Time-domain Finite Element Method Research Articles

Coupled Electromagnetic and Hydrodynamic Semiconductor Modeling for Terahertz Generation

Terahertz (THz) electrical signal generation from a photoactive semiconductor device illuminated by an optical pulse is modeled and simulated. Hydrodynamic equations in time domain are numerically solved for both electrons and holes using the discontinuous Galerkin time-domain finite element method (DGTD-FEM) for the high-frequency charge transport that occurs in the semiconductor device. The obtained frequency spectra of photocurrent in various semiconductor materials under illumination of an ultrashort light pulse are presented. The inertia effects and ballistic transport of carriers play an important role to determine the frequency response of these materials, and the developed hydrodynamic model (HDM) solver delivers a transport analysis by predicting higher and wideband frequency capabilities for GaAs and Ge detectors over Si-photodetectors.

A Fast 3-D finite element modeling algorithm for land transient electromagnetic method with OneAPI acceleration

The land transient electromagnetic (TEM) method is a geophysical prospecting method with a wide range of applications. In this paper, we develop an algorithm that carries out 3-D TEM modeling for loop-source devices. The algorithm is based on the time-domain finite element method with unstructured edge-based meshes, and an unconditional stable adaptive time-stepping method is developed to acquire stable solutions. We verify the algorithm with a 1-D analytical solution. And as case studies, we discuss the TEM responses of both large-loop and small-loop devices in the presence of topography. It is found that the modeling accuracy is more sensitive to space meshing than time discretization. The proposed algorithm is packed as software, TEMF3DT, which is open-source and publicly available together with the above-mentioned sample models. TEMF3DT is designed for PC users, but is also constructed through a higher-level MPI parallelization and a lower-level OpenMP parallelization for potential workstation or cluster uses. Also, TEMF3DT is accelerated by the modern Fortran and Intel OneAPI library to deliver state-of-the-art computational efficiency.

Seismic performance analysis of underground structures based on random field model of soil mechanical parameters

Soils with spatial variability are the product of natural history. The mechanical properties tested by soil samples from boreholes in the same soil layer may be different. Underground structure service in surrounding soils, their seismic response is controlled by the deformation of the surrounding soils. The variability of soil mechanical parameters was not considered in the current research on the seismic response of underground structures. Therefore, a random field model was established to describe the spatial variability of surrounding soils based on the random field theory. Then the seismic response of underground structures in the random field was simulated based on the time-domain explicit global FEM analysis, and the soil mechanical parameters and earthquake intensity influencing the seismic response of surrounding soils and underground structures were studied. Numerical results presented that, the randomness of soil parameters does not change the plastic deformation mode of surrounding soils significantly. The variation coefficients of inter-story deformation of structures and lateral deformation of columns are much smaller than that of mechanical parameters, and the randomness of soil parameters has no obvious effect on the structural deformation response.

An Explicit Time-Domain Finite-Element Boundary Integral Method for Analysis of Electromagnetic Scattering

A numerical scheme, which hybridizes the element-level dual-field time-domain finite-element domain decomposition method (ELDDM) and the time-domain boundary integral (TDBI) method to accurately and efficiently analyze open-region transient electromagnetic scattering problems, is proposed. Element-level decomposition decouples Maxwell equations on a discretization element from those on its neighboring elements using equivalent currents defined on their faces. For any element inside the computation domain, the equivalent currents are obtained from fields in the neighboring elements. For any element on the boundary of the computation domain, the equivalent currents are obtained using the fields generated by TDBI. To generate these fields, TDBI “radiates” equivalent currents on a Huygens surface enclosing the scatterer. This approach when combined with a leapfrog-type time updates results in a fully explicit numerical scheme that allows ELDDM and TDBI to use different time steps. Numerical results that demonstrate the applicability of the proposed method to concave and disconnected scatterers are presented.

Parallel Higher Order DGTD and FETD for Transient Electromagnetic-Circuital-Thermal Co-Simulation

A hybrid higher order discontinuous Galerkin time-domain (DGTD) method and finite-element time-domain (FETD) method with parallel technique is proposed for electromagnetic (EM)–circuital–thermal co-simulation in this article. For electromagnetic simulation, DGTD method with higher order hierarchical vector basis functions is used to solve Maxwell equation. Circuit simulation is carried out by modified nodal analysis method. For thermal simulation, FETD method with higher order interpolation scalar basis functions is adopted to solve heat conduction equation. To implement electromagnetic–circuital–thermal co-simulation, the electromagnetic and circuital equations are strongly coupled through voltages, currents, and electric fields at the lumped ports first. Then the electromagnetic and thermal equations are weakly coupled with electromagnetic loss and temperature-dependent medium parameters. Finally, large-scale parallel technique is used to accelerate the process of multiphysics simulation. Numerical results are given to validate the correctness and capability of the proposed electromagnetic–circuital–thermal co-simulation method.

Port Parameter Extraction-Based Self-Consistent Coupled EM-Circuit FEM Solvers

Self consistent solution to electromagnetic (EM)-circuit systems is of significant interest for a number of applications. This has resulted in exhaustive research on means to couple them. In time domain, this typically involves a tight integration (or coupling) with field and non-linear circuit solvers. This is in stark contrast to coupled analysis of linear/weakly non-linear circuits and EM systems in frequency domain. Here, one typically extracts equivalent port parameters that are then fed into the circuit solver. Such an approach has several advantages; (a) the number of ports is typically smaller than the number of degrees of freedom, resulting in cost savings; (b) is circuit agnostic; (c) can be integrated with a variety of device models. Port extraction is tantamount to obtaining impulse response of the linear EM system. In time domain, the deconvolution required to effect this is unstable. Recently, a novel approach was developed for time domain integral equations to overcome this bottleneck. We extend this approach to time domain finite element method, and demonstrate its utility via a number of examples; significantly, we demonstrate that self consistent solutions obtained using either a fully coupled or port extraction is identical to the desired precision for non-linear circuit systems. This is shown within a nodal network. We also demonstrate integration of port extracted data directly with drift diffusion equation to model device physics.

Thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity and nonlinear finite element analysis

In non-isothermal conditions, numerous experimental and theoretical investigations reveal that the elastic constants and thermal conductivity in piezoelectric solids depend on temperature distribution. This work aims to investigate thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity. The nonlinear time-domain finite element method is developed to directly solve nonlinear finite element governing equations, which maximally avoids the precision losses within the applications of the integrated transformation method. As a numerical example, the developed method is applied to analyze nonlinear transient thermo-electromechanical responses of a two-dimensional orthotropic piezoelectric plate of crystal class mm2. The achieved results reveal that temperature-dependent thermal conductivity and elastic constants remarkably affect the structural dynamic responses, whilst thermal wave or elastic wave will travel faster and the electrical energy harvesting ability is significantly elevated.

A self-aligned lithography method based on Fabry-Perot resonator effect

Fabry-Perot (F-P) resonator is widely applied in the field of optics such as micro-ring resonator and photonic crystal, but there are not yet relevant reports about optical imaging. We propose a self-aligned lithography method based on F-P resonator effect and realize self-aligned effect successfully by controlling film stack parameters. The self-aligned structure is composed of Ag/photoresist/Ag film stack and wafer layer which contains SiO2 layer and SiO2/Si gratings. A rapid simulation model based on Rigorous Coupled Wave Analysis algorithm is established to optimize the best parameters of the self-aligned structure. Then rigorous Finite Difference Time Domain model and Finite Element Method model are used to verify the self-aligned effect and the results show that such process has extremely large mask critical dimension (CD) and overlay variation. The mask CD could be tuned more than 50% of structure period while the wafer CD maintains in the range less than 10%, and the maximum mask overlay offset could be ± 25% of half pitch while the wafer pattern center maintains unchanged. All the results show that the proposed method has lots of process robustness and could increase the application area of imaging lithography technology.

High-order GPU-DGTD method based on unstructured grids for GPR simulation

The finite element time-domain (FETD) method is an appealing electromagnetic (EM) field-solving procedure for the derivation of high-resolution field distribution of complex geological models. However, the arising computational burden has become a main bottleneck restricting the efficient implementation of ground penetrating radar (GPR) simulation at a high speed and large scale. In this research, we developed a high-efficiency EM solver to discretize the partial differential equations on unstructured triangular meshes, using a high-order graphics processing unit (GPU)-finite element discontinuous Galerkin time-domain (DGTD) method. By introducing a semi-discrete strong format instead of solving large stiffness matrices, and by employing the Runge-Kutta temporal integration scheme, the DGTD method can effectively overcome the problem of memory shortage and thereby solves the issue of instability. Besides, the uniaxial perfectly matched layer (UPML) is extended to match the lossy medium and used as an absorbing boundary condition to simulate an open space. Three models were manufactured to compare the DGTD method with the state-of-art methods (FDTD, FETD) of different grids in terms of computing accuracy, the dispersion degree of the rough interface, and memory occupied. To be specific, we explored the detailed effect of both the grid sizes and the order of basis functions on the modeling accuracy for the proposed GPU-DGTD method. We finally verified the numerical solution and demonstrated its applications by simulating a complex model for tunnel geological forecast. The experimental results reveal the order of basic function N and the size of the grid d are closely concerned with the wavelength λ of EM waves, for example, an appropriate definition is d/N ≈ λ/15.

A hybrid algorithm for electromagnetic problems involving fine structures based on FDTD and FETD with unstable modes removing

We put forward a novel hybrid algorithm, based on merging finite-element time-domain (FETD) with finite-difference time-domain (FDTD) methods, to solve electromagnetic problems involving fine structures. The FETD method with unstable modes removing (UMR-FETD) is employed in regions relating to fine structures, while the FDTD method is adopted in the other regions. The suggested hybrid approach reduces the dimension of the system matrix for the UMR-FETD method, thus decreasing the consumption of computing resources. Besides, the hybrid algorithm makes it possible to adopt a uniform and large time step in the whole computational domain, thus improving computational efficiency. Numerical results confirm the good performance of the proposed hybrid algorithm to solve electromagnetic problems involving fine structures.

A Detailed FEM Study on the Vibro-acoustic Behaviour of Crash and Splash Musical Cymbals

Advanced numerical simulations, that include modal and frequency response function finite element analysis, frequency domain and time domain finite element method – boundary element method analysis, are performed to study the vibro-acoustic behaviour of crash and splash musical cymbals. The results of the modal analysis agree well with experimental measurements found in literature. The frequency domain and time domain coupled finite – boundary element method simulations, despite their high computational resources and time demands, are used for the crucial comparison of the velocity spectrograms on the cymbal to the radiated sound pressure spectrograms in the air. The computational analysis results show that the splash cymbal is characterized by a faster decay and a higher frequency content compared to the crash cymbal. The advanced multiphysics vibro-acoustic simulations that correlate the displacements and velocities of the vibrated structure with the radiated sound pressure results demonstrate the future capability to synthesize the sounds of cymbal music instruments.

A Parallel Dissipation-Free and Dispersion-Optimized Explicit Time-Domain FEM for Large-Scale Room Acoustics Simulation

Wave-based acoustics simulation methods such as finite element method (FEM) are reliable computer simulation tools for predicting acoustics in architectural spaces. Nevertheless, their application to practical room acoustics design is difficult because of their high computational costs. Therefore, we propose herein a parallel wave-based acoustics simulation method using dissipation-free and dispersion-optimized explicit time-domain FEM (TD-FEM) for simulating room acoustics at large-scale scenes. It can model sound absorbers with locally reacting frequency-dependent impedance boundary conditions (BCs). The method can use domain decomposition method (DDM)-based parallel computing to compute acoustics in large rooms at kilohertz frequencies. After validation studies of the proposed method via impedance tube and small cubic room problems including frequency-dependent impedance BCs of two porous type sound absorbers and a Helmholtz type sound absorber, the efficiency of the method against two implicit TD-FEMs was assessed. Faster computations and equivalent accuracy were achieved. Finally, acoustics simulation of an auditorium of 2271 m3 presenting a problem size of about 150,000,000 degrees of freedom demonstrated the practicality of the DDM-based parallel solver. Using 512 CPU cores on a parallel computer system, the proposed parallel solver can compute impulse responses with 3 s time length, including frequency components up to 3 kHz within 9000 s.

The Dilemma of Resolving the Low-Frequency Breakdown Problem in Microwave Components via Traditional and Improved Finite-Element Time-Domain Techniques

This paper developed an improved numerical methods for calculating electromagnetic field at low frequencies, and compared the performance with the traditional method. Traditional finite-element time-domain (FETD) is known to suffer from low frequency breakdown (LFB) problem, where system matrix becomes ill-conditioned, and leads to instability of small size electrical structures. In this paper, we proposed a mixed FETD (mFETD) method in resolving the LFB anomaly in the traditional FEM, with a particular reference to transmission line, inductor, and coaxial cable. We considered wave equation of E-field with incorporation of divergence constraint equation (DCE) as a function of Lagrange multiplier using current continuity equation (CCE) and Gauss’s law. For spatial discretization, both nodal basis functions and Curl conforming vector basis functions were selected, and we employed implicit Newmark beta algorithm (NBA) for integration of time. We describe how the components constructed via DCE in system matrix mitigate the singularity impact of the stiffness matrix, which consequently led to significant improvement of the system matrix. Numerical experiment and results demonstrate how the mFETD obtains stable numerical solution and attains faster rate of convergence while using an iterative solver, as such, improves the computational efficiency. Therefore, the mFETD method handles the transient problems in transmission line, which causes LFB anomaly in the traditional FETD, but not efficient in terms of computational time and iteration at solving the coaxial cable problem.

A Full-Wave Discontinuous Galerkin Time-Domain Finite Element Method for Electromagnetic Field Mode Analysis

A Full-Wave Discontinuous Galerkin Time-Domain Finite Element Method for Electromagnetic Field Mode Analysis

Implementation of the novel perfectly matched layer element for elastodynamic problems in time-domain finite element method

For the numerical simulation of infinite domain problems in finite element method (FEM), unwanted reflection from the artificial boundaries of the model is a limiting factor. Therefore, in this paper, based on the theory of perfectly matched layer (PML), a novel element is derived to deal with absorbing boundary conditions in the framework of time-domain finite element method (TDFEM). Then, by combining with the viscoelastic model and modified Newmark algorithm, a novel method is proposed to absorb outgoing waves in unbounded domains. Numerical results show that the proposed method can efficiently absorb the elastic wave, and it can be employed to solve infinite domain problems.

Fully 3D ship hydroelasticity: Monolithic versus partitioned strategies for tight coupling

This paper analyzes the partitioned and monolithic strategies to simulate tightly coupled hidroelastic problems. The seakeeping hydrodynamics solver used is based on a first-order linear time-domain FEM model with forward speed and double-body linearization. The structural dynamics solver is based on a full 3D time-domain FEM with corotational shell elements accounting for the geometric non-linearity. Both solvers are implemented under the same programming framework, which allows to implement the monolithic strategy, and to minimize the communication overheads of the partitioned strategy. Two case studies are used to test and compare the partitioned and monolithic coupling: a flexible catamaran in oblique waves, and a large floating reticulated structure made of fiber reinforced plastic. In both cases, the monolithic strategy is between three and four times faster than the partitioned strategy.This project has been developed under the H2020 project FIBRESHIP aimed at developing the technology to design and build the structure of large-length vessels in fiber reinforced polymers.

Transient Overvoltage on HVDC Overhead Transmission Lines With Background DC Space Charges and Impulse Corona

The space charges around a HVDC transmission line may not only lead to electromagnetic environmental problems but also affect the occurrence of impulse corona and then the transient overvoltage propagation. This paper derives the equations governing the transient overvoltage propagation along a HVDC transmission line when there is either space charges surrounding the line or impulse corona. In contrast to conventional transmission line equations, the proposed equations adopted the dynamic capacitance C ′ and conductance G to characterize the corona discharge in all cases, which can be obtained by a time-domain finite element method. A finite-difference time-domain method is introduced to solve the nonlinear transmission line equations. The validity of the proposed approach is verified by comparison with the lightning overvoltage waveforms measured in a literature. The transient overvoltage propagation along a long UHVDC transmission line surrounded by space charges is analyzed.

Surface acoustic wave attenuation in polycrystals: Numerical modeling using a statistical digital twin of an actual sample

Grain boundary scattering-induced attenuation and phase-velocity dispersion of Rayleigh-type surface acoustic waves are studied with a time-domain finite-element method (FEM). The FEM simulation incorporates a realistic material model based on matching the spatial two-point correlation function of a Laguerre tessellation with that obtained from optical micrographs of a previously studied aluminum sample. Plane surface acoustic waves are excited in a multitude of statistically equivalent virtual polycrystals, and their surface displacement fields are averaged for subsequent extraction of the coherent-wave attenuation coefficient and phase velocity. Comparisons to previous laser-ultrasonic experiments, an analytical mean-field model, and the FEM results show good agreement in a broad frequency range from about 10 to 130MHz. Observed discrepancies between models and measurement reveal the importance of spatial averaging in the context of mean-field approaches and suggest improvement strategies for future experimental studies and advanced analytical models. A different attenuation power law for Rayleigh waves is found in the stochastic scattering regime compared to bulk acoustic waves.

Finite element sound field analysis on measurement of absorption coefficient in a reverberation room -Relationships between inclination of walls and measurement results-

The absorption coefficients in a reverberation room are most representative measure for evaluating absorption performance of architectural materials. However, it is well known that measurement results of the coefficient vary according to a room shape of the measurement and area of the specimen. Numerical analyses based on wave acoustics are effective tools to investigate these factors on absorption coefficient measurement in reverberation room. In this study, sound fields for the measurement of absorption coefficient in reverberation room are analyzed by time domain finite element method (TDFEM). This study shows effectiveness of the analysis for investigation on causes of variation in the measurement results and improvement methods of the measurement. First, some measurement sound fields for absorption coefficient in reverberation rooms the walls of which are incline or decline are analyzed by the TDFEM. Next, reverberation times in each sound fields are calculated from the results obtained by TDFEM and the absorption coefficients are evaluated from the reverberation time of the room with and without specimen. Finally, the relationships among room shape, degree of inclination of the wall, the sound absorption coefficient of the specimen, frequencies and the measurement absorption coefficient are investigated.

A Subgridding Unconditionally Stable FETD Method Based on Local Eigenvalue Solution

A subgridding unconditionally stable finite-element time-domain method based on local eigenvalue solution (SUSL-FETD) is proposed to solve multiscale modeling. In this method, subgridding elements are used to discrete a multiscale computational domain, and the explicit central-difference method is applied for temporal discretization. Compared with traditional elements, the subgridding elements have a more complex distribution of edges and nodes. Therefore, an efficient subgridding scheme is given to form the element matrix for each subgridding element. Such system matrices assembled by all element matrices are symmetric. The subgridding FETD (S-FETD) is then further developed into the subgridding unconditionally stable FETD (SUS-FETD) by filtering spatial unstable modes. It is time-consuming to obtain the unstable modes by global eigenvalue decomposition. In this article, the local eigenvalue decomposition is proposed to get the unstable modes, which further reduces the memory storage and computing time. Numerical examples certify that the proposed SUSL-FETD has high accuracy and efficiency.