Mengtao Yuan

A direct discrete complex image method from the closed-form Green's functions in multilayered media

Sommerfeld integration is introduced to calculate the spatial-domain Greens functions (GF) for the method of moments in multilayered media. To avoid time-consuming numerical integration, the discrete complex image method (DCIM) was introduced by approximating the spectral-domain GF by a sum of exponentials. However, traditional DCIM is not accurate in the far- and/or near-field region. Quasi-static and surface-wave terms need to be extracted before the approximation and it is complicated to extract the surface-wave terms. In this paper, some features of the matrix pencil method (MPM) are clarified. A new direct DCIM without any quasi-static and surface-wave extraction is introduced. Instead of avoiding large variations of the spectral kernel, we introduce a novel path to include more variation before we apply the MPM. The spatial-domain GF obtained by the new DCIM is accurate both in the near- and far-field regions. The CPU time used to perform the new DCIM is less than 1 s for computing the fields with a horizontal source-field separation from 1.6/spl times/10/sup -4//spl lambda/ to 16/spl lambda/. The new DCIM can be even accurate up to 160/spl lambda/ provided the variation of the spectral kernel is large enough and we have accounted for a sufficient number of complex images.

A stable solution of time domain electric field Integral equation for thin-wire antennas using the Laguerre polynomials

In this paper, a numerical method to obtain an unconditionally stable solution of the time domain electric field integral equation for arbitrary conducting thin wires is presented. The time-domain electric field integral equation (TD-EFIE) technique has been employed to analyze electromagnetic scattering and radiation problems from thin wire structures. However, the most popular method to solve the TD-EFIE is typically the marching-on in time (MOT) method, which sometimes may suffer from its late-time instability. Instead, we solve the time-domain integral equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically and stable results can be obtained even for late-time. Furthermore, the excitation source in most scattering and radiation analysis of electromagnetic systems is typically done using a Gaussian shaped pulse. In this paper, both a Gaussian pulse and other waveshapes like a rectangular pulse or a ramp like function have been used as excitations for the scattering and radiation of thin-wire antennas with and without junctions. The time-domain results are compared with the inverse discrete Fourier transform (IDFT) of a frequency domain analysis.

Solving time domain electric field Integral equation without the time variable

An improved testing procedure using the marching-on-in-order method to solve the time-domain electric field integral equation (TD-EFIE) for conducting objects using the Laguerre polynomials is presented. Exact temporal testing is performed before the spatial testing, therefore the retarded terms composed of the spatial and the temporal variables can be analytically separated. The uniqueness of this testing procedure is that the time variable can be analytically integrated out and the accuracy can be improved. This paper is then an improvement over the earlier marching-on-in-order method. In addition, this methodology is quite different from the conventional marching-on-in-time algorithm as the present method leads to a set of final equations which need to be numerically solved containing only the spatial variables. Therefore, there is no requirement to have a Courant stability condition in this procedure. How the singular integrals are treated is also discussed. Several examples are simulated both for radiation and scattering problem. The results are compared with the inverse discrete Fourier transform of the frequency domain data and they agree well.

Solving large complex problems using a higher-order basis: parallel in-core and out-of-core integral-equation solvers

The future of computational electromagnetics is changing drastically with the new generation of computer chips, which are multi-cored instead of single-cored. Previously, advancements in chip technology meant an increase in clock speed, which was typically a benefit that computational code users could enjoy. This is no longer the case. In the new roadmaps for chip manufacturers, speed has been sacrificed for improved power consumption, and the direction is multi-core processors. The burden now falls on the software programmer to revamp existing codes and add new functionality to enable computational codes to run efficiently on this new generation of multi-core processors. In this paper, a new roadmap for computational code designers is provided, demonstrating how to navigate along with the chip designers through the multi-core advancements in chip design. A new parallel code, using the method of moments (MoM) and higher-order functions for expansion and testing, and executed on a range of computer platforms, will illustrate this roadmap. The advantage of a higher-order basis over a subdomain basis is a reduction in the number of unknowns. This means that with the same computer resources, a larger problem can be solved using higher-order basis than using a subdomain basis. The matrix filling for MoM with subdomain basis must be programmed with multiple loops over the edges of the patches to account for the interactions. However, higher- order basis functions, such as polynomials, can be calculated more efficiently with fewer integrations, at least for the serial code. In terms of parallel integral-equation solvers, the differences between these categories of basis functions must be understood and accommodated.

Conditions for generation of stable and accurate hybrid TD-FD MoM solutions

Broadband characterization of any electromagnetic (EM) data (e.g., surface currents, radiation pattern, and network parameters) can be carried out using partial information in the time domain (TD) and the frequency domain (FD). In this hybrid TD-FD approach, one generates the early time response using a TD code at a spatial location and uses a FD code to generate the low-frequency response at the same place. Then, the partial complementary information in both the TD and FD is fit by a set of orthogonal functions and its Fourier transform having the same expansion coefficients. Three different types of functions, namely, Hermite, Bessel-Chebyshev, and Laguerre, have been used for extrapolation. Once the expansion coefficients for these functions are known, the response can be extrapolated either for late times or high frequencies using the initial partial information. The objective of this paper is to explore the conditions under which this hybrid approach yields a stable and accurate solution. We investigate bounds for both the number of orthogonal functions needed to carry out the extrapolation and the scale factors needed to accurately fit the data in time and in frequency. Numerical examples have been presented to illustrate the efficacy of these bounds. It is important to point out that, in this hybrid approach of extrapolation, we are not creating new information but processing the available information in an intelligent fashion

Computation of the Sommerfeld Integral tails using the matrix pencil method

The oscillating infinite domain Sommerfeld integrals (SI) are difficult to integrate using a numerical procedure when dealing with structures in a layered media, even though several researchers have attempted to do that. Generally, integration along the real axis is used to compute the SI. However, significant computational effort is required to integrate the oscillating and slowly decaying function along the tail. Extrapolation methods are generally applied to accelerate the rate of convergence of these integrals. However, there are difficulties with the extrapolation methods, such as locations for the breakpoints. In this paper, we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the SI. In this paper, we fit the tail by a sum of finite (usually 10 to 20) complex exponentials using the matrix pencil method (MPM). The integral of the tail of the SI is then simply calculated by summing some complex numbers. No numerical integration is needed in this process, as the integrals can be done analytically. Good accuracy is achieved with a small number of evaluations for the integral kernel (60 points for the MPM as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods) along the tails of the SI. Simulation results show that to obtain the similar accuracy in the evaluation of the SI, the MPM is approximately 10 times faster than the traditional extrapolation methods. Moreover, since the MPM is robust to the effects of noise, this method is more stable, especially for large values of the horizontal distances. The method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the Greens function for a layered media in the spatial domain.

A comparison of performance of three orthogonal polynomials in extraction of wide-band response using early time and low frequency data

The objective of this paper is to generate a wideband and temporal response of three-dimensional composite structures by using a hybrid method that involves generation of early time and low-frequency information. The data in these two separate time and frequency domains are mutually complementary and contain all the necessary information for a sufficient record length. Utilizing a set of orthogonal polynomials, the time domain signal (be it the electric or the magnetic currents or the near/far scattered electromagnetic field) could be expressed in an efficient way as well as the corresponding frequency domain responses. The available data is simultaneously extrapolated in both domains. Computational load for electromagnetic analysis in either domain, time or frequency, can be thus significantly reduced. Three orthogonal polynomial representations including Hermite polynomial, Laguerre function and Bessel function are used in this approach. However, the performance of this new method is sensitive to two important parameters-the scaling factor l/sub 1/ and the expansion order N. It is therefore important to find the optimal parameters to achieve the best performance. A comparison is presented to illustrate that for the classes of problems dealt with, the choice of the Laguerre polynomials has the best performance as illustrated by a typical scattering example from a dielectric hemisphere.

Solution of large complex problems in computational electromagnetics using higher-order basis in MoM with out-of-core solvers

In a recent invited paper in the IEEE Antennas and Propagation Magazine, some of the challenging problems in computational electromagnetics were presented. One of the objectives of this note is to simply point out that challenging to one may be simple to another. This is demonstrated through an example cited in that article. The example chosen is a Vivaldi antenna array. What we discuss here also applies to the other examples presented in that article, but we have chosen the Vivaldi antenna array to help us make our point. It is shown in this short article that a higher-order basis using a surface integral equation a la a PMCHWT (Poggio-Miller-Chu-Harrington-Wu-Tsai) method-of-moments formulation may still be the best weapon that one have in todays arsenal to deal with challenging complex electromagnetic analysis problems. Here, we have used the commercially available code WIPL-D to carry out all the computations using laptop/desktop systems. The second objective of this paper is to present an out-of-core solver. The goal is to demonstrate that an out-of-core 32-bit-system-based solver can be as efficient as a 64-bit in-core solver. This is quite contrary to the popular belief that an out-of-core solver is generally much slower than an in-core solver. This can be significant, as the difference in the cost of a 32-bit system can be 1/30 of a 64-bit system of similar capabilities using current computer architectures. For the 32-bit system, we consider a Pentium 4 system, whereas for the 64-bit system, we consider an Itanium 2 system for comparison. The out-of-core solver can go beyond the 2 GB limitation for a 32-bit system and can be run on ordinary laptop/desktop; hence, we can simultaneously have a much lower hardware investment while better performance for a sophisticated and powerful electromagnetic solver. The system resources and the CPU times are also outlined.

Time and Frequency Domain Solutions of EM Problems: Using Integral Equations and a Hybrid Methodology

Preface. Acknowledgments. List of Symbols. Acronyms. Chapter 1 Mathametical Basis of a Numerical Method. Chapter 2 Analysis of Conducting Structures in the Frequency Domain. Chapter 3 Analysis of Dielectric Objects in the Frequency Domain. Chapter 4 Analysis of Composite Structures in the Frequency Domain. Chapter 5 Analysis of Conducting Wires in the Time Domain. Chapter 6 Analysis of Conducting Structures in the Time Domain. Chapter 7 Analysis of Dielectric Structures in the Time Domain. Chapter 8 An Improved Marching-on-in-Degree (MOD) Methodology. Chapter 9 Numerical Examples for the New and Improved Marching-on-in-Degree (MOD) Method. Chapter 10 A Hybrid Method Using Early-Time and Low-Frequency Information to Generate a Wideband Response. Appendix User Guide for the Time and Frequency Domain EM Solver Using Integral Equations (TFDSIE). Index. About the Authors.

A comparison of marching-on in time method with marching-on in degree method for the TDIE solver

One of the most popular methods to solve a time domain electric field integral equation (TD-EFIE) is the marching-on-in-time(MOT) method. Recently, a new method called marching-on-in- degree(MOD) that uses Laguerre polynomials as temporal basis functions has been developed to eliminate the late time instability of the MOT method. A comparison is presented between these two methods from the standpoint of formulation, stability, cost and accuracy. Numerical results are presented to illustrate these features in the comparison.