Tomasz P. Stefanski

Accuracy of the Discrete Green's Function Formulation of the FDTD Method

This paper reports an evaluation of the accuracy of the discrete Greens function (DGF) formulation of the finite-difference time-domain (FDTD) method. Recently, the closed-form expression for the DGF and its efficient numerical implementation were presented, which facilitates applications of the DGF in FDTD simulations of radiation and scattering problems. So far, the accuracy of the DGF formulation of the FDTD method has been rather marginally treated in the literature. Moreover, although windowing has been reported as an efficient method of DGF waveform truncation and a remedy for stability issues, the accuracy and usability of this technique have not yet been fully evaluated. In this paper, previously unrevealed accuracy limitations of the DGF formulation of the FDTD method are demonstrated in several numerical tests. Specifically, the truncation errors are compared for the most frequently applied windowing functions, with the best performance shown for the Hanns window.

Implementation of FDTD-Compatible Green’s Function on Heterogeneous CPU-GPU Parallel Processing System

This paper presents an implementation of the FDTD- compatible Greens function on a heterogeneous parallel processing system. The developed implementation simultaneously utilizes computational power of the central processing unit (CPU) and the graphics processing unit (GPU) to the computational tasks best suited for each architecture. Recently, closed-form expression for this discrete Greens function (DGF) was derived, which facilitates its applications in the FDTD simulations of radiation and scattering problems. Unfortunately, implementation of the new DGF formula in software requires a multiple precision arithmetic and may cause long runtimes. Therefore, an acceleration of the DGF computations on a CPU-GPU heterogeneous parallel processing system was developed using the multiple precision arithmetic and the OpenMP and CUDA parallel programming interfaces. The method avoids drawbacks of the CPU- and GPU-only accelerated implementations of the DGF, i.e., long runtime on the CPU and signiflcant overhead of the GPU initialization respectively for long and short length of the DGF waveform. As a result, the sevenfold speedup was obtained relative to the reference DGF implementation on a multicore CPU thus applicability of the DGF in FDTD simulations was signiflcantly improved.

Fast Implementation of FDTD-Compatible Green's Function on Multicore Processor

In this letter, numerically efficient implementation of the finite-difference time domain (FDTD)-compatible Greens function on a multicore processor is presented. Recently, closed-form expression of this discrete Greens function (DGF) was derived, which simplifies its application in the FDTD simulations of radiation and scattering problems. Unfortunately, the new DGF expression involves binomial coefficients, whose computations may cause long runtimes and numerical problems. The proposed fast implementation of the DGF is based on the multiple precision arithmetic and employs a common programming language extended with the OpenMP parallel programming interface. As a result, the speedup factor of three orders of magnitude compared to the previous implementation was obtained, thus applicability of the DGF in FDTD simulations was significantly improved.

Hybrid Technique Combining the FDTD Method and Its Convolution Formulation Based on the Discrete Green's Function

In this letter, a technique combining the finite-difference time-domain (FDTD) method and its formulation based on the discrete Greens function (DGF) is presented. The hybrid method is applicable to inhomogeneous dielectric structures that are mutually coupled with wire antennas. The method employs the surface equivalence theorem in the discrete domain to separate the problem into a dielectric domain simulated using the FDTD method and a wire antenna simulated using the DGF formulation of the FDTD method. Therefore, both methods can be perfectly coupled without introducing any additional errors to the FDTD solution. Applications of the hybrid FDTD method are illustrated by two canonical problems involving half-wavelength dipole antennas and a dielectric object. If the DGF length is equal to the number of iterations in a simulation, the presented hybrid technique returns the same results as the direct FDTD method (assuming infinite numerical precision of computations).

Electromagnetic Problems Requiring High-Precision Computations

An overview of the applications of multiple-precision arithmetic in CEM was presented in this paper for the first time. Although double-precision floating-point arithmetic is sufficient for most scientific computations, there is an expanding body of electromagnetic problems requiring multiple-precision arithmetic. Software libraries facilitating these computations were described, and investigations requiring multiple-precision arithmetic were presented. In particular, numerical-precision issues were demonstrated based on the example of the discrete Greens function. Finally, some open problems in electromagnetics were pointed out for further investigations.

APPLICATIONS OF THE DISCRETE GREEN'S FUNCTION IN THE FINITE-DIFFERENCE TIME-DOMAIN METHOD

In this paper, applications of the discrete Greens function (DGF) in the three-dimensional flnite-difierence time-domain (FDTD) method are presented. The FDTD method on disjoint domains was developed employing DGF to couple the FDTD domains as well as to compute the electromagnetic fleld outside these domains. Hence, source and scatterer are simulated in separate domains and updating of vacuum cells, being of little interest from a user point of view, can be avoided. In the developed method, the fleld radiated by an FDTD domain is computed as a convolution of DGF with equivalent current sources measured over two displaced Huygens surfaces. Therefore, the computed electromagnetic fleld is compatible with the FDTD grid and can be applied as an incident wave in a coupled total- fleld/scattered-fleld domain. In the developed method, the DGF waveforms are truncated using the Hanns window and windowing parameters assuring accuracy of computations are pointed out. The error of the fleld computations varies between i90dB and i40dB depending on the DGF length and excitation waveform. However, if the DGF length is equal to the number of iterations in a simulation, the presented DGF-based techniques return the same results as the direct FDTD method.

A New Expression for the 3-D Dyadic FDTD-Compatible Green’s Function Based on Multidimensional

In this letter, a new analytic expression for the time-domain discrete Greens function (DGF) is derived for the 3-D finite-difference time-domain (FDTD) grid. The derivation employs the multidimensional Z-transform and the impulse response of the discretized scalar wave equation (i.e., scalar DGF). The derived DGF expression involves elementary functions only and requires the implementation of a single function in the multiple-precision arithmetic. For its verification, antennas were simulated in the DGF formulation of the FDTD method with the use of the derived expression demonstrating the correctness of the derivation.

{\cal Z}

An approach for the crosstalk effect description in coupled coplanar waveguides with ideally grounded central strip conductor (C-CPWGS) that, for the first time, takes into account nonideal grounding by means of multimode propagation is presented in this paper. The frequency-domain full-wave computations of modal eigenvectors and propagation delays combined with multiconductor transmission line equations have been employed to obtain near- and far-end crosstalk waveforms. Developed theory has been verified experimentally by comparison with results of the time-domain crosstalk measurement of selected test structures. A very good degree of coherence between numerically computed and experimentally measured data has been achieved

–Transform

In this letter, a new closed-form expression for the time-domain discrete Greens function (DGF) of a plane wave propagating in the 2-D finite-difference time-domain (FDTD) grid is derived. For the sake of its verification, the time-domain implementation of the analytic field propagator (AFP) technique was developed for the plane wave injection in 2-D total-field/scattered-field (TFSF) FDTD simulations. Such an implementation of AFP requires computations of time-domain DGF for the plane wave with the use of multiple-precision arithmetic. Then, excitations at the TFSF interface can be computed as a time-domain convolution of a source function with DGF. The developed time-domain implementation of AFP demonstrates the leakage error across the TFSF interface around the numerical noise level that validates the correctness of the DGF derivation.

Experimental and Numerical Investigation of Crosstalk Effect in Coupled Coplanar Waveguides—Part II: Multimode Coupled Line Representation

Analysis applicable for a class of coplanar transmission lines with a single ground plane has been worked out with use of the spectral domain approach (SDA). Representative results for the single-ground-plane coplanar waveguide are provided. Despite line geometrical simplicity, results of its full-wave analysis have not been presented in literature so far. Comparison with experimental data has yielded good agreement, proving usefulness of the method