Spectral-element Time-domain Method Research Articles

Transient simulation of dielectric breakdown during high-power microwave propagation based on the SETD method

This article is mainly devoted to the research of dielectric breakdown phenomenon during high power microwave propagation. Under the force of the high-intensity fields, bound charges break free and a part of an insulator becomes electrically conductive, which may lead to electrical breakdown and thermal breakdown in high power microwave (HPM) devices or on the output window. A three-dimensional (3D) multi-physics electromagnetic-thermal model is developed and solved by spectral-element time-domain (SETD) method. The nonlinear conductivity caused by HPM is introduced into Maxwell's equations, which makes its nonlinear. The heat flux from transient power loss is utilized to construct the heat source for solving the thermal conduction equation. In the SETD process, the Galerkin's method and central difference scheme are employed for the space discretization and temporal discretization, respectively. The numerical results show that physical mechanism of electrical breakdown, thermal effect and nonlinear effect can be captured accurately during high power microwave propagation. Once the strength of the electric field exceeds the critical value experienced by the dielectric, the current increases rapidly, along with the temperature change is very severe. The validity and accuracy of the proposed method are demonstrated, and our research is beneficial for the HPM devices protection.

An efficient thin layer equivalent technique of SETD method for thermo-mechanical multi-physics analysis of electronic devices

A coupled thermo-mechanical simulation technique is proposed for reliability analyses of electronic devices based on the spectral element time domain (SETD) method. The transient spatial distribution of temperature, deformation and stress in electronic devices with different spatial scales can be obtained by using the implicit time integration method in the proposed technique. Through the thermo-mechanical equations, thin layers of electronic devices in the coupled fields can be made equivalent to surface boundaries to avoid volumetric meshing, thus reducing the number of degrees of freedom in computation and greatly improving the numerical efficiency of reliability analyses. Finally, through the thermo-mechanical analyses of different electronic devices such as a coaxial through-silicon via (TSV), and an integrated circuit (IC) package, various stress mechanisms related to the failure of electronic devices are successfully predicted to further demonstrate the capabilities of the technique to analyze the reliability of large-scale electronic devices.

Numerical Simulation of Streamer Discharge Modeled by Drift-Diffusion Equations Based on SETD Method

Dynamic characteristics of streamer discharge in a parallel-plane electrode system are described within the framework of a drift-diffusion model coupled with Poisson’s equation at atmospheric pressure. The spectral-element time-domain (SETD) method is applied to the solution of streamer discharge problems, and the flux-corrected-transport (FCT) algorithm is also applied to suppress possible numerical divergence or numerical oscillation. The performance of the proposed method is examined in a number of numerical tests. Then the tempo-spatial evolutions of the streamer are obtained in detail under the different situations. Numerical results show that after the initial stage of adjustment, the streamers propagate in a steady-state mode, where the characteristics of the steady state are decided by background ionization frequency which is determined by pressure and background electric field together. And space charge effect is a dominant factor for the distortion of spatial electric field, making the discharge channel expand toward both electrodes faster. These works presented here are instructive for high-voltage insulating device protection and plasma application.

Numerical simulation of multi-carrier microwave breakdown in air-SF6 mixtures

In this paper, the multi-carrier microwave breakdown in air-SF6 mixtures is analyzed with the spectral-element time-domain method. In this process, a three-dimensional multi-physics model coupling Maxwell's equations with electron fluid equations is established. The tail-erosion and frequency shift phenomenon caused by multi-carrier microwave breakdown in different proportions of air-SF6 mixtures can be observed. Numerical results demonstrate that multi-carriers will make the wireless communication system sensitive to microwave breakdown. On the other hand, the different proportions of air-SF6 mixtures can obviously improve the breakdown threshold to inhibit the multi-carrier microwave breakdown, which is favorable to the propagation of multi-carrier microwaves in air. Meanwhile, increasing the pressure can suppress the frequency shift phenomenon, and the proportion of different SF6 in the mixed gas has little effect on the frequency shift of the transmitted wave. Our research provides theoretical guidance for comprehensively exploring the characteristics and physical mechanism of multi-carrier microwave breakdown in air-SF6 mixtures and is helpful for protection of microwave devices and plasma application.

Simulation of high-power microwaves gas breakdown with a modified multi-physical model

In this paper, a modified multi-physics method for transient analysis of high-power microwaves (HPM) gas breakdown is proposed. Distinguished from previous works, the proposed method couples the plasma fluid equations with Maxwell's equations to fully consider the interaction between plasma and electromagnetic waves. To perform the numerical simulation, the spectral-element time-domain method is employed, which has the advantages of spectral accuracy and block diagonal mass matrix. Numerical simulations are conducted to demonstrate the accuracy of the proposed method. Moreover, with an external DC magnetic field, HPM breakdown can be effectively delayed by increasing its breakdown threshold. Simultaneously, the phase shift of electromagnetic waves during the HPM breakdown can also be controlled by the external DC magnetic field, which can improve the quality of the phase-modulated signal in HPM illumination. This proposed framework is expected to provide an effective numerical tool for analyzing the microwave propagation characteristics and suppressing the HPM breakdown in gas-filled microwave devices.

Transient analysis of light brightness emitted from high power microwave nitrogen breakdown under external dc magnetic field

A three-dimensional (3D) multi-physics model is developed to describe the characteristics of light emitted from high power microwave nitrogen breakdown. This model consists of electromagnetic (EM) fields and plasma physics in which plasma physics and EM fields are controlled by plasma fluid equations and Maxwell's equations. A continuity equation of excited molecule (ion) is introduced into the fluid model to describe the light brightness produced in the breakdown system. The resulting multi-physics system is analyzed and described with the spectral-element time-domain method. The external dc magnetic field applied in breakdown volume is used to prolong the breakdown time. The light brightness is weakened by the dc magnetic field before the occurrence of breakdown, and the variation in light brightness with different wavelengths produced by breakdown is discussed. The position of the maximum light brightness spot can be changed by the influence of the dc magnetic field on the electron concentration. Our research provides theoretical guidance for further understanding the physical process and physical phenomena in microwave nitrogen breakdown.

Efficient transient thermal analysis based on spectral element time domain method with curvilinear hexahedrons

AbstractIn this paper, a three‐dimensional transient thermal simulation algorithm based on spectral element method is proposed. This algorithm uses distorted hexahedron for mesh generation, which not only keeps the high efficiency of hexahedron element calculation, but also improves the flexibility of mesh generation. It supports efficient forward difference and unconditionally stable backward difference in time step. Through practical examples and comparison with commercial software, the reliability and stability of the algorithm are verified, and it has obvious advantages in memory consumption and computing efficiency.

Transient Analysis for Electrothermal Properties in Nanoscale Transistors

Due to the significance of electron and heat transfer in designing the nanoscale semiconductor devices, the transient analysis of electrothermal properties has attracted extensive attention. In this paper, the density-gradient and dual-phase-lag (DPL) equations are first combined to predict the electron and heat transport in nanoscale transistors. The DPL equation is solved with the consideration of the temperature jump boundary condition that dealing with phonon–wall collisions. We have shown that the temporal and spatial distributions of related physical variables can be obtained by self-consistently solving these equations. Furthermore, the spectral element time-domain method is used to discretize these equations. Numerical results of electrothermal properties for both 2-D and 3-D field-effect transistors have been demonstrated to show the robustness and universality of the proposed model. Therefore, the model we proposed can be used with the temporal and spatial distributions, which could be helpful for evaluating the electrothermal performance and computational designing of nanoscale transistors.

Efficient Analysis of Ferrite RF Devices by Explicit Time-Domain Method in Unstructured Meshes

The spectral-element time-domain (SETD) method, which has an explicit solution scheme, is proposed to analyze ferrite RF devices. First, the time-domain expression of the ferrite tensor permeability is derived. Then, the Helmholtz equation is expressed as time-domain convolution form. For the SETD method, high-order orthogonal Lagrange interpolation polynomial is used as a basis function and curved hexahedrons are used to mesh the computational space. The general electric field iterative formula is derived according to the SETD method. In the formula, the explicit solution scheme is preserved and the CPU time can be saved spontaneously. Two classical numerical results demonstrate the ability and accuracy of this method.

Efficient Wideband Numerical Simulations for Nanostructures Employing a Drude-Critical Points (DCP) Dispersive Model

A highly efficient numerical approach for simulating the wideband optical response of nano-architectures comprised of Drude-Critical Points (DCP) media (e.g., gold and silver) is proposed and validated through comparing with commercial computational software. The kernel of this algorithm is the subdomain level discontinuous Galerkin time domain (DGTD) method, which can be viewed as a hybrid of the spectral-element time-domain method (SETD) and the finite-element time-domain (FETD) method. An hp-refinement technique is applied to decrease the Degrees-of-Freedom (DoFs) and computational requirements. The collocated E-J scheme facilitates solving the auxiliary equations by converting the inversions of matrices to simpler vector manipulations. A new hybrid time stepping approach, which couples the Runge-Kutta and Newmark methods, is proposed to solve the temporal auxiliary differential equations (ADEs) with a high degree of efficiency. The advantages of this new approach, in terms of computational resource overhead and accuracy, are validated through comparison with well-known commercial software for three diverse cases, which cover both near-field and far-field properties with plane wave and lumped port sources. The presented work provides the missing link between DCP dispersive models and FETD and/or SETD based algorithms. It is a competitive candidate for numerically studying the wideband plasmonic properties of DCP media.

A Hybrid Volume–Surface Integral Spectral-Element Time-Domain Method for Nonlinear Analysis of Microwave Circuit

This letter presents a field–circuit coupling method for analysis of microwave circuit included with nonlinear physical-model-based semiconductor devices. The electromagnetic field is analyzed by the time-domain volume–surface integral equation (TD-VSIE) and the physical-model-based semiconductor is solved by spectral-element time-domain method. The discrete Newton–Raphson method is employed to solve the proposed field–circuit coupling equations. Compared to the traditional field–circuit coupling method in TD-VSIE, the proposed method can analyze not only the equivalent-model-based semiconductor circuit, but also the physical-model-based one. Finally, numerical results are given to demonstrate the accuracy and efficiency of the proposed method.

A Hybrid Spectral-Element Finite-Difference Time-Domain Method for Electromagnetic Simulation

A hybrid spectral-element finite-difference time-domain (FDTD) method is proposed for electromagnetic simulation in this letter. This proposed hybrid method takes full advantage of the efficiency of FDTD method with the traditional Yee's grid and the flexibility of spectral-element time-domain method in modeling complex geometry, and it inherits the powerful ability in parallelism. Furthermore, the discontinuous Galerkin method is employed to improve the efficiency in dealing with nonconforming meshes. Numerical results demonstrate the accuracy and robustness of the proposed method.

EB Scheme-Based Hybrid SE-FE DGTD Method for Multiscale EM Simulations

This communication presents an EB scheme subdomainlevel discontinuous Galerkin time domain (DGTD) method for multiscale simulations. It is an extension of the previous subdomain-level DGTD research by combining the degree of freedom efficiency of spectral element time domain method and the mesh flexibility of the finite element time domain method. Thus, the multiscale problems can be solved efficiently by separating the geometrically fine and coarse parts and meshing them with hexahedrons and tetrahedrons, respectively, via a nonconformal mesh. The implicit–explicit Runge-Kutta method is applied to the EB scheme DGTD method to obtain an efficient time integration approach.

Multiphysics Coupling of Dynamic Fluid Flow and Electromagnetic Fields for Subsurface Sensing

Nanoparticles designed with high electric conductivity and magnetic permeability are injected into oil reservoirs to enhance fluid flow monitoring. The movement of nanoparticles with the flow in a porous medium can be modeled by solving the flow transport equation. In this research, the three-dimensional spectral-element time-domain method based on Gauss-Lobatto-Legendre polynomials is employed to solve the fluid flow equation to obtain the nanoparticle (NP) concentration distribution in reservoirs. This method shows spectral accuracy, as the error decreases exponentially with the order of basis functions. The injected fluid with high contrast NPs increases the electric conductivity and magnetic permeability in the flooded zone, thus enhancing the electromagnetic (EM) signals in the receivers. Based on the coupling of the dynamic fluid flow and crosswell EM measurement, we are able to analyze the detection range of EM sensing with the high contrast NPs injection. The EM responses with different types of NPs injection are investigated under both an electric dipole and a magnetic dipole. The magnetic contrast NPs excited by a magnetic dipole source can generate a detectable signal while the electric contrast NPs can generate a detectable signal when excited by an electric dipole. The EM response of an inhomogeneous formation with a low permeable region shows that the signal at the producer near the barrier is lower than the other producers. The proposed multiphysics coupling technique of fluid flow and EM measurements can provide guidance for NPs field application and help monitor the flow movement in reservoirs.

A fluid model simulation of a simplified plasma limiter based on spectral-element time-domain method

A simplified plasma limiter prototype is proposed and the fluid model coupled with Maxwell's equations is established to describe the operating mechanism of plasma limiter. A three-dimensional (3-D) simplified sandwich structure plasma limiter model is analyzed with the spectral-element time-domain (SETD) method. The field breakdown threshold of air and argon at different frequency is predicted and compared with the experimental data and there is a good agreement between them for gas microwave breakdown discharge problems. Numerical results demonstrate that the two-layer plasma limiter (plasma-slab-plasma) has better protective characteristics than a one-layer plasma limiter (slab-plasma-slab) with the same length of gas chamber.

An Efficient 3-D Time-Domain Method for High Power Microwave Propagation Problems

In this paper, the spectral-element time-domain (SETD) method based on Gauss-Lobatto-Legendre (GLL) polynomials is applied to the solution of Maxwell’s Equations coupled to fluid model in 3-D microwave gas breakdown simulation of high-power microwave (HPM) propagation problems. The Galekin’s method is employed for the space discretization and the central difference scheme is used for time stepping. Numerical examples, compared with reported results demonstrate the ability and effectiveness of the SETD method for the analysis of microwave gas breakdown phenomena.

Performance analysis of FET microwave devices by use of extended spectral-element time-domain method

The extended spectral-element time-domain (SETD) method is employed to analyse field effect transistor (FET) microwave devices. In order to impose the contribution of the FET microwave devices into the electromagnetic simulation, the SETD method is extended by introducing a lumped current term into the vector Helmholtz equation. The change of currents on each lumped component can be expressed by the change of voltage via corresponding models of equivalent circuit. The electric fields around the lumped component must be influenced by the change of voltage on each lumped component, and vice versa. So a global coupling about the EM–circuit can be built directly. The fully explicit solving scheme is maintained in this extended SETD method and the CPU time can be saved spontaneously. Three practical FET microwave devices are analysed in this article. The numerical results demonstrate the ability and accuracy of this method.

Transient analysis of microwave Gunn oscillator using extended spectral element time domain method

In this study, the microwave Gunn oscillator is analyzed by a hybrid electromagnetic circuit simulator, which is based on the spectral element time domain (SETD) method. The Gunn diode within the oscillator is treated as a lumped element, while the passive distributed part of the oscillator is modeled using the SETD method. In order to incorporate the contribution of the Gunn diode into the SETD context, the SETD method is extended by introducing a lumped current term into the second‐order vector wave equation. When Galerkin's method is used for the space discretization and the central difference scheme is used for time stepping, a global SETD system involving the Gunn diode is assembled. Furthermore, the global system matrix is block‐diagonal and the inversion of this matrix can be easily implemented, and thus the extended SETD method is a fully explicit solver and CPU time can be significantly reduced. By virtue of this method, the strong nonlinear feature of the Gunn oscillator is well characterized in the time domain, such as the phenomenon of injection locking. Numerical results demonstrate the ability and effectiveness of the extended SETD method for the fast analysis of microwave Gunn oscillator.

A 3-D Discontinuous Spectral Element Time-Domain Method for Maxwell's Equations

A discontinuous spectral element time-domain method is proposed to analyze transient electromagnetic properties of general 3-D structures. This method is advantageous in that its mass matrices are block-diagonal due to the Gauss-Lobatto-Legendre polynomials, and it allows different orders of basis functions for each subdomain. The Riemann solver is employed in the boundary integral terms to communicate fields between adjacent subdomains. Perfectly matched layers are utilized to truncate the computational domain. Galerkin method is used for spatial discretization, and a fourth-order Runge-Kutta scheme is employed for the time integration. The validity of the proposed approach is demonstrated through several numerical examples of initial value problems and scattering problems.

A 3-D Spectral-Element Time-Domain Method for Electromagnetic Simulation

A spectral-element time-domain (SETD) method is proposed to solve 3-D transient electromagnetic problems based on Gauss-Lobatto-Legendre polynomials. It has the advantages of spectral accuracy and block-diagonal mass matrix. With the inexpensive inversion of the block-diagonal mass matrix, the proposed method requires only a trivial sparse matrix-vector product at each time step, thus significantly reducing CPU time and memory requirement. Galerkin's method is used for spatial discretization, and a fourth-order Runge-Kutta scheme is employed for the time integration. The perfectly matched layer (PML) is employed to truncate the boundary in unbounded problems. The pseudospectral time-domain method is used to simplify the treatment of the PML inside the proposed SETD method. Numerical examples are shown to verify the efficiency and the spectral accuracy with the order of basis functions