Time-domain Finite Element Method Research Articles

Design and time-domain finite element simulation of multi-functional transformation optical device

In this paper, we first proposed mathematical model equations for wave propagation in a multi-functional transformation optical device, namely, an electromagnetic rotation concentrator. This device can concentrate electromagnetic energy while rotating electromagnetic waves. We also demonstrate the stability of the model equation in the continuous case. Next, we designed the multi-functional device with multiple layers. We then proposed a time-domain finite element method for simulating wave propagation in this device and conducted a stability analysis of the model equations in the discrete case. Finally, we implemented the proposed algorithm and obtained numerous numerical results that demonstrate the validity of our model equations. To the best of our knowledge, this is the first work on time-domain modeling and analysis of multi-functional electromagnetic devices.

Total and scattered field decomposition technique in mixed FETD methods and its applications for electromagnetic cloaks

In this paper, we apply the total and scattered field plane wave excitation method to the mixed finite element time-domain (FETD) method for solving Maxwell’s equations to compute the scattered field of electromagnetic cloaks. This method can quantify the performance and operating frequency range of the cloak. We also present a mixed FETD scheme, which is coupling with perfectly matched layers technique. It can deal with various physical quantities more flexibly when solving the scattered field of complex dispersive media. Numerical results confirm the effectiveness of our algorithm, and quantify the performances of our electromagnetic cloaks at different frequency. We can conclude that the farther the incident wave’s frequency is from the cloak’s optimal operating frequency, the worse its performance.

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

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

Symplectic time-domain finite element method (STD-FEM) extended with wave propagation in porous materials for automotive interior acoustic modeling

The prediction of sound field evolving inside automotive interiors has gained significant attention in recent years, both for acoustic design purposes and virtual reality applications. Recently, a novel numerical simulation method was proposed by the present authors termed as symplectic time-domain finite element method. This paper discusses the numerical method and its application for simulating sound fields inside vehicle interiors. The presented case study includes the effect of seat absorption and non-rigid boundaries by applying either locally reacting, or elastic surface models exhibiting extended reactivity.

3D Inversion of Grounded-source Transient Electromagnetic Data

The grounded-source transient electromagnetic method has the characteristics of convenient installation of emission source and large emission power, and is being widely used. To get a fine interpretation of observation data, we introduce a three-dimensional inversion algorithm for the grounded-source transient electromagnetic data. Firstly, the unstructured time-domain finite-element method is used to calculate the electromagnetic response, and then the quasi Newton method is used for data inversion. Finally, the reliability of this algorithm is verified by applying it to the theoretical model.

A basic study on presentation of improvement effect of sound environments by use of computational simulation

The purpose of this study is to propose a method of presenting information so that architectural designers who do not specialize in architectural acoustics can easily understand the problems of the sound environment. This paper focuses on presenting the effects of the sound absorbing material using the time domain finite element method (TDFEM) as a computational simulation method. First, the sound fields of different room shapes and sound absorption boundaries are analyzed using TDFEM, and the changes between the sound fields are confirmed by room acoustic parameters at each sound receiving point. Next, visualization and auralization of those sound fields are attempted. The visualization allowed for a detailed capture of changes in sound pressure distribution due to differences in room boundary conditions. As for auralization, subjective differences in sound fields with different boundary conditions were confirmed using the paired comparison method.

Finite element analysis of sound fields in the corridors of the hospital ward: Investigation on installing patterns of sound absorbing materials

In this paper, using the time-domain finite element method (TDFEM), an effective installation pattern of sound absorbing materials in corridors of the hospital ward is investigated. First, several models with different installation patterns of sound absorbing materials are analyzed by TDFEM. Next, spatial distributions of the squared sound pressure, the sound pressure level and the speech intelligibility index are calculated in each model. As a result, the amount of decrease of the sound pressure level by installing sound absorbing materials on the ceiling and part of the wall in case that room average (α¯) equals 0.18 is larger than those by installing sound absorbing materials on the ceiling in case that α¯ = 0.20. Finally, several models with different installation patterns of sound absorbing materials, of which is the same, are analyzed by TDFEM, and compared among the amount of decrease of sound pressure levels in each condition.

Investigation on measurement sound field of absorption coefficient in reverberation room by numerical simulation - Relationship between room shapes and measurement results -

In this study, the relationship among the shape and volume of the reverberation room, the sound absorption coefficient of the specimen, the frequency, and the obtained measurement results of the absorption coefficient in reverberation room are investigated by time-domain finite element method. First, finite element models are created for 11 types of reverberation rooms with different room shapes and volumes, and the models are analyzed in the case that all the boundaries are rigid walls and in the case that a measurement specimen is installed on one of the boundaries. Next, the absorption coefficients in each reverberation room are calculated and relationships among the results of the absorption coefficients, the shape and volume of the room, the absorption coefficients of the specimen and the frequency are shown. As the results, it is shown that relationship between absorption coefficient in reverberation room and absorption coefficient of specimen was varied by the absorption coefficient of the specimen and frequency more than room volume in heptahedral irregularly shaped reverberation room.

Symplectic time-domain finite element method (STD-FEM) for room acoustic modeling

A new, extended symplectic time-domain finite element method (STD-FEM) is proposed for room acoustic modeling. As a mathematical model for sound propagation and reflection, the classical time-domain wave equations are used, which can be extended with air absorption. Frequency-dependent locally reactive boundary conditions are also introduced to the model. Spatially, a third-order tensor product type spectral element discretization is applied, which allows us to use explicit time steps. For this purpose, a partitioned Runge-Kutta method is employed, which is an extension of a third-order symplectic time-discretization. The method is validated on a number of examples and the performance and stability benefits are presented. We present the implementation of the method in the soundy.ai application.

A high-order explicit time-domain FEM using 15-node tetrahedral elements for room acoustics modeling: Basic performance

Time-domain room acoustic modeling using mass-lumped higher-order tetrahedral finite elements with an explicit time-marching scheme is highly attractive because of its excellent geometrical flexibility with unstructured meshing and applicability into massively parallel computing. However, the standard mass-lumped tetrahedral elements yield an unstable scheme, and only implicit time-marching schemes are available. This study proposes a novel wave-based room acoustics solver based on a high-order explicit time-domain FEM. The present solver uses mass-lumped 15-node tetrahedral elements for spatial discretization and a dissipation-free two-stage partitioned Runge-Kutta time integration for time discretization. The 15-node tetrahedral elements had been developed to apply mass-lumping methods to 10-node tetrahedral elements, which are the most common finite element in engineering applications, but its applicability in room acoustics problems is unknown. Higher accuracy and efficiency of the proposed method over the standard method using 10-node tetrahedral elements is presented through an eigenvalue analysis of a long duct model and acoustic simulations in a small room. Additionally, frequency-dependent sound absorbing boundary is implemented by revising an auxiliary differential equation method.

Second Harmonic Modulation for Ultrasonic Signals Based on the Design of the Phononic Crystal Filter.

Nonlinear ultrasonic non-destructive testing (NDT) is a widely used method for detecting micro-damages in various materials and structures due to its high sensitivity and directional capability. However, the extraction and modulation of extremely weak nonlinear ultrasonic signals is quite a challenge in practical applications. Therefore, this paper focuses on the second harmonic modulation signal method in nonlinear ultrasonic NDT and proposes the design of the phononic crystal filter (PC filter) to achieve this filtering function. Through finite element simulations, it is demonstrated that the filtering frequency of the filter is influenced by the structural configuration, material wave speed, and geometric characteristics. Then, the design method for cubic PC filters is established. Furthermore, a time-domain finite element method is introduced to verify the filtering ability of the filter and further validate the rationality of this design approach.

Analysis and application of a time-domain finite element method for the Drude metamaterial perfectly matched layer model

In this paper, we develop a finite element method (FEM) to solve the Drude metamaterial perfectly matched layer (PML) model by edge elements. Both the stability analysis and error estimate for the scheme are established. To our best knowledge, this is the first paper on developing and analyzing a FEM for this Drude PML model. Numerical results are presented to justify the theoretical error estimate and demonstrate the effectiveness of this PML in absorbing outgoing waves in the Drude metamaterial.

Temperature-drift effect analysis of microstrip filters based on parallel high-order DGTD and FETD method with memory reduction technique

The temperature-drift effect of microstrip filters is analyzed by the proposed electromagnetic-thermal co-simulation method based on parallel high-order discontinuous Galerkin time domain (DGTD) and finite-element time-domain (FETD) algorithms with a memory reduction technique. The element matrices of DGTD method are factorized into the product of coefficient matrices and universal matrices. The coefficient matrices are different for each tetrahedral element and need to be stored for all the elements. While the universal matrices are the same for all the tetrahedral elements and only need to be stored for one element. Since the sizes of the coefficient matrices are much smaller than the element matrices of DGTD method, the proposed method avoids storing the large element matrices and greatly reduce the memory requirement of the DGTD method. Thus it reduces the memory requirement of the whole electromagnetic-thermal co-simulation which is dominated by the memory consumption of the DGTD method. Large-scale parallel technique is adopted to accelerate the process of electromagnetic-thermal co-simulation. The proposed method provides a very powerful tool for temperature-drift effect analysis of microstrip filters.

An energy stable discontinuous Galerkin time-domain finite element method in optics and photonics

In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell’s equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new capabilities of methods of this type are to efficiently model linear and nonlinear effects, for example of Kerr nonlinearities. Energy stable discretizations both at the semi-discrete and the fully discrete levels are presented. In particular, the proposed semi-discrete scheme is optimally convergent in the spatial variable on Cartesian meshes with Qk-type elements, and the fully discrete scheme is conditionally stable with respect to a specially defined nonlinear electromagnetic energy.

Accurate simulation of THz generation with finite-element time domain methods.

We investigate the accurate full broadband simulation of complex nonlinear optical processes. A mathematical model and numerical simulation techniques in the time domain are developed to simulate complex nonlinear optical processes without the usual used slowly varying envelope approximation. We illustrate the accuracy by numerical simulations. Furthermore, they are used to elucidate THz generation in periodically poled Lithium Niobate (PPLN) including optical harmonic generation.

Three-Dimensional Inversion of Long-Offset Transient Electromagnetic Method over Topography

The long-offset transient electromagnetic method (LOTEM) is widely employed in geophysical exploration, including environmental investigation, mineral exploration, and geothermal resource exploration. However, most interpretations of LOTEM data assume a flat Earth, and the commonly used one-dimensional (1D) interpretation encounters significant challenges in achieving reliable geological interpretations when topography is ignored. To address these challenges, this study presents an effective three-dimensional (3D) LOTEM inversion method. In this study, we discretize the simulation domain using unstructured tetrahedra to accurately simulate complex geological structures. The finite-element time-domain (FETD) method is utilized to calculate the LOTEM forward responses, and the limited-memory BFGS (L-BFGS) optimization method is employed for 3D LOTEM inversion. To avoid explicit calculation of sensitivity, we obtain the product of the transposed sensitivity matrix and the vector through adjoint forward modeling. Several synthetic models are used to verify the developed program, and the influence of topography on LOTEM inversion is examined. The numerical results demonstrate that topography can significantly impact the inversion result, potentially leading to incorrect geological interpretations. Finally, the developed inversion algorithm is applied to a realistic ore model from Voisey’s Bay, Labrador, Canada. The 3D inversion successfully reconstructs the spatial distribution of the ore body, further confirming the effectiveness of the developed algorithm.

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.