Time-domain Green Function Research Articles

Frequency- and time-domain Green's functions for a phased semi-infinite periodic line array of dipoles

We extend a previous prototype study of Felsen and Capolino (see ibid. vol.48, p.921-931, June 2000) of frequency-domain (FD) and time-domain (TD) Green's functions for an infinite periodic phased line array of dipoles to account for the effects of truncation, as modeled by a semi-infinite array. These canonical problems are to be used eventually for the systematic analysis and synthesis of actual rectangular TD plane phased arrays. In the presentation, we rely on the analytic results and phenomenologies pertaining to the infinite array, which are reviewed. Major emphasis is then placed on the modifications introduced by the truncation. Finite Poisson summation is used to convert the individual dipole radiations into collective truncated wavefields, the FD and TD Floquet waves (FW). In the TD, exact closed-form solutions are obtained, and are examined asymptotically to extract FD and TD periodicity-matched conical truncated FW fields (both propagating and nonpropagating), corresponding tip-diffracted periodicity-matched spherical waves, and uniform transition functions connecting both across the FD and TD-FW truncation boundaries. These new effects can again be incorporated in a FW-modulated geometrical theory of diffraction. A numerical example of radiation from a finite phased TD dipole array with band-limited excitation demonstrates the accuracy and efficiency of the FW-(diffracted field) asymptotic algorithm when compared with an element-by-element summation reference solution.

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

A speedy computation of the time-domain Green's function for microstrip structures is performed. The spatial Green's function in the frequency domain is written as the sum of real- and complex-image terms, which are respectively converted into the time domain analytically and numerically via fast Fourier transforms. The coefficients of the complex-image terms are both space and frequency independent and are computed only once, which results in a speedy algorithm.

An approximate time-domain Green's function for a microstrip structure

In this letter, an approximate time-domain Green's function of a microstrip structure is presented, and is applied to analyze an electrically thin microstrip transmission line. Numerical examples show that the approximate time-domain Green's function is effective. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 25: 423–425, 2000.

Time-domain Green's function for an infinite sequentially excited periodic line array of dipoles

Green's functions based on truncated periodicity play an important role in the efficient analysis of radiation from, or scattering by, phased-array antennas, frequency selective surfaces and related applications. Such Green's functions exploit the equivalence between summation over the contributions from individual elements in an array and their collective treatment via Poisson summation in terms of an infinite series of Floquet waves (FW). While numerous explorations have been carried out in the frequency domain (FD), much less has been done for transient excitation. In order to gain understanding of the FW critical parameters and phenomenologies governing time-domain (TD) periodicity, we consider the simple canonical problem of radiation from an infinite periodic line array of sequentially pulsed axial dipoles. This problem can be solved in closed form and also by a variety of alternative representations, which include inversion from the FD, spectral decomposition into TD plane waves, the complex space-time analytic signal formulation, and the Cagniard-de Hoop method. These alternatives, some of which apply traditionally only for nondispersive TD events, are shown to still work here because of the special character of the FW dispersion. Particular attention is given to evanescent TB-FWs and their transition through cutoff. Asymptotic techniques grant insight into the TD-FW behavior by identifying their instantaneous frequencies, wavenumbers, and other physics-based parameterizations. A basic question concerns the definition of what constitutes a physically "observable" (causal, etc.) TD-FW. The proposed answer is based on consistency among models arrived at by alternative routes.

Waveguide bandpass filter analysis and design using multimode parallel FDTD diakoptics

This paper presents an analysis and design method based on finite-difference time-domain diakoptics. A complex structure is divided into several smaller subsections. The characteristics of the subsections are analyzed entirely in the time domain using mode-type discrete time-domain Green's functions. A multimode parallel algorithm is proposed to connect the subsections. Several filter analysis and design examples are presented. The effectiveness and accuracy of this method is demonstrated by comparison with other computational methods and measurements.

A time-domain prediction method of ship motions

A time-domain analysis is used to predict wave loading and motion responses for a ship traveling at a constant speed in regular oblique waves. Considered as a distribution of normal velocities on the wetted hull surface, the combined diffraction and radiation perturbations caused by the forward moving ship and her motions are determined simultaneously. This way, the ship-hull boundary condition is exactly fulfilled. The 3-D time domain Green's function is used to express the combined diffraction/radiation potential in terms of impulsive and memory potentials. Application of the Bernoulli equation yields the pressure distribution and accordingly, the necessary hydrodynamic forces. The equations of motion of the ship are then developed and solved in the time domain. Forces and motions at forward speed are predicted for a Wigley ship-hull in head waves and for a catamaran-ferry in oblique waves. Comparison is made with published theoretical and experimental results for the Wigley ship-hull, and the agreement is good. For the catamaran, a self-propelled model is built and tested both in a large towing tank and in a seakeeping basin in order to measure the six-degrees-of-freedom forces, moments and motions at forward speed in regular waves of different directions. For the longitudinal motions, the agreement between measurements and predictions is generally good. For the transverse motions, however, acceptable discrepancy exists. The discrepancy is thought to be mainly due to the exclusion from the analysis of the rudder forces and viscous damping. The inclusion of such nonlinear effects in the time domain simulation involves complex analysis and this problem is left to a future research.

Time-domain analysis of TM scattering from conducting cylinders using a hybrid method

In this paper, the finite-element method (FEM) is used to solve open-region problems utilizing the time-domain differential form of Maxwell's equations. The radiation boundary condition for the open-region problem is enforced through the time-domain Green's function as used in integral-equation methods, yet keeping the sparsity of the FEM matrices. In this paper, the proposed method is applied to the time-domain analysis of TM scattering from conducting cylinders. At each time step, the fields inside the discretized domain are calculated using the FEM. The computed induced currents of earlier time steps, together with contributions from the present time step, give the radiation condition at the terminating surface. Numerical results are presented to illustrate the applicability of this technique.

An ordinary differential equation for the Green function of time-domain free-surface hydrodynamics

In this paper a general fourth-order ordinary differential equation is derived for a class of functions including the time-domain Green function of linearized free-surface hydrodynamics and all its spatial derivatives. Among all the applications following from this new result, the acceleration of numerical computations in BEM solutions of time-domain hydrodynamics was the initial motivation of this work. Two new alternative methods for the computation of convolution integrals based on the new ODEs are suggested and illustrated by a numerical example.

Reconstruction of the velocity and density in a stratified acoustic half-space using a short-pulse point source

The reconstruction of the velocity and density in a stratified half-space using the reflection data generated by a short-pulse point source is considered. Transverse spatial Hankel transform is applied to the transient reflected and incident pressures on the surface. The reflection kernel in the Hankel-transformed space is obtained through a deconvolution. The time-domain Green function approach based on the wave splitting is then used to reconstruct the parameters. This time-domain approach to the inverse problem is exact and noniterative. Numerical results for some synthetical examples are presented to illustrate the Hankel transform, deconvolution, and the reconstruction. The finite-difference time-domain method is used to generate the transient reflection data in the physical space in a numerical simulation. The reconstruction using obliquely incident plane waves is also considered in an Appendix.

Gaussian pulse propagation in a linear, lossy chiral medium

Pulse propagation in a linear, lossy chiral medium with single-resonance dispersion is considered. A relevant time-domain Green function is derived, after assuming that the medium is weakly dispersive. As an example, the propagation of Beltrami–Gaussian pulses in the slow-amplitude approximation is analyzed and graphically explained.

Design of reflectionless slabs for obliquely incident transient electromagnetic waves

A method for designing reflectionless plane-stratified conducting and dispersive slabs for obliquely incident transient plane waves is presented. The slabs are temporally dispersive with a spatially varying impedance and conductivity. It is shown that the effects from the variation of the impedance can be matched by the temporal dispersive effects and the conductivity for given incident directions. The problem of finding reflectionless slabs are formulated as an inverse problem for the TE and TM modes where the constitutive relation is to be determined as a function of depth given a reflection kernel that is zero for given incident directions. The inverse problem is solved by a time domain Green functions technique.

An Optimization Approach To the Design of Weakly Reflecting Slabs for Obliquely Incident Transient Electromagnetic Waves

An optimization approach is used in the design of weakly reflecting plane-stratified slabs where transient plane waves impinges obliquely. The slabs are dispersive with a spatially varying impedance and conductivity. In the optimization process, the direct problem is solved iteratively by a time-domain Green functions technique which deals with scattering kernels. Given the prescribed reflection and transmission kernels, an objective functional is minimized for a time larger than one roundtrip and for given incident directions. By introducing dual functions, the exact and explicit expressions for the gradients are derived for the TE and TM modes.

The design, construction and application of a large aperture lens-less line-focus PVDF transducer

A large aperture lens-less line-focus transducer for materials characterization is described. The transducer design is based on a time-domain Green's function formalism, which also yields good theoretical corroboration of the experimental results. The transducer construction is readily achieved by conforming commercial polyvinylidene fluoride (PVDF) film to a cylindrical (convex) surface, followed by casting a tungsten-powder-loaded epoxy resin backing material into an attached housing. This transducer can be used to characterize sample material properties by simultaneously measuring surface wave speeds and bulk wave transit times, from which the thickness and anisotropy may be deduced.

Asymptotic Representation of Sound Pulse Propagation in Shallow Water

The purpose of the present investigation is to propose asymptotic representation for calculating the sound pulse in shallow water, with the sound velocity increasing exponentially from the sea surface to the bottom. We present the time-domain acoustical ray representation, obtained from the convolution of the time-domain Green's function, and the modulated pulse source function for calculation of the waveform at the observation point. Comparison of the ray solution with the reference solution obtained from the mode theory reveals the accuracy and the numerical efficiency of the ray representation. We clarify quantitatively the influences of the bottom losses on the waveform of the sound pulse.

Efficient TLM diakoptics for separable structures

An efficient yet rigorous application of diakoptics to TLM simulation of discontinuities in homogeneously filled waveguides is proposed. The method, based on the expansion of the time-domain Green's function into frequency independent eigenfunctions, leads to a dramatic reduction of the numerical effort when compared to the standard Johns Matrix approach. Numerical results show that this new approach provides wide band absorbing boundaries for waveguide problems where several modes (whether propagating or evanescent) are present. In this way, the computational domain is also reduced to just a small region around the discontinuity, with the absorbing boundaries placed just a few cells away. >

Design of reflectionless media for transient electromagnetic waves

A method for modelling reflectionless conductive dispersive media is presented. The media are either half-spaces or finite dispersive slabs with a spatially varying impedance. The problem of finding reflectionless media for plane waves at normal incidence is formulated as an inverse problem where the constitutive relation is to be determined as a function of depth given a reflection kernel which is zero. The inverse problem is solved by a time-domain Green function technique. It is seen that non-reflecting half-spaces can be constructed in a number of different ways, whereas non-reflecting slabs can only be found if the back-wall is non-conducting.

Closed-form solution for lossy exponential transmission line problem in frequency and time domains

An exact and explicit solution for the reflection and transmission problem of a lossy exponential transmission line of finite length is derived in both the frequency and the time domain via a wave-splitting approach. The problem is formulated first in the frequency domain. Wave-splitting is defined and the solution for internal voltages and currents is derived. Closed-form solutions for the reflection and transmission coefficients are obtained. The explicit solution for a transmission line consisting of several exponential pieces (each with different taper) in series is then easily written down. To obtain the transient response of the lossy exponential line, a time domain Green function approach based on wave-splitting is used. Linear partial differential equations for the Green functions together with the initial and boundary conditions are derived and solved explicitly. The exact and explicit solutions for the transient reflection and transmission up to arbitrary large times are given.

Generalized characteristic method of elastodynamics

A generalized characteristic method to solve two-dimensional time domain elastodynamics problems is developed. The (real) characteristic surfaces in x, y, t-space for the Navier's equations are continued to the complex domain, in which they are called generalized characteristics. The first order ordinary differential equations along the generalized characteristics which are equivalent to the Navier's equations are used to simplify an initial-boundary value problem of elastodynamics to a set of algebraic equations whose unknowns are the first order derivatives of the displacement components. The reflection coefficients of longitudinal and transverse waves, whose fronts can be of arbitrary convex shape, from a traction free boundary are also found to be algebraic expressions. The method makes the inversion of Laplace transform required by Cagniard's technique unnecessary and can be used directly to analyse the head wave and the regions of influence of the reflected waves. Closed form expressions for the time domain Green's function in the whole plane and the solution of Lamb's problem for a buried concentrated force are given as applications of the method. Formulae for the surface displacement take on a simpler form than those reported previously. Finally, some numerical results for the displacement of receivers on and below the surface are given. The displacements of reflected waves approach infinity when they are treated separately but superposing the displacements due to the reflected p- and s-waves shows that the transient Rayleigh pulse is finite.

Efficient 3D-SCN-TLM diakoptics for waveguide components

In this paper, the efficiency of the diakoptic procedure, when applied to three-dimensional waveguide discontinuity problems, is improved by taking advantage of the separability of the time domain Green's function that holds for homogeneous waveguides. The procedure has been applied to the analysis of waveguide discontinuities showing how absorbing boundaries generated with the modal diakoptic procedure provide wide-band matching for the fundamental mode as well as all of the TE and TM modes excited by the discontinuity. In addition, the modal approach leads to the generalized S matrix of a general discontinuity with a single TLM simulation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Transient image theory for 2-D and 3-D conducting wedge problems

In the present paper, two- and three-dimensional transient scattering from a perfectly conducting wedge is studied. The exciting sources analyzed are an infinite impulsive line current parallel to edge of the conductor and an arbitrarily oriented electric dipole. The analysis presented is based on the time-harmonic image solution found for the scattered field. The frequency-domain image current corresponding to the field contribution from the wedge is an exact function expressed in terms of simple trigonometric functions. It is dependent only on the coordinates and the amplitude of the source, but it is independent of the observation point. It is shown that the transient scattering can be interpreted as arising from an image source by generalizing the time domain Green's function to complex source points.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>