz/dt responses. Results show that the attraction or repulsion of the electrical inhomogeneity would affect the diffusion speed of the electromagnetic fields, which is the essential in the two source effects. Besides, from view of the ground Ex and dBz/dt responses, the relative anomaly of SOTEM shadow effect is almost twice those of the SOTEM source overprint effect, i.e. the SOTEM shadow effect is easier to record, especially for dBz/dt responses. In addition, owing to the shadow effect, SOTEM may fail to identify the real target anomaly, whereas the influence of the source overprint effect for recognizing the target anomaly mainly occurs on all-time dBz/dt responses and early-time Ex responses (before about 10 ms), that is, observing late-time SOTEM Ex responses can effectively avoid such influence. Hence, to fully ensure avoiding the influence of the source overprint effect, we suggest adopting high-power transmission to increase the late-time signal-to-noise ratio in field measurements.

Binaural Auralization of Room Acoustics with a Highly Scalable Wave-Based Acoustics Simulation

This paper presents a proposal of an efficient binaural room-acoustics auralization method, an essential goal of room-acoustics modeling. The method uses a massively parallel wave-based room-acoustics solver based on a dispersion-optimized explicit time-domain finite element method (TD-FEM). The binaural room-acoustics auralization uses a hybrid technique of first-order Ambisonics (FOA) and head-related transfer functions. Ambisonics encoding uses room impulse responses computed by a parallel wave-based room-acoustics solver that can model sound absorbers with complex-valued surface impedance. Details are given of the novel procedure for computing expansion coefficients of spherical harmonics composing the FOA signal. This report is the first presenting a parallel wave-based solver able to simulate room impulse responses with practical computational times using an HPC cloud environment. A meeting room problem and a classroom problem are used, respectively, having 35 million degrees of freedom (DOF) and 100 million DOF, to test the parallel performance of up to 6144 CPU cores. Then, the potential of the proposed binaural room-acoustics auralization method is demonstrated via an auditorium acoustics simulation of up to 5 kHz having 750,000,000 DOFs. Room-acoustics auralization is performed with two acoustics treatment scenarios and room-acoustics evaluations that use an FOA signal, binaural room impulse response, and four room acoustical parameters. The auditorium acoustics simulation showed that the proposed method enables binaural room-acoustics auralization within 13,000 s using 6144 cores.

Analysis of Transmission Characteristics of EBG Structures by Subgridding Unconditionally Stable FETD Method

Subgridding unconditionally-stable finite-element time-domain method based on spatial modes filtering (SSMF-FETD) is combined with the Floquet theorem and used to analyze the transmission characteristics of 2-D dielectric pillar-array electromagnetic bandgap (EBG) structures with cross-section shapes of square and H. The computational stress is effectively reduced by exploiting the periodicity of the EBG structure and subgridding technique. Through the spatial modes filtering (SMF) method, the subgridding FETD (S-FETD) method is developed into the SSMF-FETD with larger time steps and higher computational efficiency. The effect of geometric and electromagnetic parameters on transmission characteristics of EBG structures are analyzed and compared in detail, the conclusions are as follows: the optimal filling ratio of the dielectric square-pillar EBG structure is 0.5, the composite H-pillar EBG structure has multiple bandgaps and can effectively save metal materials while satisfying the design requirements. The effect of electromagnetic parameters can be uniformly analyzed from the perspective of the average relative permittivity; with its increase, the central frequency of the bandgap becomes lower. It should be noted that the bandgap distribution and variation of composite H-pillar EBG structure are related to how its dielectric parameters change and combine. The results can serve as a reference for similar structures design.

Retracted] Analysis of VLF Wave Field Components and Characteristics Based on Finite Element Time‐Domain Method

Most traditional sound field calculation methods regard the seabed as the horizontal stratified liquid sea bottom and conduct simulation analysis based on the frequency domain. Hence, the generality of the above research methods is limited to varying degrees. To accurately clarify the propagation characteristics and mechanism of very low‐frequency (VLF, ≤100 Hz) sound waves in the shallow sea, a numerical calculation model is established using the finite element time‐domain method (FETD) based on the three‐dimensional cylindrical coordinate system. Using this model, the effects of sea‐bottom topographies and geoacoustic parameters on the composition and characteristics of VLF sound fields in the shallow sea and their corresponding mechanism are investigated through the comparative analysis of various numerical simulation examples. The simulation results demonstrate that the low‐frequency sound field in the full waveguide of the shallow sea is composed of normal mode waves in the seawater layer, Scholte waves at the liquid‐solid interface, and elastic waves at the sea bottom. Compared with the soft sea bottom, which has a more negligible elastic impedance, the hard sea bottom is more conducive to the long‐distance propagation of normal mode waves and the excitation of Scholte waves. The Scholte waves on the hard sea bottom are significantly stronger than those on the soft sea bottom. Compared with the horizontal sea bottom, the uphill topography enhances the sound energy leakage to the sea bottom. It is more favorable to receive Scholte waves at shallow depths, whereas the influence laws of downhill topography are the opposite.

Electromagnetic-Thermal Modeling of Nonlinear Magnetic Materials

A nonlinear electromagnetic (EM)-thermal coupled solver is developed for modeling ferromagnetic materials widely used in electric motors. To accurately predict machine performance, the time-domain finite element method is employed to solve this multiphysics problem. By adopting the nonlinear B-H models to account for hysteresis effects, magnetic core losses are computed as the major sources of power dissipation for magnetic materials. The resulting temperature change is then obtained and its effect on the magnetic properties is subsequently evaluated. Due to different time scales of EM field variations and heat transfer processes, different time step sizes are adopted to enhance the simulation speed. During thermal time marching, the EM solver is invoked adaptively based on material property changes, and EM losses are calculated and updated through extrapolation, resulting in an efficient EM-thermal coupling scheme. Numerical examples are presented to validate the accuracy and capabilities of the proposed EM-thermal co-simulation framework.

Dynamic Phasor Finite-Element Modeling of a DFIG for Grid Connection Studies

Co-simulation studies of electric power systems and electric machines have been always a challenge. In order to reduce the simulation time to a reasonable value, lumped-parameter Electric-Machines models are commonly used in electric power system modeling software packages to avoid the heavy computational burden of more accurate modeling methods especially Finite Element Method (FEM) on the expense of less accuracy. The proposed technique in this paper combines the Dynamic Phasor Modeling technique for power system simulations with FEM to accurately model the DFIG while connected to the grid. The utilization of dynamic phasors enables adopting large simulation time-steps resulting in a significant reduction in the simulation time compared to the conventional time-domain FEM modeling. The mathematical foundation of the proposed modeling method is presented including the generator's core saturation. Custom-written C++ codes have been developed by the authors to execute the new dynamic phasor FEM algorithm and the conventional time-domain FEM in order to fairly compare their accuracy and numerical performances. As the proposed method combines time and frequency domains, a unique capability of modeling the rotor movement can be achieved. The rotation can be represented by physically incrementing the rotor and airgap mesh as in regular time-domain solvers, by mathematically representing the rotation using the Virtual Blocked Rotor method as in frequency-domain solvers, and the proposed method of combining the two aforementioned approaches. The three methods of modeling rotor rotation are discussed and their simulation results are compared to give a guide to choose the proper method for the different modeling targets. The results show that the proposed dynamic phasor FEM is capable of producing comparable results to the traditional time-domain solver at a substantially reduced simulation time.

3-D Forward Modeling of Transient EM Field in Rough Media Using Implicit Time-Domain Finite-Element Method

In a heterogeneous medium (usually called a rough medium) with fractured formations, the propagation of an electromagnetic (EM) field is a type of subdiffusion. Current mainstream geophysical EM data processing methods cannot be applied to data acquired on heterogeneous Earth, as they are not governed by the classic diffusion theory. To evaluate the influence of roughness on the transient EM (TEM) signal for a complex model and contribute to data inversion, we proposed a novel three-dimensional (3-D) forward modeling scheme for TEM in rough media. First, we derived the governing equation with a fractional-order time derivative for the subdiffusion of EM waves in rough media. Then, we proposed a novel time discretization using an unequal step length for the Caputo operator, which significantly reduces the total number of time steps. Finally, an implicit time-domain finite-element method using unstructured tetrahedron discretization was adopted to solve the 3-D forward problem. Furthermore, an efficient time segmentation strategy combined with parallel RHS construction was proposed to accelerate modeling. The numerical results prove that the proposed method is accurate and efficient, and will be a powerful numerical method for analyzing TEM wave propagation and processing TEM data in areas with multiscale fractures or porosity.

High potential of small-room acoustic modeling with 3D time-domain finite element method

Applicability of wave-based acoustics simulation methods in the time domain has increased markedly for performing room-acoustics simulation. They can incorporate sound absorber effects appropriately with a local-reaction frequency-dependent impedance boundary condition and an extended-reaction model. However, their accuracy, efficiency and practicality against a standard frequency-domain solver in 3D room acoustics simulation are still not known well. This paper describes a performance examination of a recently developed time-domain FEM (TD-FEM) for small-room acoustics simulation. This report first describes the significantly higher efficiency of TD-FEM against a frequency-domain FEM (FD-FEM) via acoustics simulation in a small cubic room and a small meeting room, including two porous-type sound absorbers and a resonant-type sound absorber. Those sound absorbers are modeled with local-reaction frequency-dependent impedance boundary conditions and an extended-reaction model. Then, the practicality of time-domain FEM is demonstrated further by simulating the room impulse response of the meeting room under various sound absorber configurations, including the frequency component up to 6 kHz. Results demonstrated the high potential and computational benefit of time-domain FEM as a 3D small room acoustics prediction tool.

Numerical modeling and data signal analysis of GPR array based on dual-field domain-decomposition time-domain finite element method

Traditional ground-penetrating radar (GPR) systems typically use a single transceiver antenna unit, which is challenging to achieve high-fidelity, ultra-narrow pulse transmission. It leads to problems such as limited detection resolution and insufficient data acquisition. This paper proposes a multi-polarization GPR array that uses multiple antenna elements to work synergistically. An electromagnetic field solving algorithm that enables parallel computation is introduced the time-domain finite element method of dual-field decomposition to achieve efficient and wideband simulation of the electromagnetic characteristics of large arrays. Each antenna element of the array system is treated as a subdomain during the solution process, and the electric and magnetic field values for each subdomain are calculated separately. Adjacent antenna elements are explicitly connected by equivalent surface currents on the interface of the subdomains. Through the method, numerically simulates the antenna array, establishes the spatial multi-polarization input signal, and analyzes the polarization response of the ground-penetrating radar (GPR) electromagnetic signal under the antenna array structure to the target body. The research results demonstrate that under the ground-penetrating radar array observation mode, the target's multi-polarization signal information can accurately and effectively reflect it's corresponding position and morphological relationship. The multi-polarized input signal can better compress the width of the wavelet and improve the range resolution of the target body. AAt the same time, the antenna array excites pulse signals with the same center frequency to be superimposed in the equivalent amplitude and same phase on space. The formed plane beam signal increases the radiation energy, improves the signal-to-noise ratio of the data, and eliminates the flicker caused by the radar cross-section changing with the observation angle, and weakens the influence of the discontinuity of the profile data in the horizontal direction caused by the antenna's unstable pattern and strengthens the data quality.

A novel enriched degree of freedom method for absorbing boundary conditions in the time-domain finite element method

A novel enriched degree of freedom method for absorbing boundary conditions in the time-domain finite element method

Numerical Simulation and Application of Transient Electromagnetic Detection Method in Mine Water-Bearing Collapse Column Based on Time-Domain Finite Element Method

Mine floods caused by water-bearing collapse columns are one of the most significant types of coal mine disasters in advanced detection. The transient electromagnetic method (TEM), one of the most effective means, can detect the collapse column in coal mines. However, the research on TEM used on the ground is mainly limited to half-space that does not follow underground mining conditions. This research used the whole-space TEM to detect the water-bearing collapse columns in front of the roadway. Based on the time-domain finite element method (TDFEM) and actual coal-measure strata data, this paper built the whole-space geo-electric models, summarized response characteristics, and proposed “geometric gravity center” effect. The results showed that the simulation based on TDFEM could accurately reflect the TEM response law, and the advanced detection using TEM in a mine environment was consistent with the actual situation.

Exact artificial boundary condition and 1D time-domain method for seismic response analysis of layered saturated poroelastic half-space

This study proposed a one-dimensional (1D) time-domain finite element method (FEM) for seismic response analysis of a layered saturated soil half-space under obliquely incident plane waves, based on Biot's u-w wave equations. The spatially two-dimensional problem was transformed into an equivalent 1D time-domain problem along the depth according to Snell's law. An exact artificial boundary condition for saturated poroelastic media was developed to simulate the wave absorption and input effects of the truncated half-space. Using the displacement and stress continuity conditions between the adjacent saturated poroelastic-medium layers and combining all finite elements and the exact artificial boundary condition, the total dynamic equation for the spatially 1D problem was obtained. The 1D dynamic equation was solved using the FEM with explicit time integration. The proposed method was verified by analyzing two engineering sites in the time domain and a comparison with the frequency-domain transfer matrix method with fast Fourier transform.

A novel time‐domain numerical methodology for the electromagnetic analysis of an H‐plane tee power divider

A time-domain numerical methodology for the transient analysis of multisection waveguide power dividers is proposed. Waveguide power dividers are essential components of microwave systems for high-power applications. A numerical strategy based on the 3D discontinuous Galerkin time-domain finite element method is used to estimate the electromagnetic propagation inside a power divider with three ports. The proposed approach leads to simulations that are fast, robust, and accurate, this being the result of a parallel local discretisation of the full-wave time-domain Maxwell's equations on unstructured tetrahedral meshes. The stability of the overall numerical scheme is obtained using an upwind numerical flux, an implicit second-order accurate time integration scheme, and Whitney's edge elements. Good agreements are obtained when the computed results are compared with other HFSS simulation results, and with measurement results found in the literature.

Developing and analyzing a finite element method for simulating wave propagation in graphene-based absorber

In this paper, we are concerned about a graphene-based absorber model, which incorporates both the interband conductivity and intraband conductivity of the graphene. We first establish an energy identity and stability for the continuous model. Then we propose a finite element time-domain method for solving the model by edge elements. Numerical stability and optimal error estimate are proved for the scheme. Numerical results are presented to justify the error estimate and demonstrate the wave absorbing phenomenon by graphene slab.