Speedy computation of time-domain Green's functionfor microstrip structures

We consider the computation of the harmonic 3D spatial-domain Green's function of the surface of a piezoelectric substrate. Starting from the Green's function expressed in the spectral domain, the singular contributions are isolated and treated separately. It is found that the surface acoustic wave contributions give rise to an anisotropic generalization of the Hankel function H (2) 0 , the spatial Green's function for the scalar two-dimensional wave equation. The asymptotic behavior at infinity and at the origin are also explicitely treated. The remaining non-singular part of the spatial Green's function is obtained numerically by a combination of fast Fourier transform and quadrature. Illustrations are given in the case of a substrate of Y + 128-cut lithium niobate.

The spatial Green's function for the open microstrip structure, especially with a thick substrate, is generally represented in the time-consuming Sommerfield integrals. Through the Sommerfield identity, a closed-form spatial Green's function of a few terms is found from the quasi-dynamic images, the complex images, and the surface waves. With the numerical integration of the Sommerfeld integrals thus avoided, this closed-form Green's function is computationally very efficient. Numerical examples show that the closed-form Green's function gives less than 1% error for all substrates and source-to-field distances. >

A new technique for efficient calculation of spatial Green's function of open-radiating rectangular cavity is presented. The method is based on separability assumption of the original structure and characteristic Green's function method. Using complex image (CI) technique in spectral domain and well-known Weyl's identity, a closed-form relation for spatial Green's function can be derived. To obtain more accurate closed-form Green's function, before applying CI, discrete spectrum contribution part of the derived relation is modified by replacing more accurate reflection coefficients of surface wave modes from walls of the open-radiating cavity. Verification of the derivations of the proposed method is shown for dielectric loaded metallic box which is a separable structure. Method of moment + multilevel fast multipole method solution and also exact numerical integration approach for open-radiating rectangular cavity are considered to search the accuracy as well as speed of the proposed method. It is shown that the main advantage of the proposed method lies in its speed as well as its simple implementation while the accuracy is preserved.

Periodic arrays of radiating or scattering elements play an important role in phased array antennas, frequency selective surfaces and related applications. To gain an understanding of the sparsely explored time domain (TD) behavior of such structures, we have initiated a systematic investigation of relevant canonical TD dipole-excited Green's functions (GF), which so far include those for infinite and truncated line periodic arrays, parameterized in terms of TD-Floquet waves (FW) and truncation-induced TD-FW-modulated tip diffractions. Such waves on semi-infinite and finite square arrays of dipoles have been investigated in the frequency domain, and shown to be useful in practical array applications. This article extends our TD studies to an infinite periodic sequentially pulsed planar array. Like the predecessor GFs, this canonical prototype is simple enough to admit closed form exact solutions, whose interpretation is discussed phenomenologically aided by asymptotic parameterization in terms of instantaneous frequencies. Preliminary numerical results demonstrate the efficiency of the TD-FW algorithms.

A dynamic model of both charge aud current images is constructed to give rise to a frequency-dependent dyadic Green's function in the space domain for rnicrostriplines. While the spatial Green's function is approximate, its image model is very simple, and the propagation constants calculated from it agree well with published results.

A spatial Green's function of multilayer media by complex images, is now very simple in form. The spectral Green's function, from which the spatial function is derived, is still very cumbersome especially for media of many layers. The paper completes the simplification, by rewriting the spectral function in a novel series of wave transmission matrices. This leads to much simplicity in evaluation and to physical insights.

In this work, an FFT-accelerated MOT solver is used to analyze broadband scattering phenomena in a half-space environment. The multilevel space-time FFT scheme accelerates both the matrix-fill and marching times by exploiting the translational invariance of the underlying integral kernel through the use of uniform spatial meshes. All time domain Green's functions are computed by inverse Fourier transforming their frequency domain counterparts, which, in turn, are computed by adaptive evaluation of Sommerfeld integrals. In what follows, the proposed method is applied to the analysis of transient scattering from PEC bodies residing above a dielectric half-space. The method is flexible enough to be used in the analysis of layered media with more complicated Green's functions and can be extended to nonuniformly meshed scatterers using the time domain adaptive integral method.

A new TLM‐based concept analogous to the Green's function approach in classical electromagnetic theory is presented. It employs the procedure known as time domain diakoptics. The response of a TLM mesh to a unit impulse excitation at selected input points is interpreted as a discrete Green's function in the time domain, and the term ‘Johns matrix’ is proposed for this characteristic response. As in classical theory, the response of the mesh to an arbitrary excitation is found by convolving the excitation with its Johns matrix. This concept extends the generalized scattering parameter concept into the time dimension, opens unprecedented possibilities for partioning time domain problems at the field level, and permits large‐scale preprocessing of substructures for computer‐aided design. It also represents and elegant way of modelling broadband absorbing boundary conditions, imperfectly conducting walls and general frequency dispersive boundaries in the time domain.

Time domain responses of porous media have been studied by some authors, but generally the possible descriptions have been given in the frequency domain. The aim of this paper, limited to materials with rigid skeleton considered as equivalent fluids, is to compare the descriptions by Johnson-Allard ($JA$%) as well as by Pride-Lafarge ($PL$) with i) some analytical, approximate formulas, based upon asymptotic high frequency expansion ; ii) the exact formula by Zwikker and Kosten for the case of cylindrical pores. The paper starts with a short summary of the statement of the different general full frequency models ($JA$ and $PL).$ The Green function in the time domain is shown to exhibit interesting properties of materials. In particular the maximum response depends on one dimensionless parameter only, which is denoted $\xi $ and is the ratio of the travelled distance to the product of the \textquotedblleft frozen\textquotedblright\ sound speed and a characteristic viscous relaxation time. The distance $\xi $ is related to a time domain Stokes number. The numerical computation of the Green function is done by FFT, with some precautions, because of the importance of the higher frequencies on the response shape. The $PL$ description is shown to be the best full frequency general model, but some discrepancies with the exact model appear at short times or short distances. When the distance $\xi $ increases from zero, the asymptotic expansion shows that the maximum of the Green function decreases first as $1/\xi ^{2}$, then exponentially.

A novel method for transient analysis of Iossy transmission lines with arbitrary nonlinear terminal networks is presented. The uniqueness of this approach is that we develop time-domain Green's functions for the multiport transmission-line systems by terminating the ports in quasi-matched loads. This ensures Green's functions of a short duration. Hence, the amount of frequency-domain data necessary to obtain time-domain Green's functions is modest. These Green's functions are then convolved with the line port voltages. With this technique one can analyze responses of multiconductor transmission lines with arbitrary nonlinear loads (even with memory) as we have at any instant of time Thevenin's equivalent of the linear portion of the system. An example is presented to illustrate the application of this technique to multiconductor nonlinearly loaded transmission lines.

A robust approach for the derivation of closed-form Green's functions is considered based upon a three level approximation procedure, which can give more accurate evaluation of the spatial Green's functions even without the advance investigation of the spectral functions in comparison with the previous method.

A new calculation of Green's function for Poisson's equation in plane polar coordinates is presented. The method consists in first calculating the solution to the simpler problem, but with the same Green's function, that is obtained with the homogenization of the boundary conditions and then inferring Green's function by comparing this calculated solution with Green's solution formula. Depending on how the solution to the simplified problem is calculated, Green's function may result as an integral or an infinite series, but it is finally presented in a closed form, because it is possible to calculate the integral or the sum of this series.

Understanding the characteristics of underwater sound channels is essential for various remote sensing applications. Typically, the time-domain Green's function or channel impulse response (CIR) is obtained using computationally intensive acoustic propagation models that rely on accurate environmental data, such as sound speed profiles and bathymetry. Ray-based blind deconvolution (RBD) offers a less computationally demanding alternative using plane-wave beamforming to estimate the Green's function. However, the presence of noise can obscure low coherence ray arrivals, making accurate estimation challenging. This paper introduces a method using the waveguide invariant to improve the signal-to-noise ratio (SNR) of broadband Green's functions for a moving source without prior knowledge of range. By utilizing RBD and the frequency shifts from the striation slope, we coherently combine individual Green's functions at adjacent ranges, significantly improving the SNR. In this study, we demonstrated the proposed method via simulation and broadband noise data (200-900 Hz) collected from a moving ship in 100 m deep shallow water.

The fast Hankel transform (FHT) algorithm and complex image method (CIM) are employed to evaluate the spatial-domain Green's function for a multilayered microstrip structure. The results are compared with those obtained by exact numerical integration. It is found that both techniques have high efficiency and the FHT has better accuracy than the CIM.

When a scatterer is located in a diffuse noise field, time domain Green's function between two different receivers can be extracted from cross-correlation of ambient noise which is recorded by the two receivers so that target detection can be implemented. However, the method based on cross-correlation strongly depends on timing synchronization of each receiver, otherwise there will be a time drift in the cross-correlation result, which can bring error in the positioning detection. Besides, two receivers that are far from each other must communicate with each other to implement cross-correlation in real-time data processing, but big data transmission is difficult in the ocean. Compared with cross-correlation, autocorrelation means that each receiver works independently and only the final autocorrelation result is to be transmitted. Actually, the scattered wave of target is always so weak that it is submerged in the autocorrelation result of the ambient noise. In this paper, we propose a method of processing the autocorrelation of the ambient noise. When the averaging noise autocorrelation of all receivers is subtracted from the autocorrelation result of the noise recorded by each receiver, the signalnoise ratio of the scattered wave will be significantly enhanced. With the help of Kirchhoff migration algorithm, detection of a scatterer can be implemented. We have conducted a scatterer passive detection experiment in Shilaoren beach, Qingdao, and accurately detected the position of a polyviny chloride pipe (about 8 m away from the nearest receiver) using only 12 min surf noise data. The experimental result shows that the processing of autocorrelation could replace cross-correlation in passive target detection when the ambient noise is time steady and the statistical characteristics of the background noise at different receivers are the same. Unlike Green's function extracted from cross-correlation of ambient noise, each receiver can work independently without considering the problems of massive data transmission and timing synchronization, which may be suitable for target detection using multi-receivers and mobile platform.