Discontinuous Galerkin Time-domain Research Articles

Broadband spectral analysis of chiral nanophotonic structures at circularly polarized incidence using DGTD solver

Abstract A transient circularly polarized excitation and its implementation in a generalized dispersive material (GDM) model based discontinuous Galerkin time-domain (DGTD) solver are proposed for spectral analysis of chiral nanophotonic structures. The expression of a circularly polarized pulse with a certain bandwidth, which is real-valued and enables multi-physics and nonlinearity, is derived comprehensively. Numerical examples for nanophotonic structures, such as reflection of a metal mirror, transmission of an S-shaped dielectric metasurface, and chiroptical response of C4-symmetrically arranged right-handed enantiomers are presented to demonstrate the accuracy and capability of the proposed method.

A hybrid room acoustic modeling approach combining image source, acoustic diffusion equation, and time-domain discontinuous Galerkin methods

In this paper a hybrid model is introduced that constructs a broadband room impulse response using a geometrical (image source method) and a statistical method (acoustic diffusion equation) for the high-frequency range, supported by a wave-based method (time-domain discontinuous Galerkin method) for the low-frequency range. A crucial element concerns the construction of the high-frequency impulse response where a transition from a predominantly specular (image source) to a predominantly diffuse sound-field (diffusion equation) is required. To achieve this transition an analytical envelope is introduced. A key factor is the room-averaged scattering coefficient which accounts for all scattering behavior of the room and determines the speed of transition from a specular to a non-specular sound-field. To evaluate its performance, the model is compared to a broadband wave-based solver for two reference scenarios. The hybrid model shows promising results in terms of reverberation time (T20), center time (Ts) and bass-ratio (BR). Aspects such as the used geometrical complexity, the ‘room-averaged’ scattering coefficients, and other model simplifications and assumptions are discussed.

Electron beams traversing spherical nanoparticles: Analytic and numerical treatment

We present an analytic, Mie theory-based solution for the energy loss and the photon-emission probabilities in the interaction of spherical nanoparticles with electrons passing nearby and through them, in both cathodoluminescence and electron energy-loss spectroscopies. In particular, we focus on the case of penetrating electron trajectories, for which the complete fully electrodynamic and relativistic formalism has not been reported as yet. We exhibit the efficiency of this method in describing collective excitations in matter through calculations for a dispersive and lossy system, namely a sphere described by a Drude permittivity. Subsequently, we use the analytic solution to corroborate the implementation of electron-beam sources in a state-of-the-art numerical method for problems in electrodynamics, the discontinuous Galerkin time-domain (DGTD) method. We show that the two approaches produce spectra in good mutual agreement, and demonstrate the versatility of DGTD via simulations of spherical nanoparticles characterized by surface roughness. The possibility of simultaneously employing both kinds of calculations (analytic and numerical) facilitates a better understanding of the rich optical response of nanophotonic architectures excited by fast electron beams. Published by the American Physical Society 2024

A Novel 3-D DGTD-FDTD Hybrid Method withOne Overlapping Virtual Layer

Compared with the traditional finite difference time-domain (FDTD) method, the discontinuous Galerkin time-domain (DGTD) method may face the issue of intense computation. In this paper, a novel 3-D DGTD-FDTD hybrid method is proposed to dramatically reduce the unknowns of the DGTD method. Instead of the common mass-lumped elements, this virtual layer of the Yee grid is implemented on the intersecting boundary, which simplifies the mesh generation and reduces the number of unknowns. To validate the proposed method, two examples of sphere scattering and horn antenna are considered. The simulation results demonstrate the effectiveness of the proposed method.

Efficient Improved Local Time Stepping with the Leapfrog Scheme for Transient 3-D Electromagnetic Analyses

An alternate boundary local time stepping (ABLTS) method is proposed for the discontinuous Galerkin time domain method for transient electromagnetic simulations to reduce the computation complexity of the local time stepping (LTS) method. The proposed method exhibites lower storage and time complexity than the conventional LF-LTS method . The stability, accuracy, and effectiveness of the ABLTS method are verified by applying it to the simulation of a resonator cavity and multi-layer microstrip antenna. The numerical results revealed that the developed method is effective for the transient electromagnetic simulation of antennas.

A data-driven reduced-order modeling approach for parameterized time-domain Maxwell's equations

<p>This paper proposed a data-driven non-intrusive model order reduction (NIMOR) approach for parameterized time-domain Maxwell's equations. The NIMOR method consisted of fully decoupled offline and online stages. Initially, the high-fidelity (HF) solutions for some training time and parameter sets were obtained by using a discontinuous Galerkin time-domain (DGTD) method. Subsequently, a two-step or nested proper orthogonal decomposition (POD) technique was used to generate the reduced basis (RB) functions and the corresponding projection coefficients within the RB space. The high-order dynamic mode decomposition (HODMD) method leveraged these corresponding coefficients to predict the projection coefficients at all training parameters over a time region beyond the training domain. Instead of direct regression and interpolating new parameters, the predicted projection coefficients were reorganized into a three-dimensional tensor, which was then decomposed into time- and parameter-dependent components through the canonical polyadic decomposition (CPD) method. Gaussian process regression (GPR) was then used to approximate the relationship between the time/parameter values and the above components. Finally, the reduced-order solutions at new time/parameter values were quickly obtained through a linear combination of the POD modes and the approximated projection coefficients. Numerical experiments were presented to evaluate the performance of the method in the case of plane wave scattering.</p>

A Stable Discontinuous Galerkin Time-Domain Method with Implicit-Explicit Time-Marching for Lossy Media

A Stable Discontinuous Galerkin Time-Domain Method with Implicit-Explicit Time-Marching for Lossy Media

Novel Efficient Discontinuous Galerkin Time-Domain Modeling of Dispersive Chiral Metamaterials via Media Homogenization

Novel Efficient Discontinuous Galerkin Time-Domain Modeling of Dispersive Chiral Metamaterials via Media Homogenization

Simulation of Electromagnetic Waves in Magnetized Cold Plasma by a Novel BZT-DGTD Method

This work presents a novel discontinuous Galerkin time domain (DGTD) approach based on second-order bilinear <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> transform (BZT) to analyze the behavior of electromagnetic waves in a magnetized cold plasma. The Maxwell’s equations and current density equation are utilized to formulate the governing mathematical expressions of magnetized plasma, and the BZT approach is employed to construct the time domain iterative formula. The suggested technique outperforms existing methods in terms of stability, performance, and aliasing effect avoidance. The efficacy of the suggested BZT-DGTD approach is investigated by analyzing electromagnetic wave propagation in unmagnetized and magnetized cold plasmas, and a comprehensive comparison is performed with commercial software WCT and COMSOL to validate its practicality. Furthermore, the features of electromagnetic wave propagation in plasma are investigated under numerous circumstances, and these instances are compatible with plasma physics.

A Global-Local Error-Driven -Adaptive Scheme for Discontinuous Galerkin Time-Domain Method With Local Time-Stepping Strategy

In this paper, a highly efficient <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive scheme has been developed for discontinuous Galerkin time domain (DGTD) method with local time stepping (LTS) strategy. In the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive procedure, the dual-fold error driven scheme has been developed. Compared to the global error range corresponding to the preset base order range, the local maximal error in each discretized element is used to determine the allowable local range of the base order. The local error in each element is compared with the local error range to determine which operation, i.e., the base order increasing or decreasing, is implemented. The resulting two error thresholds are insensitive in the dynamic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive procedure. When applying the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive scheme into the LTS method, a simple grouping approach in terms of the time steps related to the base orders has been developed to rapidly perform the marching-on-in time procedure. Several numerical examples including scattering from a missile, radiation of a ridge gap waveguide (RGW) antenna and transmission of a cylindrical cavity filter are given to demonstrate good accuracy and high efficiency of the proposed method.

Novel Discontinuous Galerkin Time-Domain Method for Analyzing Scattering From 3-D Bi-Isotropic Objects

Novel Discontinuous Galerkin Time-Domain Method for Analyzing Scattering From 3-D Bi-Isotropic Objects

The Effect of Nanoparticle Composition on the Surface-Enhanced Raman Scattering Performance of Plasmonic DNA Origami Nanoantennas.

A versatile generation of plasmonic nanoparticle dimers for surface-enhanced Raman scattering (SERS) is presented by combining a DNA origami nanofork and spherical and nonspherical Au or Ag nanoparticles. Combining different nanoparticle species with a DNA origami nanofork to form DNA origami nanoantennas (DONAs), the plasmonic nanoparticle dimers can be optimized for a specific excitation wavelength in SERS. The preparation of such nanoparticle dimers is robust enough to enable the characterization of SERS intensities and SERS enhancement factors of dye-modified DONAs on a single dimer level by measuring in total several thousands of dimers from five different dimer designs, each functionalized with three different Raman reporter molecules and measured at four different excitation wavelengths. Based on these data, SERS enhancement factor (EF) distributions have been determined for each dimer design and excitation wavelengths. The structures and measurement conditions with the highest EFs are suitable for single-molecule SERS (SM-SERS), which is realized by placing single dye molecules into hot spots. We demonstrate that the probability of placing single molecules in a strongly enhancing hot spot for SM-SERS can be increased by using anisotropic nanoparticles with several sharp edges, such as nanoflowers. Combining a Ag nanoparticle with a Au particle in one dimer structure allows for a broadband excitation covering almost the whole visible range. The most versatile plasmonic dimer structure for SERS combines a spherical Ag nanoparticle with a Au nanoflower. Employing the discontinuous Galerkin time domain method, we numerically investigate the bare, symmetric dimers with respect to spectral and near-field properties, showing that, indeed, the nanoflowers induce multiple hot spots located at the edges which surpass the intensity of the spherical dimers, indicating the possibility for SM-SERS. The presented DONA structures and SERS data provide a robust basis for applying such designs as versatile SERS tags and as substrates for SM-SERS measurements.

An Asymmetrical Mixed Higher-Order Discontinuous Galerkin Time Domain Method for Electromagnetic Scattering from the Plasma Sheath around a Hypersonic Vehicle

The plasma sheath during reentry of hypersonic vehicle is an unmagnetized and weakly ionized nonuniform plasma flow, which causes radio frequency blackout and strong plasma attenuation of electromagnetic wave. The physical properties of the nonuniform plasma flow were obtained using computational fluid dynamics software with unstructured grids. In this study, a detailed computational model was reconstructed with the high-order Lagrange grids for the nonuniform plasma flow region and the high-order Serendipity grids for the homogeneous medium region. In order to calculate the numerical flux between the two types of grids in the discontinuous Galerkin time domain (DGTD) algorithm, an asymmetric high-order element is constructed as a transition unit. Finally, the simulation results in the plasma sphere show that the above method improves the computational accuracy and decreases calculation. The amplitude and scattering about electromagnetic wave in nonuniform plasma flow are clarified in detail. It is suggested that the presented method could be an effective tool for investigating interaction between electromagnetic waves and plasma flow.

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.

A body-of-revolution discontinuous Galerkin time domain method based on curved mesh for Maxwell equations

ABSTRACT Numerical simulation of body-of-revolution (BoR) or axisymmetric structures for scattering and radiation problems has a broad spectrum of technology applications in microwave and optical engineering. In this work, we propose a high-order BoR discontinuous Galerkin time-domain method (BoR-DGTD) for solving Maxwell equations in the cylindrical coordinate system. The presented approach is based on or (m is the mode number and φ is the azimuth) expansions for different field components and thus yields a real-valued final system of equations. It saves half of the unknowns as compared to the existing method in which all the field components are assumed to have the same φ variation, i.e. . In contrast to the common practice of deriving variational formulation for the BoR Maxwell equations on two-dimensional grids in the meridian plane, we build it on three-dimensional coaxial toroidal subdomains. As a result, the singularity difficulty induced by the cylindrical coordinates is eliminated naturally. In addition, for BoR with curved material interfaces in the angular cross-section, a solution using curved grids in conjunction with the low-storage weight-adjusted approximation scheme is provided, which significantly enhances the simulation quality. Particularly, to achieve a set of optimized interpolation shape functions for the isoparametric transformation, an essential assistant in calculating the coefficient matrices, a heuristic procedure is developed to properly position the geometric control points on the curved grids. Some numerical experiments are conducted to demonstrate the accuracy and performance of our proposed BoR-DGTD method.

Advanced Numerical Methods for Graphene Simulation with Equivalent Boundary Conditions: A Review

Since the discovery of graphene, due to its excellent optical, thermal, mechanical and electrical properties, it has a broad application prospect in energy, materials, biomedicine, electromagnetism and other fields. A great quantity of researches on the physical mechanism of graphene has been applied to engineering in electromagnetism and optics. To study the properties of graphene, different kinds of numerical methods such as the mixed finite element method (Mixed FEM), the mixed spectral element method (Mixed SEM), Method of Auxiliary Sources (MAS), discontinuous Galerkin time-domain method (DGTD) and interior penalty discontinuous Galerkin time domain (IPDG) have been developed for simulating the electromagnetic field effects of graphene and equivalent boundary conditions such as impedance transmission boundary condition (ITBC), surface current boundary condition (SCBC), impedance matrix boundary condition (IMBC) and surface impedance boundary condition (SIBC) have been employed to replace graphene in the computational domain. In this work, the numerical methods with equivalent boundary conditions are reviewed, and some examples are provided to illustrate their applicability.

Time-Domain Shielding Effectiveness Analysis Based on DGTD Method Accelerated by Local Time-Stepping and Parallel Techniques

The discontinuous Galerkin time-domain (DGTD) method accelerated by local time-stepping (LTS) and parallel techniques is employed to analyze the time-domain shielding effectiveness (TDSE) of metallic enclosures. The detailed formulations and implementation procedures of the DGTD method and LTS and parallel techniques are introduced. Numerical results validate the correctness of the proposed method. Moreover, the influence of various design parameters of the metallic enclosure, including aperture dimensions, wall thickness, spacing of aperture arrays, etc., on the TDSE are analyzed by the proposed method. Some rules are given for the design of the enclosure with rectangular apertures from the perspective of TDSE. The proposed method provides an extremely powerful tool for the evaluation of TDSE.

Multidimensional Generalized Riemann Problem Solver for Maxwell’s Equations

Approximate multidimensional Riemann solvers are essential building blocks in designing globally constraint-preserving finite volume time domain and discontinuous Galerkin time domain schemes for computational electrodynamics (CED). In those schemes, we can achieve high-order temporal accuracy with the help of Runge–Kutta or ADER time-stepping. This paper presents the design of a multidimensional approximate generalized Riemann problem (GRP) solver for the first time. The multidimensional Riemann solver accepts as its inputs the four states surrounding an edge on a structured mesh, and its output consists of a resolved state and its associated fluxes. In contrast, the multidimensional GRP solver accepts as its inputs the four states and their gradients in all directions; its output consists of the resolved state and its corresponding fluxes and the gradients of the resolved state. The gradients can then be used to extend the solution in time. As a result, we achieve second-order temporal accuracy in a single step. In this work, the formulation is optimized for linear hyperbolic systems with stiff, linear source terms because such a formulation will find maximal use in CED. Our formulation produces an overall constraint-preserving time-stepping strategy based on the GRP that is provably L-stable in the presence of stiff source terms. We present several stringent test problems, showing that the multidimensional GRP solver for CED meets its design accuracy and performs stably with optimal time steps. The test problems include cases with high conductivity, showing that the beneficial L-stability is indeed realized in practical applications.

Model order reduction for parameterized electromagnetic problems using matrix decomposition and deep neural networks

A non-intrusive model order reduction (MOR) method for solving parameterized electromagnetic scattering problems is proposed in this paper. A database collecting snapshots of high-fidelity solutions is built by solving the parameterized time-domain Maxwell equations for some values of the material parameters using a fullwave solver based on a high order discontinuous Galerkin time-domain (DGTD) method. To perform a prior dimensionality reduction, a set of reduced basis (RB) functions are extracted from the database via a two-step proper orthogonal decomposition (POD) method. Intrinsic coordinates of the high-fidelity solutions are further compressed through a convolutional autoencoder (CAE) network. Singular value decomposition (SVD) is then used to extract the principal components of the low dimensional coding matrices generated by CAE, and a cubic spline interpolation-based (CSI) approach is employed for approximating the dominating time- and parameter-modes of these matrices. The generation of the reduced basis and the training of the CAE and CSI are accomplished in the offline stage, thus the RB solution for given time/parameter values can be quickly recovered via outputs of the interpolation model and decoder network. In particular, the offline and online stages of the proposed RB method are completely decoupled, which ensures the validity of the method. The performance of the proposed CAE-CSI ROM is illustrated with numerical experiments for scattering of a plane wave by a 2-D dielectric disk and a multi-layer heterogeneous medium.