Time-domain Volume Integral Equation Research Articles

A Time-Domain Thin Dielectric Sheet (TD-TDS) Integral Equation Method for Scattering Characteristics of Tunable Graphene

A time-domain thin dielectric sheet (TD-TDS) integral equation method is presented to analyze the transient scattering of thin graphene films with the electrostatic bias. In this method, the volume integral of the time-domain volume integral equation is transformed to surface integral to reduce the scale of calculation. In this method, the Rao–Wilson–Glisson basis function and the pulse functions are employed as a spatial basis function while the fourth-order Lagrangian basis functions are employed as temporal basis functions. The main advantages of the TD-TDS method are: 1) this method provides a new way for the simulation of graphene device; 2) only the surfaces of the targets need to be meshed when the targets are modeled as surfaces instead of volumes. As a result, the computational resources and time are greatly reduced; 3) broadband electromagnetic response characteristics can be obtained only after one time computation; and 4) this TD-TDS method is suitable for analyzing the dispersive dielectric material whose permittivity is a Drude model with a time convolution operation. Numerical examples are demonstrated to show the accuracy and efficiency of the TD-TDS method.

A Novel TD-VIE Based on MOT Scheme for Analysis of Dispersive Objects

A novel time-domain volume integral equation (TD-VIE) is proposed to analyze the transient electromagnetic scattering from inhomogeneous dispersive objects. In this TD-VIE method, the higher order Nystrom method is applied in spatial domain. Namely, the curvilinear tetrahedron elements are utilized to discretize dielectric objects and resulting unknowns are volume electric current density. The Lagrange interpolation polynomials are used to represent spatial basis functions. In temporal domain, the marching-on-in-time (MOT) scheme is applied and the shifted Lagrange interpolation functions are used to represent temporal basis functions. Moreover, the point-matching method is applied both in spatial and temporal domain. Compared with the traditional spatial Schaubert–Wilton–Glisson basis based on TD-VIE, this novel TD-VIE method is more efficient. Several numerical examples have demonstrated that the proposed method is accurate, stable, and also more efficient than the traditional TD-VIE.

Numerical Solution of Time-Domain Volume Integral Equations for Transient Electromagnetic Scattering by Dielectric Objects

Electromagnetic (EM) interaction with penetrable objects can be described by volume integral equations (VIEs) in integral equation approach and time-domain VIEs (TDVIEs) are required for formulating transient EM problems with such objects. The TDVIEs are usually solved by combining the method of moments (MoM) with well-designed basis function in space domain and a march-on-in-time (MOT) scheme in time domain. The space-domain MoM requires conforming meshes in geometric discretization and twofold numerical integrations in matrix generation while the MOT in time domain suffers from a late-time instability problem. In this communication, we propose an alternative approach that uses the Nystrom method to discretize the VIEs in space domain while employing the MoM with Laguerre basis and testing functions to discretize the equations in time domain. The proposed approach can simplify the numerical implementation and produce a march-on-in-degree procedure similar to that in frequency-domain approaches. Numerical examples are presented to illustrate the approach and good results have been observed.

Porting an explicit time-domain volume-integral-equation solver on gpus with openacc [open problems in cem

Graphics processing units (GPUs) are gradually becoming mainstream in high-performance computing, as their capabilities for enhancing performance of a large spectrum of scientific applications to many fold when compared to multi-core CPUs have been clearly identified and proven. In this paper, implementation and performance-tuning details for porting an explicit marching-on-in-time (MOT)-based time-domain volume-integral-equation (TDVIE) solver onto GPUs are described in detail. To this end, a high-level approach, utilizing the OpenACC directive-based parallel programming model, is used to minimize two often-faced challenges in GPU programming: developer productivity and code portability. The MOT-TDVIE solver code, originally developed for CPUs, is annotated with compiler directives to port it to GPUs in a fashion similar to how OpenMP targets multi-core CPUs. In contrast to CUDA and OpenCL, where significant modifications to CPU-based codes are required, this high-level approach therefore requires minimal changes to the codes. In this work, we make use of two available OpenACC compilers, CAPS and PGI. Our experience reveals that different annotations of the code are required for each of the compilers, due to different interpretations of the fairly new standard by the compiler developers. Both versions of the OpenACC accelerated code achieved significant performance improvements, with up to 30× speedup against the sequential CPU code using recent hardware technology. Moreover, we demonstrated that the GPU-accelerated fully explicit MOT-TDVIE solver leveraged energy-consumption gains of the order of 3× against its CPU counterpart.

Explicit Solution of the Time Domain Volume Integral Equation Using a Stable Predictor-Corrector Scheme

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposed method is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

A Marching-on-in-Degree Solution of Volume Integral Equations for Transient Electromagnetic Scattering by Bi-Isotropic Objects

A time-domain volume integral equation solved by the marching-on-in-degree scheme is presented for the analysis of transient electromagnetic scattering from three-dimensional inhomogeneous bi-isotropic objects. Based on the volume equivalence principle, the volume-based coupled integral equations for electric and magnetic flux densities are formulated. The transient variations of the electric and magnetic flux densities are expanded in terms of weighted Laguerre polynomials. With the use of the Galerkin spatial and temporal testing procedure, the proposed algorithm overcomes the late-time instability problem that often occurs in the marching-on-in-time approach. Numerical results are presented to illustrate the accuracy and versatility of the proposed algorithm.

Marching‐on‐in‐degree solution of volume integral equations for analysis of transient electromagnetic scattering by inhomogeneous dielectric bodies with conduction loss

AbstractA time‐domain volume integral equation (TDVIE) solved by the marching‐on‐in‐degree (MOD) scheme is presented for the analysis of transient electromagentic scattering from a three‐dimensional inhomogeneous dielectric object of arbitrary shape with conduction loss.The volume of the object is discretized into curvilinear hexahedral elements, and conformal basis functions are utilized to expand the spatial variation of the electric flux density in the TDVIE. The transient variation of the electric flux density is expressed in term of weighted Laguerre polynomials so that the first, second, and third temporal derivatives of the electric flux density can be handled analytically. By applying the Galerkin spatial and temporal testing procedure, the TDVIE is converted into a recursive matrix equation in terms of the orders of the weighted Laguerre polynomials. Because of the elimination of the time variable in the MOD scheme, the proposed algorithm overcomes the late‐time instability problem that often occur in the conventional marching‐in‐on‐time (MOT) approach. Numerical results are presented to illustrate the good performance of the TDVIE algorithm. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1104–1109, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25897

A Time-Domain Volume Integral Equation and Its Marching-On-in-Degree Solution for Analysis of Dispersive Dielectric Objects

A marching-on-in-degree (MOD)-based scheme for analyzing transient electromagnetic scattering from three-dimensional dispersive dielectric objects is proposed. A time-domain volume integral equation (TDVIE) for the electric flux density throughout the object is first formulated and then solved using the MOD scheme. With the use of weighted Laguerre polynomials as entire-domain temporal basis functions, the convolution of the electric flux density and the medium susceptibility and its derivatives can be handled analytically. By employing the Galerkin temporal testing procedure, the time variable is eliminated in the resultant recursive matrix equation so that the proposed algorithm overcomes the late-time instability problem that may occur in the conventional marching-on-in-time (MOT) approach. Some complex dispersive media, such as the Debye, Lorentz, and Drude media, are simulated to illustrate the validity of the TDVIE-MOD algorithm.

Wavelet-based analysis of transient electromagnetic wave propagation in photonic crystals.

Photonic crystals and optical bandgap structures, which facilitate high-precision control of electromagnetic-field propagation, are gaining ever-increasing attention in both scientific and commercial applications. One common photonic device is the distributed Bragg reflector (DBR), which exhibits high reflectivity at certain frequencies. Analysis of the transient interaction of an electromagnetic pulse with such a device can be formulated in terms of the time-domain volume integral equation and, in turn, solved numerically with the method of moments. Owing to the frequency-dependent reflectivity of such devices, the extent of field penetration into deep layers of the device will be different depending on the frequency content of the impinging pulse. We show how this phenomenon can be exploited to reduce the number of basis functions needed for the solution. To this end, we use spatiotemporal wavelet basis functions, which possess the multiresolution property in both spatial and temporal domains. To select the dominant functions in the solution, we use an iterative impedance matrix compression (IMC) procedure, which gradually constructs and solves a compressed version of the matrix equation until the desired degree of accuracy has been achieved. Results show that when the electromagnetic pulse is reflected, the transient IMC omits basis functions defined over the last layers of the DBR, as anticipated.

Time-domain volume integral equation for transient scattering from inhomogeneous objects—2D TE case

This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse electric case. This integral equation is solved by using an MOT scheme. Numerical results obtained using this method agree very well with those obtained using the FDTD method.

A time-domain volume-integral equation approach for analyzing scattering from 2-D nonlinear objects under TM illumination

A new algorithm is presented for analyzing scattering from two-dimensional (2-D) nonlinear penetrable objects that are illuminated by transient transverse magnetic (TM) polarized fields. The proposed scheme solves a time-domain volume-integral inequation (TDVIE) using a marching-on-in-time (MOT) technique. Numerical results obtained using this technique and the finite-difference-time-domain (FDTD) method are in excellent agreement. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 26: 419–423, 2000.