Stochastic Galerkin Methods For Transient Maxwell\u27s Equations With Random Geometries

The generalized polynomial chaos expansion was broadly introduced to model systems with uncertain inputs, including random material properties and random computational geometries. This paper focuses solving electromagnetic field when the geometry contains multi-randomness. A linear transformation always maps spatial random variables into grids with fixed length. Hence a great advantage of the method is that the numerical mesh is not changed despite geometrical variations. We applied efficient stochastic Galerkin methods to time-domain Maxwell\u27s equations when thicknesses of two-layer media are uncertain. High-order Runge-Kutta discontinuous Galerkin methods were performed on the resulting system of the expansion coefficients

Discontinuous Galerkin Time-domain Analysis Of Power/ground Plate Pairs With Wave Port Excitation

In this work, a discontinuous Galerkin time-domain method is developed to analyze the power/ground plate pairs taking into account arbitrarily shaped antipads. To implement proper source excitations over the antipads, the magnetic surface current expanded by the electric eigen-modes supported by the corresponding antipad is employed as the excitation. For irregularly shaped antipads, the eigen-modes are obtained by numerical approach. Accordingly, the methodology for the S-parameter extraction is derived based on the orthogonal properties of the different modes. Based on the approach, the transformation between different modes can be readily evaluated

An AWE-Enhanced Wideband Subdomain DG-RTC Algorithm In Solving Electromagnetic Problems

In this research, a Robin transmission condition enriched frequency-domain discontinuous Galerkin (DG-RTC) method is proposed to solve the electromagnetic problems. The proposed DG-RTC method directly discretizes the vector wave equation in each subdomain, and the numerical flux is used for the information communication of solutions between neighbor subdomains. Compared with the traditional Maxwell\u27s equations-based DG (ME-DG) method, the proposed DG-RTC method merely solves the E-field in the whole computational region, while the H-field is only present at the interfaces of adjacent subdomains, which thus significantly reduces the number of unknowns. Moreover, the finalized globally coupled matrix equation is split into a number of small local matrix equations pertinent to each subdomain, a finite-element tearing and interconnecting (FETI)-like procedure is developed. In this way, the direct solver PARDISO can be applied to solve them with trivial cost in a parallel way. In addition, for efficient wideband analysis, the asymptotic waveform evaluation (AWE) is incorporated into the subdomain DG-RTC solver, where merely a few points need to be evaluated in a broadband. Finally, to benchmark the accuracy and efficiency of the proposed algorithm, a microstrip transmission line and a SIW filter are investigated

Numerical Modeling Of PCB Power/ground Plate-pairs By DGTD Method Taking Into Account Decoupling Capacitors

A discontinuous Galerkin time-domain (DGTD) method is proposed in this work to analyze printed circuit board (PCB) power/ground plate-pair having arbitrarily shaped anti-pads. To apply proper excitation source over the irregular anti-pad, the implemented wave port magnetic current excitation is expanded by the electric eigen-modes of the anti-pad that are calculated via either numerical approach or analytical method. Based on the orthogonality of eigen-modes, the temporal mode expansion coefficient for each mode can be conveniently extracted. Besides, considering the presence of decoupling capacitors, the whole physical system can be split into field and circuit subsystems. For the field subsystem, it is governed by the Maxwell\u27s equations, thus it will be solved by DGTD method. For the circuit subsystem, the modified nodal analysis (MNA) is applied. In order to achieve the coupling between the field and circuit subsystems, a lumpled port is defined at the interface between the field and circuit subsystems. To verify the proposed algorithm, several representative examples are benchmarked

Fast Data Pattern Based Electromagnetic Interference Evaluation For IC Packaging

Electromagnetic interference (EMI) is becoming more serious when the data rate of the digital system continues increasing. However, its modeling and analysis are very challenging. In this paper, a novel electromagnetic superposition method is developed to model the IC packaging electromagnetic emission. It employs the equivalence principle to obtain the electromagnetic field response over a broad spectrum. Then it uses the linear property of the passive parasitic system to superpose the contribution of different signals on the packaging. As a result, with certain pre-calculations, it is convenient to compute the electromagnetic emission efficiently from different signals with various data pattern combinations, which benefits identifying worst case scenario. In addition, data reconstruction can be evaluated through the phase shift, which simplifies identifying the EMI of any pulse bit pattern. This work provides a basic modeling framework for comprehensive radiation studies

Electromagnetic Characterization For Graphene By The PEEC Method

The electromagnetic (EM) features of graphene are characterized by the partial element equivalent circuit (PEEC) model for the first time with an impedance boundary condition. By incorporating the impedance boundary condition into the PEEC model, a novel surface conductivity circuit is proposed for graphene. Furthermore, the definition of the absorption cross section (σabs) and the scattering cross section (σsca) are revisited to make them feasible for PEEC analysis. The application of the impedance boundary condition significantly alleviates the memory consumption and the CPU time. To validate the proposed algorithm, numerical examples are presented and compared with existing references

Machine Learning Based Neural Network Solving Methods For The FDTD Method

In this paper, two novel computational processes are proposed to solve Finite-Difference Time-Domain (FDTD) based on machine learning deep neural networks. The field and boundary conditions are employed to establish recurrent neural network FDTD (RNN-FDTD) model and convolution neural network FDTD (CNN-FDTD) model respectively. Numerical examples from scalar wave equations are provided to benchmark the performance of the proposed methods. The results demonstrate that the newly proposed methods could solve FDTD steps with satisfactory accuracy. According to our knowledge, these are unreported new approaches for machine learning based FDTD solving methods

Graphene-Based Terahertz Holographic Conformal Antenna

In this paper, a conformal graphene holographic antenna designed for terahertz (THz) band is proposed. The radiation principle of the proposed pattern reconfigurable antenna is based on the holographic technology. The surface reactance modulation and pattern steering capability can be easily facilitated by a tunable DC-biased graphene patch array. Thanks to the super thin structure and excellent mechanical property of graphene, the proposed THz graphene holographic antenna can be designed conformal to required platforms easily. Besides, the equal size as well as same spacing of graphene patches make it easy to modeling and manufacture. To verify the proposed idea, an antenna conformal to a cylinder is designed and simulated. The results of full wave simulation software HFSS shown that the conformal antenna has great performance

A Fast AWE-Augmented Wideband Discontinuous Galerkin Frequency-Domain Method In Solving Electromagnetic Wave Equations

In this research, a discontinuous Galerkin frequency-domain (DGFD) method is proposed to solve the electromagnetic wave equations. Different to the explicit time-domain analysis, the electric-field and magnetic-field in frequency-domain wave equations are coupled together implicitly, thus the established matrix equation is globally coupled, which is computational expensive if solving it directly. To address this issue, a Block-diagonal preconditioner and a restriction operator are applied to the matrix equation, which splits the global matrix into a number of small local matrix systems pertinent to each subdomain. Then, a direct solver can be employed to solve them with a FETI-like procedure. Besides, to further speed up the wideband analysis, the asymptotic waveform evaluation (AWE) is implemented into the DGFD solver, which only needs to calculate a few frequency points in a broadband. To benchmark the proposed algorithm, a SIW filter is investigated

Using Subdivision Surface Technique To Solve Generalized Debye Sources Based EFIE

In this work, we extend the idea of generalized Debye sources (GDS) method to electric field integral equation (EFIE) and establish a new well-conditioned GDS-EFIE. The principal challenge in implementing this approach arises from the difficulty in developing a robust solver for the surface Laplacian equation. In this paper, we propose using subdivision surfaces that permits such a solution due to the higher order continuous nature of the surface representation. This permits an efficient and effective solution. Thus, GDS-EFIE can be resolved within isogeometric analysis framework as an emerging approach for design-through-analysis. Several numerical results are provided to validate the proposed formulation