Efficient Evaluation of Green's Functions for Lossy Half-Space Problems (original) (raw)

On the evaluation of time-domain Green function

Ocean Engineering, 2007

An analytical method has been developed to evaluate the wave part of the time-domain Green function and its derivatives. Based on Taylor series expansion, the Green function is obtained by solving a fourth-order ordinary differential equation. The method accelerates the convergence of the summation of an infinite series in the numerical computation. The accuracy of this method was demonstrated by its comparison with other method and its application to solve the radiation problem of a floating hemisphere using a panel-free method. The computed hydrodynamic coefficients agree well with the analytical solutions.

Modeling of Environmental Effects by Numerical Green's Function in Electromagnetic Applications

IEEE Transactions on Magnetics, 2008

The finite-element boundary element method has been successfully used to provide proper truncation for numerical computation in an unbounded region. The information of the exterior environment can be incorporated whenever the corresponding Green's function is available. In this paper, we extend the method by computing Green's functions numerically so that general exterior environments can also be incorporated into the boundary element computation. Once the numerical Green's function is computed for a given environmental configuration, it can be reused for other instances of electromagnetic devices. This method is especially beneficial if a small portion of geometry needs to be repeatedly changed.

The Evaluation of an Asymptotic Solution to the Sommerfeld Radiation Problem Using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

Electronics

A recently developed high-frequency asymptotic solution for the famous “Sommerfeld radiation problem” is revisited. The solution is based on an analysis performed in the spectral domain, through which a compact asymptotic formula describes the behavior of the EM field, which emanates from a vertical Hertzian radiating dipole, located above flat, lossy ground. The paper is divided into two parts. We first demonstrate an efficient technique for the accurate numerical calculation of the well-known Sommerfeld integrals. The results are compared against alternative calculation approaches and validated with the corresponding Norton figures for the surface wave. In the second part, we introduce the asymptotic solution and investigate its performance; we compare the solution with the accurate numerical evaluation for the received EM field and with a more basic asymptotic solution to the given problem, obtained via the application of the Stationary Phase Method. Simulations for various frequ...

Analysis of Lightning-Radiated Electromagnetic Fields in the Vicinity of Lossy Ground

IEEE Transactions on Electromagnetic Compatibility, 2005

An antenna theory (AT) approach in the frequency domain is presented to compute electromagnetic fields radiated by a lightning return stroke. The lightning channel is modeled as a lossy-wire monopole antenna (a wire antenna with distributed resistance) energized by a current source at its base, and the ground is modeled as a lossy half-space. The method of moments is used for solving the governing electric field integral equation (EFIE) in the frequency domain. The resultant current distribution along the channel is used to calculate electromagnetic fields at different distances from the channel. All field components are evaluated using a rapid but accurate procedure based on a new approximation of Sommerfeld integrals. In contrast with the previous models, the approach proposed here is characterized by a self-consistent treatment of different field components in air or on the surface of a lossy half-space. It is shown that the omission of surface wave terms in the general field equations, as done in the perfect-ground approximation, can strongly affect model-predicted field components.

Lightning electromagnetic field calculations in the presence of a conducting ground: the numerical treatment of Sommerfeld's integrals

Institution of Engineering and Technology eBooks, 2022

The constrained interpolation profile (CIP) method has been recently applied to analyzing lightning electromagnetic fields. This method has an advantage that it is capable of computing electromagnetic fields reasonably accurately even when a relatively coarse grid is used. However, in analyzing small structures (in comparison with grid size) in the field point, this advantage of the CIP method is no longer valid and a locally fine grid would need to be employed. In this letter, a subgridding technique is applied to analyzing lightning electromagnetic fields in the three-dimensional space with the CIP method. Index Terms-Constrained interpolation profile (CIP) method, electromagnetic field, finite-difference time-domain (FDTD) method, lightning, subgridding technique.

Improved Evaluation of Sommerfeld Integrals for Microstrip Antenna Problems

An improved technique for accurate evaluation of the Sommerfeld integrals appearing in the Gzx component single layer microstrip Green's function is described here that utilizes closed-form evaluation of the infinite tail, and numerical integration of a finite integral. The overall method avoids: (a) any pole calculations, and, (b) the traditional large argument approximation of the Bessel function of the Sommerfeld integrand. Initial numerical results from this proposed method are included. Since the method avoids any pole calculations, it can be expected to provide improvement for full-wave analysis of a wider class of microstrip patches on electrically thick substrates.

Numerical Computations and Integrations of the Wave Resistance Green's Function

Theoretical and Computational Fluid Dynamics, 1998

In order to develop an efficient method, using Kelvin-Havelock singularities, to compute the steady lifting flow around a ship with forward speed, the accuracy of computations of Green's function and boundary integrations have been investigated. The computations have been done using interpolation from tables for the nonoscillatory term of Green's function and using series for the oscillatory one; it has been shown that a region exists, close to the free-surface, where this last term must be computed by complete integration to ensure a prescribed error. Three schemes of boundary integrations have been studied; first boundary integrations have been performed using a Gauss method. Then, to improve accuracy, Fourier and boundary integrations have been interchanged either only for the oscillatory term or for both terms. Numerical results are compared and discussed taking into account both precision and computational time, for a submerged ellipsoid and for a lifting surface-piercing body.