Recursive Gate-Controlled Convolution for Remote Sensing Detection

To improve the computation accuracy of the transient radiation fields in gas insulated substation (GIS), surface-patch model is proposed in this paper, and the method of vector fitting combining with recursive convolution is applied to substitute the method of fast Fourier transform (FFT) in the process of field calculation. The transient radiation fields of an actual 125-kV GIS are calculated to confirm the correctness of the model and the method. It is seemed from the simulation that the method of vector fitting combining with recursive convolution can overcome the conventional problems of FFT and reduces the computer memory and CPU time successfully, and the results from surface-patch model are more accurate than those from thin-line model.

A three-dimensional (3-D) finite difference time domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) is presented for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of coordinate-stretching variables. We extend the recursive convolution (RC) and piecewise linear recursive convolution (PLRC) approaches to arbitrary dispersive media in a more general form. The algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media, i.e., Lorentz medium, unmagnetized plasma, and Debye medium. Excellent agreement between the FDTD results and analytical solutions is obtained for all testing cases with both RC and PLRC approaches. We demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine-like objects, cylinders, and spheres buried in a dispersive half-space and the mapping of a curved interface. Because of their generality, the algorithm and computer program can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media.

The PEEC method and solvers are continuously evolving as more new features are added to the approach. Finite dielectrics were added to solve a new class of multi dielectric problem. Dielectric losses are becoming more important with the recent increase in the frequencies in the problems which need solving. In this work, we provide an approach which is applied to the dielectric model to include losses. Recursive convolution and circuit synthesis techniques are employed to take into account the dispersive behavior of the dielectric. Presently, the algorithm has been applied to materials with a Lorentzian model for the complex permittivity. The accuracy of the proposed approach is demonstrated by an example.

Inaccuracies due to the frequency warping in simulation of electrical systems using combined state–space nodal analysis

The paper is devoted to the problem of mapping algorithms onto regular and synchronous processor arrays. The authors consider problems which are defined by Systems of Affine Recurrence Equations. From such statements, a geometrical coding is proposed to express the data dependencies in terms of two classes of vectors: the generating vectors and the inductive vectors. These vectors are used to implement constraints on the timing or the allocation functions. The authors differentiate two classes of constraints: the causal ones induced by the system of equations and the architecture-related ones. These constraints are taken into account to compile affine timing functions and allocations by projection. The authors illustrate these tools with the examples of the Gaussian elimination and the recursive convolution. >

The Cooray-Rubinstein formula has been widely used for evaluating the horizontal component of the electric field generated by a lightning return stroke over a lossy ground. An accurate and efficient time domain method is presented in this study, by means of piecewise recursive convolution. The recursive convolution is achieved by expressing the kernel function of the ground surface impedance by a piecewise exponential function, in which the integral form of the modified Bessel function of the first kind is evaluated using the trapezoidal numerical integration. Since the time-domain analytical expression of the ground surface impedance kernel function has been adopted, the computational error can be directly controlled within a reasonable tolerance. The validity and efficiency of the proposed method are demonstrated by the extensive comparisons with the method in other literature.

Two general discrete time-domain transient analysis algorithms for the modeling of lossy and dispersive transmission lines are reviewed and compared. The first is based on the generalized method of characteristics through recursive convolution while the second is based on the more recent Pade macromodeling approach using synthesized lumped networks. The different approximations made in these two algorithms are compared and computational evidence is presented to show that these two methods complement rather than compete with each other.

A semiimplicit and frequency-dependent 3-D finite-difference time-domain (FDTD) scheme with relaxed numerical stability was presented for wideband analysis of multilayer printed circuit boards (PCBs) with thin conductive and dielectric layers. This new scheme is formulated by directionally and magnetically introducing the Newmark-beta method into the conventional FDTD explicit scheme based on the recursive convolution (RC) approach for the so-called extended Debye model with an effective dc conductivity. No dependence of mesh step in the normal direction to the PCB layers is included in its stable condition. Interestingly, the presented semiimplicit scheme can be reduced to the RC-based explicit FDTD when the Newmark parameter is chosen as zero. The scheme was carefully verified in applications to rectangular power-bus structures, an irregular power-bus structure with decoupling capacitors and multilayer PCBs with planar electromagnetic bandgap structures. It was demonstrated in these test problems that the calculation time was reduced by a factor of 1/4-1/30 in comparison with the explicit scheme, while maintaining the same level of accuracy.

The computational cost and memory requirements of classical marching‐on‐in‐time (MOT)‐based time‐domain integral‐equation (TDIE) solvers for analyzing scattering of electromagnetic waves from surfaces residing in lossy media scale asO(NN) andO(NNt), respectively; here,NsandNtare the number of spatial and temporal degrees of freedom of the surface currents. The quadratic dependency of these costs uponNsandNtprevents these methods from being applied to the analysis of large‐scale scattering phenomena. Here, an accelerator is proposed to improve the scaling of these TDIE solvers' computational complexity and memory requirements withNt. The accelerator casts temporal tails in convolutions of the lossy medium‐wave‐equation Green's function and TDIE solver temporal‐current basis functions in terms of a Prony series. This representation enables computation of the fields produced by surface currents within an MOT framework via recursive convolution. A technique that allows the reuse of Prony series poles for extended spatial interaction ranges, thereby greatly enhancing the scheme's efficacy, is proffered. The scheme's computational cost and memory requirements scale asO(NNtlogNt) andO(NlogNt), respectively, with fairly small multiplicative factors. Besides being useful in the analysis of scattering from electromagnetically small objects residing in lossy backgrounds, the proposed scheme also constitutes a key building block in the construction of improved lossy‐medium plane‐wave time‐domain algorithms with efficient near‐field evaluation capability. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 223–230, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20595

Novel CDRC-TLM algorithm for the analysis of magnetized plasma

Various kinds of optical near-field apertures have been proposed for higher throughput and smaller spot size. However, few studies have mentioned the readout characteristics of the recorded marks on an optical disk illuminated by a near field optical light. In this paper, we have investigated the scattering light by a two-dimensional recorded mark on a phase change disk with Finite-Difference Time-Domain (FDTD) simulations. Instead of using Recursive Convolution (RC) and Piecewise Linear Recursive Convolution (PLRC) scheme, we integrated the motion equation of free electron into conventional FDTD method to solve the electromagnetic field in the metallic materials. The validity of the proposed method is illustrated by comparing its results with those from the analytic exact solution. We analyzed the distributions of optical near-field around a two-dimensional metallic nano-aperture, and then calculated the far-field scattering pattern from a two-dimensional recorded mark on a phase change disk while it was illuminated by an optical near-field though a nanoaperture. The sum signal by a condenser lens was calculated from far-field pattern, and its relationships with the width of recorded mark and the thickness of each layer in the phase change disk were illustrated. The cross-talk between the recorded marks was also discussed.

Weighted Laguerre finite-difference time-domain (Laguerre-FDTD) method is an efficient and unconditionally stable time-domain numerical method. The complex frequency-shifted perfectly matched layer (CFS-PML) is the main absorbing boundary condition in the Laguerre-FDTD method. The implementations of CFS-PML in the Laguerre-FDTD method, which have been reported, include the use of auxiliary variables and auxiliary differential equations. These implementations make CFS-PML sensitive to its parameters and timescale parameter s of weighted Laguerre polynomials and result in potential instability and poor absorption issues in numerical simulations. In this paper, we proposed an efficient and stable implementation of CFS-PML based on recursive convolution in the Laguerre-FDTD method. The accuracy of the proposed implementation is theoretically validated. Its numerical dispersion is theoretically derived for choosing the key parameters of CFS-PML in the Laguerre-FDTD scheme. The numerical dispersion demonstrates that the timescale factor s needs to match the simulated signal frequency and the CFS-PML parameter $\alpha $ is chosen as $0.5s\varepsilon _{0}$ to obtain the minimum dispersive error. Numerical examples validate the theoretical predictions and verify that the proposed implementation of CFS-PML is robust and retains the advantages of CFS-PML in classical FDTD method, such as effectively absorbing evanescent as well as guided waves. It requires nonsplits of electromagnetic field components, no auxiliary variables, and no modifications when applying it to inhomogeneous, lossy, and dispersive media. The CFS-PML formulas can directly be converted into computer codes of the Laguerre-FDTD method.

A Kretschmann-type surface plasmon resonance waveguide sensor is analyzed using the wide-angle beam- propagation method (BPM) with the complex Pade approximant and the finite-difference time-domain (FDTD) methods based on the recursive convolution (RC) and piecewise linear RC (PLRC) techniques. The wavelength responses of the sensor are calculated, and a detailed comparison of the numerical results is made. The BPM results are validated through a comparison with the FDTD results, in which the PLRC technique is required in terms of accuracy. The waveguide sensor shows a maximum absorption wavelength shift from 0.609 to 0.623 mum, as the refractive index of an analyte is increased from 1.330 to 1.334, which is comparable to the sensitivity of the conventional Kretschmann configuration.

In this paper, a magnetized plasma is analyzed using the finite-difference time-domain (FDTD) method combined with the piecewise linear recursive convolution (PLRC) scheme. Expressions of the electric field update equations are provided in detail. Numerical results show that the PLRC scheme greatly improves accuracy over the original recursive convolution (RC) approach.

We present a 3D FDTD algorithm with the PML absorbing boundary condition for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of the coordinate stretching variables. A single formulation is developed to include recursive convolution and piecewise linear recursive convolution for arbitrary dispersive media. Several applications are demonstrated for subsurface radar detection (GPR-ground penetrating radar) of cylinders and a sphere buried in a dispersive half-space. The algorithm proposed is ideal for parallel computation since the same code is shared by both the interior computational region and the outer matched layers. Because of their generality, the algorithm and computer program developed can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media.