Method Of Moments In Time Domain Research Articles

A Marching-on-in-Time Method of Moments for Transient Modeling of a Vertical Electrode Buried in a Lossy Medium

This article proposes a full-wave time-domain method for analyzing the transient behavior of a grounding electrode buried vertically in a lossy soil. In this method, the electrode is first approximated by a thin wire, and the modified image theory is utilized to account for the soil–air interface. The governing electric field integral equation (EFIE) is then derived with the current distribution along the electrode being the unknown quantities. Finally, the EFIE is solved by the time-domain method of moments based on a marching-on-in-time (MOT) procedure. This is done by expanding the unknown currents in terms of a finite linear combination of products of appropriate spatial and temporal basis functions, and adopting the Galerkin method in space and the point matching method in time. The MOT procedure makes the proposed method more efficient computationally than its rival frequency-domain method of moments (FD-MoM). The efficiency of the proposed method is demonstrated by comparing the lightning ground potential rise of various grounding electrodes with those obtained using the FD-MoM and a commercial numerical code.

A novel space hybrid meshing technique combined with Laguerre polynomial to solve TD-EFIE

In this paper, we have developed a system of Time Domain Electric Field Integral Equation (TD-EFIE) for the resolution of a scattering electromagnetic problem by various shapes illuminated by an incident transient wave. The solvability of the TD-EFIE system is based on the Time Domain Method of Moments (TD-MoM) using Galerkin's method in space and time domains. In time domain, a linear combination of Laguerre functions is used as temporal basis functions. In order to approximate the unknown space variation of the transient current, we develop a novel space hybrid basis functions derived from the Rao-Wilton-Glisson function. The elaborated hybrid mesh technique using hexagonal and triangular mesh is applied for various analyzed structures: regular grid for planar structures and irregular grid for curved structures. The validity, the efficiency and the precision of developed meshing techniques are presented and discussed.

A comparison of three temporal basis functions for the time-domain method of moments (TD-MoM)

Three techniques are applied for the resolution of the time-domain electric field integral equation (TD-EFIE) for a thin wire antenna based on the well-known time-domain method of moments. Three temporal bases are used to approximate the unknown temporal variation. The first is derived from Dirac functions, the second from B-spline functions, and the third from Laguerre functions. Piecewise triangular functions are used for the spatial expansion and testing function for the wire structure using Galerkin’s method. The aim is to compare these three techniques in terms of their formulation, complexity, and accuracy. Numerical results are presented to identify which time technique is best suited to solve such transient electromagnetic problems.

A New Efficient Technique for Transient Scattering of Conducting Cylinders Illuminated by a TM-polarized Plane Wave

In this letter, the transient analysis of infinite conducting cylinders in free space is obtained by solving the time-domain electric field integral equation (TD-EFIE) via a time-domain method of moments (TD-MoM). The PEC cylinders with arbitrary cross section are illuminated by a transverse magnetic (TM)-polarized Gaussian plane wave. The temporal basis function is triangular, and the spatial basis function is rectangular. The two-dimensional Green's function is employed to develop the TD-MoM formulation. Two different approximations are used to calculate the self-coupling terms of the impedance matrix. It is shown that the time convolution integrals and self-terms involved in the formulation can be evaluated analytically to increase the accuracy and the stability of the proposed technique.

Performance improvement of an ESD suppressor by studying its characteristics

The finite-difference time-domain (FDTD) method was used to study the characteristics of an ESD suppressor. The obtained capacitance of the ESD suppressor filled with air was validated by measurement data and another numerical result obtained by time-domain moment method (TDMM). Under the same conditions, no large differences are found among the obtained capacitances for the ESD suppressor filled with air, neon, argon, and helium. But the ESD suppressor filled with air has a much higher trigger and clamping voltages than the ESD suppressor filled with neon, argon, or helium. Capacitance is found to decrease with the increase of the spark gap distance or the operating frequency. But the capacitance increases with increasing relative dielectric constant of the substrate or the overcoat. t is observed that ESD currents with a transient waveform reach a maximum value and decays sharply as the time increases under the condition of the spark gap distance of 5 μm. Outside the spark gap, the maximum electric field is below the breakdown strength, but the magnitude of the electric field radiated from ESD events is still very large when the distance from the ESD suppressor is less than 2 mm.

ATTACHMENT MODES IN THE METHOD OF MOMENTS IN TIME-DOMAIN

E-cient and accurate modeling of electromagnetic structures is valuable in antenna analysis and design, and time domain solutions are at a premium over frequency domain in the case of ultra wide band signals or transients. Among the full wave electromagnetic methods in time domain the method of moments in time domain (MoM-TD) is very interesting. Such a method can be implemented, as for frequency domain, either resorting to a thin wire approximation or to a surface patch model. Depending on the structure to be analyzed one or the other is most convenient. For heterogeneous structures both implementations might be needed, and the problem of the attachment between a perfectly conducting thin wire and a perfectly conducting surface is hence relevant. In this paper, attachment modes are introduced in MoM-TD. The solution is validated on a test case and against another numerical technique.

Time-domain MoM for the analysis of thin-wire structures above half-space media using complex-time Green's functions and band-limited quadratic B-spline temporal basis functions

Abstract The transient response of a thin wire in the presence of a half-space is calculated with a new formulation of the Method of Moments (MoM) in time domain, based on a novel Time-Domain Mixed Potential Integral Equation (TD-MPIE), using complex-time Green's functions. The excitation is a Gaussian voltage source and the solution is obtained by using a Marching-On-in-Time (MOT) procedure. Band-Limited Quadratic B-spline (BL-QB) functions are used as Temporal Basis Functions (TBFs). They are compared with Band-Limited Linear B-spline (BL-LB) interpolation functions. Numerical results show that the solution using BL-QB TBFs is stable and accurate, without late-time instabilities, and efficient in terms of memory usage and computation time.

A STABLE MARCHING-ON-IN-TIME SCHEME FOR WIRE SCATTERERS USING A NEWMARK-BETA FORMULATION

The aim of this work is to increase the instability of the marching-on-in-time (MOT) method that is used in the analysis of wide-band electromagnetic pulse scattering from structures made of thin wires. The stability problem has been identified with the advent of the MOT method in 1991, and although several improvements have been suggested to overcome this difficulty no exact solution has been found [1]. In this thesis two methods (the Newmark-Beta formulation and the analytic integration) to suppress the instabilities of the MOT algorithm for thin wire scatterers have been proposed and their effects on the stability have been inspected. The results are compared with the results obtained with time domain method of moments (MOM) [2] and it is observed that the results are both stable and accurate. It is shown how the stability is changed by a determined β parameter. Also, Newmark-Beta formulation results for selected different types of structures such as dipole antenna illuminated by a Gaussian pulse given in [3], three pole structure given in [4], loop antenna given in [3] has been shown. 338 Bayer and Ergin

A hybrid method combining the Time-Domain Method of Moments, the Time-Domain Uniform Theory of Diffraction and the FDTD

Abstract. In this paper a hybrid method combining the Time-Domain Method of Moments (TD-MoM), the Time-Domain Uniform Theory of Diffraction (TD-UTD) and the Finite-Difference Time-Domain Method (FDTD) is presented. When applying this new hybrid method, thin-wire antennas are modeled with the TD-MoM, inhomogeneous bodies are modelled with the FDTD and large perfectly conducting plates are modelled with the TD-UTD. All inhomogeneous bodies are enclosed in a so-called FDTD-volume and the thin-wire antennas can be embedded into this volume or can lie outside. The latter avoids the simulation of white space between antennas and inhomogeneous bodies. If the antennas are positioned into the FDTD-volume, their discretization does not need to agree with the grid of the FDTD. By using the TD-UTD large perfectly conducting plates can be considered efficiently in the solution-procedure. Thus this hybrid method allows time-domain simulations of problems including very different classes of objects, applying the respective most appropriate numerical techniques to every object.

Hybrid Space-Discretizing Method—Method of Moments for the Analysis of Transient Interference

A new efficient hybrid method combining the transmission-line matrix (TLM) and the time-domain method of moments (MoM) is introduced for the accurate modeling of the transient interference between a perfectly conducting thin surface of arbitrary shape and a complex object exhibiting compound with arbitrary electrical properties separated by large free space. For the modeling of the conducting surface, the time-domain electric-field integral equation is used along with the MoM, which relies on a triangular-patch geometrical model of the exterior surface and operates according to the marching-on-in-time technique. The complex inhomogeneous object is modeled by the TLM scheme. The electromagnetic interaction between the objects is provided by the dyadic free-space Green's function in the time domain. To validate this new approach, we have compared the results with those obtained using the pure TLM method

A Hybrid Method Combining the Multitemporal Resolution Time-Domain Method of Moments With the Time-Domain Geometrical Theory of Diffraction for Thin-Wire Antenna Problems

In this paper, a hybrid method combining a multitemporal resolution (MTR) enhanced time-domain method of moments (TD-MoM) with the TD geometrical theory of diffraction (GTD) is presented, which allows to efficiently calculate the transient fields radiated by antennas in presence of large objects. The MTR scheme tailors the time step size-and thus implicitly the duration of the temporal basis function-on the basis of the distance between source and test element. Additionally, the voltage induced by source elements far away from the test element is interpolated in time. The hybrid method is applied to calculate the radiation properties of thin-wire antennas in presence of perfectly conducting flat scatterers to demonstrate its basic features and advantages

Innovative basis and weight functions for wire junctions in time domain moment method

A wireframe implementation of the method of moments in time domain is presented, with particular attention to wire junctions. Peculiar base and weight functions will be defined at the junctions to implicitly account for current continuity and correctly take into account inter-wire coupling. This will allow implementation of both an explicit and an implicit solution. Results obtained are validated with existing frequency domain solutions.

Currents Induced in a Human Body Standing Inside a Metallic House Near a Large Wire-Array Transmission-Line NEMP Simulator

This paper describes the time-domain moment method (TDMM) and image method that have been developed for calculations of current densities induced in a human body standing inside a metallic rectangular house located near a large wire-array transmission-line nuclear electromagnetic pulse (NEMP) simulator. The TEM-mode transmission line theory and the quasi-static theory are applied in the analysis of electric fields irradiated from the NEMP simulation. The maximum current density induced on the human body with body impedance of 100 MΩ standing inside a perfectly grounded metallic house is found to be 19.7 μA/cm 2 for a distance of 30 m between the metallic house and the NEMP simulator. The value of maximum current density of 19.7 μA/cm 2 is about two times the threshold levels of neuromuscular stimulation under steady-state current flow cases. From study results, it is also found that an average shielding effect of 90% is obtained for the distance between the metallic house and the NEMP simulator when over 30 m. Remarks on health effects based on the calculated data, other scientific sources, and community public health reports are made in the conclusion.

An adaptive time-domain integral equation method for transient analysis of wire scatterer

An adaptive, implicit, multiresolution time-domain (MRTD) algorithm is applied to solve the integro-differential equation arising from the canonical straight thin wire scattering problem. The Haar wavelet system is adopted for the expansion of the induced current along the wire responding to a Gaussian pulsed plane wave electrical field. The results from our marching-on-in-time (MOT) method are compared with those from time-domain moment method where pulse basis functions are utilized. The wavelet system provides an adaptive solution to the transient problem, reducing computational cost, both in time and storage, with a controllable level of accuracy.

Electric Fields Coupling into a Vehicle Placed Inside a Large Wire-Array Transmission-Line NEMP Simulator

The time-domain moment method is used to investigate electric fields coupling into a vehicle placed inside a large wire-array transmission-line Nuclear Electromagnetic Pulse (NEMP) simulator. The Transverse Electromagnetic Mode (TEM-mode) transmission-line theory, image technique, and quasi-static condition are applied in calculations of coupled electric fields in the vehicle. Simulation results show that the best shielding effectiveness occurs with the condition of a perfectly grounded vehicle. It is also found that the coupled electric field inside the vehicle increases as the impedance between the vehicle and the ground plane increases.

A Hybrid Time Domain Method For Field Radiation Through Aperture

This paper presents a new hybrid method for the analysis of the penetration of electromagnetic field inside a metallic enclosure through slots. The model is based on a time domain approach and the solution of the electromagnetic problem is achieved by a hybrid method, characterized by the combination of the Finite Difference in Time Domain (FDTD), and the Method of Moments in Time Domain (MoMTD) that solves a magnetic field integral equation (MFIE); this technique allows to investigate the complex geometry of the problem and to evaluate the strong coupling between the source and the victim structure.

Analysis of electrical fields inside a parallel‐plate NEMP simulator by the time‐domain moment method

In this paper, the time‐domain moment method (TDMM) is used to calculate the transient electric fields and field distributions inside a parallel‐plate NEMP simulator. In the study, the concept of TEM‐mode transmission‐line theory is applied in the analysis of electric field distributions inside the simulator. Results of transient electric fields and field distributions for well matched and mismatched conditions are presented, respectively. It is found that maximum electric fields are homogeneously distributed inside the working volume of the simulator for both well matched and mismatched conditions.

Hybrid MFIE/FDTD method for analysis of metallic enclosures with slots

A method for the analysis of the electromagnetic field inside metallic enclosures with apertures is presented. The model is based on a time domain hybrid approach method, characterised by the combination of the finite difference in time domain (FDTD), and the method of moments in time domain (MoMTD) that solves a magnetic field integral equation (MFIE).

Electric Field Distributions Inside a Large Wire-Array NEMP Simulator by the Time-Domain Moment Method

The time-domain moment method (TDMM) is used to calculate the transient electric fields and field distributions inside a large wire-array NEMP simulator. The TEM-mode transmission-line theory and the quasi-static theory are applied in the analysis of electric field distributions inside the simulator. Results of transient electric fields and field distributions for well-matched and mismatched conditions are presented, respectively. In the study of the quasi-static field, it is found that the electric field in the working volume appears without any distortion. In an analysis of the TEM-mode condition, it is found that the distortion wave form of the electric field is greatly affected by the refection coefficients at both the source side and terminating end. But it is also found that the electric field is almost homogeneously distributed inside the working volume of the simulator for both well-matched and mismatched conditions. Outside the working volume, electric field increases as the field point approaches the rims of the simulator.

Theoretical and experimental characterization of transient electromagnetic fields radiated by electrostatic discharge (ESD) currents

The problem of the evaluation of the electromagnetic (EM) field radiated by an electrostatic discharge (ESD) current is examined, and an efficient numerical code for the evaluation of the radiated field is developed. The considered radiating structures, a monopole and a loop, are analyzed in the time domain using a modified electric field integral equation (EFIE). A modification of the integral equation was introduced in order to take into account the reflection of the incident pulse at the input terminals of the antenna, when fed by a transmission line. The reflected wave is very significant and its evaluation is fundamental for the comparison of theoretical and experimental data. The ESD current flowing along the wire is determined using the method of moments in time domain (MoMTD). From the knowledge of the transient current, the radiated EM field is evaluated by a standard technique. The developed model is the first stage of a project for the characterization of the measurement environment during an ESD test. All numerical results are validated by measurements and good agreement is shown.