This work presents a gradual interval mapping method (IMM) integration framework for the rapid design of multiple metasurfaces. By leveraging the deep neural networks, the gradual design framework efficiently predicts both S-parameters and geometric structures using interval folding lines as input. Unlike traditional and current approaches, the proposed method integrates IMM with a filling strategy, simplifying data processing and enhancing prediction accuracy. To validate its effectiveness, three types of frequency selective surface (FSS) are designed, one of which is fabricated and experimentally measured in a microwave chamber. Simulation and measurement results confirm the superior performance of the framework, highlighting its potential for intelligent electromagnetic device design. Finally, we conclude with a short discussion of the work, including its limitations and developability.

The time-domain discontinuous Galerkin (DGTD) method with p -adaptive and local time stepping (LTS) strategies, widely employed for simulating various electromagnetic wave phenomena, faces challenges in achieving optimal performance in parallel computing environments due to load imbalance among computational nodes caused by the dynamic change of base order. To address this issue, an adaptive load balancing adjustment strategy is proposed. The proposed load balancing strategy, based on the element diffusion model, achieves balanced computational loads by reasonably selecting and adjusting the interface elements among the computational nodes. Without the need of repartitioning the entire computational domain, the solution time consumed by the proposed method for the load balancing is reduced. Several multiscale electromagnetic examples are given to demonstrate that with the proposed load balancing method, fewer load balancing time overheads and enhanced scalability of the parallel DGTD algorithm with p -adaptive and LTS strategies are achieved, compared with widely used ParMETIS repartitioning method.

This communication proposes an improved energy technique for the convergence and stability analysis of upwind-flux-based discontinuous Galerkin time-domain (DGTD) method. By formulating the discrete energy in the energy-based stability analysis technique into a global quadratic form, the global stability condition of the upwind flux-based DGTD method is analytically derived for the first time. In order to achieve the highly efficient stability condition prediction for large and multiscale complicated problems, an elementwise stability condition has been developed by applying matrix decomposition technique into the obtained global stability condition. Due to the sole approximation in the matrix decomposition, the proposed elementwise stability estimation method is more accurate than the traditional energy-based stability analysis techniques, where multiple approximations are employed to achieve the elementwise operations. The numerical examples show the good time step bound estimation accuracy of the global and elementwise stability conditions compared to the widely used energy-based techniques, which significantly enhances the DGTD method's solution efficiency on time integration.

In this article, a time-domain localized reduced basis multiscale (TD-LRBMS) method has been developed to efficiently establish a reduced-order model (ROM) for large-scale electromagnetic (EM) analysis. In the proposed TD-LRBMS method, the computational domain is divided into several nonoverlapping subdomains, and the transient EM fields are solved by the discontinuous Galerkin time-domain (DGTD) method. At the offline stage, a local reduced basis generation strategy is developed, which employs an incremental singular value decomposition (ISVD) technique and incorporates an automatic termination condition for temporal fields to enhance efficiency. Besides, to further improve the computational efficiencies at both offline and online stages, a local reduced basis compression technique is proposed, allowing for the separate selection of appropriate domain decomposition for the offline and online procedures. Numerical results are presented to demonstrate the effectiveness of the proposed TD-LRBMS method, including sophisticated capture of broadband EM characteristics and comprehensive reductions in computational time.

Accurate predictions of river water quality are vital for sustainable water management. However, even the powerful deep learning model, i.e., long short-term memory (LSTM), has difficulty in accurately predicting water quality dynamics owing to the high non-stationarity and data limitation in a changing environment. To wiggle out of quagmires, wavelet analysis (WA) and transfer learning (TL) techniques were introduced in this study to assist LSTM modeling, termed WA-LSTM-TL. Total phosphorus, total nitrogen, ammonia nitrogen, and permanganate index were predicted in a 4 h step within 49 water quality monitoring sites in a coastal province of China. We selected suitable source domains for each target domain using an innovatively proposed regionalization approach that included 20 attributes to improve the prediction efficiency of WA-LSTM-TL. The coupled WA-LSTM facilitated capturing non-stationary patterns of water quality dynamics and improved the performance by 53 % during testing phase compared to conventional LSTM. The WA-LSTM-TL, aided by the knowledge of source domain, obtained a 17 % higher performance compared to locally trained WA-LSTM, and such improvement was more impressive when local data was limited (+66 %). The benefit of TL-based modeling diminished as data quantity increased; however, it outperformed locally direct modeling regardless of whether target domain data was limited or sufficient. This study demonstrates the reasoning for coupling WA and TL techniques with LSTM models and provides a newly coupled modeling approach for improving short-term prediction of river water quality from the perspectives of non-stationarity and data limitation.

This paper develops a field-circuit co-simulation method to dynamically analyze the space-time coding metasurface arrays. The proposed co-simulation method is to combine discontinuous Galerkin time-domain (DGTD) method based on Maxwell's equations with SPICE solver. The spacetime coding metasurface arrays are decomposed into two subsystems: one is electromagnetic structure part which is modelled by the DGTD method, and the other is circuit part including arbitrarily linear or nonlinear components which is solved by the SPICE solver. The electromagnetic and circuit parts are iteratively solved to achieve the transient response of the space-time coding metasurface arrays. Numerical examples are given to verify the proposed method, demonstrating the feasibility of field-circuit co-simulation for analysis and design of the space-time coding metasurface.

This paper establishes an electromagnetic solver based on the nodal discontinuous Galerkin time-domain (NDGTD) method with consideration of divergence correction. Firstly, divergence-cleaning method is used to enforce Gauss's laws. With the auxiliary variables and the damping terms, the damped pure hyperbolic Maxwell's equation (DPHM) system has been established. The numerical governing equations corresponding to the DPHM have been formulated in the framework of the NDGTD. Numerical examples have been presented to verify the effectiveness of the NDGTD-DPHM method.

In this study, the elimination of correlated errors with an unknown correlation in distributed fusion is investigated, and a consistent fusion method for distributed multi-sensor systems is proposed. Unlike most existing fusion methods, the proposed method guarantees the consistency of fusion results without requiring system model parameters or adopting conservative strategies. First, a universal bijection is used to quantify the uncertainty in the estimates to be fused based on the entropy of the independent scalars. Second, the correlated errors caused by unknown mutual information and common process noise are treated as avoidable uncertainties. The avoidable uncertainty is then estimated by using a similarity function based on the Kullback–Leibler divergence. Finally, the avoidable uncertainty is separated from the fusion results by employing a conditional probability model to avoid correlated errors. This method is proven to be unbiased, consistent, and more accurate than the well-known covariance intersection method and the inverse covariance intersection method. The simulation results further verify the superiority of the proposed method in terms of the consistency, accuracy, and ability to limit cumulative errors in sequential fusion processes.

In this article, a highly efficient hp-adaptive scheme has been developed for the discontinuous Galerkin time-domain (DGTD) method. In order to achieve the h-and p-adaptive behaviors, a hierarchical octree-based recursive meshing procedure has been introduced. In the hp-adaptive scheme, the transformation method of the basis function is developed to convert the fields between the parent element and the child elements and between the higher-and the lower-order bases. Instead of the time-consuming field update process according to the governing equations, the error based on modified reference solutions can be rapidly and accurately calculated in the h-and p-adaptions by using the proposed transformation, thus flexibly manipulating the hp-adaptive procedure. Some 3-D radiation and scattering examples are given to demonstrate the good accuracy and high efficiency of the proposed hp-adaptive DGTD method.

In this communication, a novel message passing interface (MPI) parallel algorithm for nodal discontinuous Galerkin time-domain (NDGTD) method has been developed. A unified MPI + MPI technique has been introduced for extreme parallelism on a large-scale computer cluster. Through the data transmission between CPU nodes using MPI persistent nonblocking two-side communication and the direct data connection between processors in the same node via MPI shared memory windows, a two-layered parallel architecture is implemented to minimize the communication. To further accelerate the solution of the multiscale problems, the local time stepping (LTS) technique has been employed in the NDGTD method. A fast time step estimation method has been presented in this communication. With high overlap between the information transmission and the data calculation, the proposed MPI + MPI scheme overcomes the degradation of the parallel efficiency of the pure MPI technique in the scenario of the LTS technique and the large-scale CPU cores. Up to 94% parallel efficiency in 6400 CPU cores is achieved for the average single-core loading about 1700 finite elements, and 18 times acceleration for time step estimation can be obtained with the fourth-order basis function. Three practical complex examples are given to demonstrate a good performance of the proposed method.

This paper proposed a discontinuous Galerkin time domain method (DGTD) with non-conformal meshes and arbitrary order bases for the solution of electromagnetic problems. A transformation relation for the basis functions defined on the interface between two adjacent elements which are non-conformal, or have different base orders, or both of them has been developed to rapidly implement the numerical flux of the DGTD method. Numerical results are given to demonstrate good performance of the proposed method.

In this letter, an improved approach for the estimation of time step bound in the discontinuous Galerkin time-domain (DGTD) method has been developed. Different from the widely used energy-based technique, the spectral radius of the system matrix in the proposed method is used to analytically derive the stability condition of the DGTD method. In order to accelerate the solution of the time step bound, the spectral radius of the local system instead of the global spectral radius is solved, and thus, the proposed elementwise estimation scheme is suitable for the practical large-scale problems. The numerical examples demonstrate that the maximal time step estimated by the proposed method is up to 0.95 times as large as the accurate one and up to 3.83 times as large as the one determined by the widely used energy technique.

In this article, a graphic processing unit (GPU)-based acceleration implementation of a hybrid discontinuous Galerkin time domain method based on Maxwell’s equations and Helmholtz vector wave equation (HDGTD) has been developed. The computational domain is discretized by tetrahedrons and the resultant meshes are categorized into two regions solved by Maxwell’s equations and Helmholtz vector wave equation, respectively. The hierarchical vector basis functions are used to expand the unknowns in the HDGTD method, and a universal matrix technique is proposed to decompose the geometry-dependent matrices in each tetrahedron into the summation of universal matrices defined in barycentric coordinates, thus giving rise to a great decrease of the memory usage. A local time stepping (LTS) method based on a simple interpolation is introduced in the proposed HDGTD method to achieve highly efficient solution of multiscale problems. Two kinds of compute unified device architecture (CUDA)-based mapping techniques, i.e., 1-D and 2-D blocks, are implemented to achieve a tradeoff between the parallel speedup and the memory usage. With the 1-D block mapping, over 590 times speedup can be achieved, and in the case of the 2-D block mapping, over 150 times acceleration and 13 times memory reduction are obtained. Some practical complex examples are given to demonstrate a good performance of the proposed parallel method.

In this article, penalty factor threshold and time step bound in discontinuous Galerkin time method based on vector wave equation (DGTD-WE) method are well estimated. Based on the semidiscrete form of the DGTD-WE method, properties of the system matrices are studied and the stability condition related to the penalty factor is derived. By decomposing the global system matrices of the DGTD-WE method into the local ones and developing an efficient iteration procedure, the lower bound threshold of the penalty factor is well estimated to guarantee the positive semidefinite property of the global system matrices. With the calculated penalty factor, the maximum time step is analytically determined by approximating spectral radius of the local system matrix. Both the penalty factor bound and the maximal time step are computed element-wise instead of a global system matrix operation, and thus, the proposed method can be efficiently applied into the large-scale meshes with different types of the basis functions and boundary conditions. Numerical examples are presented to demonstrate the validity and good performance of the proposed methods.

In this paper, we incorporate a general impedance transmission boundary condition (ITBC) into the interior penalty discontinuous Galerkin time domain (IPDG) method for the transient analysis of the graphene. In the IPDG method, the graphene is modelled as an infinite thin impedance surface, and its surface conductivity is approximated in terms of complex-conjugate pole–residue pairs by using the vector-fitting technique. The numerical examples are presented to validate and demonstrate the capabilities of the proposed approach.

A succinct explicit local time-stepping (LTS) method for Helmholtz wave equation based discontinue Galerkin time domain method has been developed to analyze 3-D multiscale electromagnetic problems. In the proposed LTS scheme, a simple linear interpolation procedure is implemented to calculate the fields in the subdomain with the larger mesh size at the time steps corresponding to its neighboring subdomains with the smaller mesh size, and thus the proposed method can be easily generalized to the situation of the multiple subdomains with arbitrary time step ratio. With the proposed LTS method, the computational efficiency can be improved for the analysis of the multiscale problems. Several numerical examples including dielectric loaded resonance cavity, microstrip filter, and Vivaldi antenna are given to illustrate good performance of the proposed succinct explicit LTS method.

In this paper, a hybridized discontinuous Galerkin time domain method consisting of interior penalty discontinuous Galerkin (IPDG) time domain based on Helmholtz vector wave equation and discontinuous Galerkin time domain (DGTD) method based on Maxwell's equations has been developed to solve the multiscale problems. The IPDG method solves the vector wave equation for the electric field E and meanwhile the magnetic field H is flexibly solved according to an auxiliary equation. The E and H are simultaneously solved by the DGTD method. With the use of the upwind flux, the IPDG and the DGTD is hybridized. With a local time stepping scheme (LTS) based on a simple interpolation technique, the different time steps restricted by the CFL stability can be used in multiple subdomains with arbitrary mesh size ratio, and thus the computational efficiency can be greatly improved. In order to accelerate the solution of the proposed hybridization method, the graphical processing units (GPU) based on compute unified device architecture (CUDA) are introduced. Some numerical examples are given to show good performance of the proposed hybrid method in the solution of multiscale problems.

This letter extends wave equation-based discontinuous Galerkin time-domain (DGTD-WE) method to analyze the graphene-based devices. The numerical fluxes related to a general impedance transmission boundary condition in the DGTD-WE method have been proposed for the first time to model the graphene sheet as an infinite thin impedance surface. A vector-fitting technique is used to approximate surface conductivity of the graphene in terms of a series of partial fractions. Several graphene-based devices have been given to demonstrate the correctness and effectiveness of the proposed method.

In this paper, a systematic procedure has been developed to analyze electromagnetic interference (EMI) emission of actual domestic induction cookers under normal operation condition. The induction cooker is divided into two subsystems: one is a printed circuit board (PCB) with some discrete components, and the other is induction heating (IH) system consisting of flux concentrators, concentric coils and a vessel made of ferromagnetic material. By using an equivalent impedance of the IH system, two subsystems are separately modeled and analyzed. In the PCB subsystem, parasitic effects of the lumped components are modelled, and a multi‐port network is developed to solve excitations at the IH system and each discrete component. In the IH subsystem, an electromagnetic‐thermal analysis is conducted. Based on the temperature distribution on the vessel, an approximate model of the vessel with the linear material and the piecewise constant temperature is built up. Simulation and measurement results are given to validate the proposed analysis approach.

A new class of tri-band bandpass filter(BPF) is presented, and harmonic passband bandwidth can be independently controlled. In the implementation, three coupling paths are used to control the bandwidth of each passband. The first coupling path is two grounded vias which are utilized to realize coupling between two short-stub loaded resonators. And the first coupling path delivers signals at the first passband. Meanwhile, the second coupling path delivers signals at both the first and second passbands. And the third coupling path only delivers signals at the third passband. Using this method, both the frequency and bandwidth of each passband can be designed and tuned easily. In this filter design, the first harmonic passband can be adjusted separately and is independent of the fundamental passband. Two grounded vias improve flexibility and form a fundamental passband and harmonic passband independently controllable passband filter. For demonstration, a tri-band BPF with three passbands at 1.5 GHz, 2.5 GHz, and 3.5 GHz with insertion losses of 0.34, 0.76 and 1.08 dB is designed, fabricated and measured. So this proposed filter will be attractive in wireless communication systems.