Can Efficient Fourier-Transform Techniques Favorably Impact on Broadband Computational Electromagnetism?

TL;DR

It is argued that a set of transformative innovations could be developed for the effective, accurate and efficient simulation of problems of wave propagation and scattering of broadband, time-dependent wavefields.

Abstract

In view of recently demonstrated joint use of novel Fourier-transform techniques and effective high-accuracy frequency domain solvers related to the Method of Moments, it is argued that a set of transformative innovations could be developed for the effective, accurate and efficient simulation of problems of wave propagation and scattering of broadband, time-dependent wavefields. This contribution aims to convey the character of these methods and to highlight their applicability in computational modeling of electromagnetic configurations across various fields of science and engineering.

Figures (11)

• Figure 1: Left: real part of the Fourier transform $F(\omega)$ of $f(t)$. Right: real part of the windowed and recentered Fourier transform $F_k^\textit{slow}(\omega)$ given in \ref{['Fkslow_int']}. Unlike the Fourier transform of $f(t)$, the Fourier transform of the windowed and recentered function $f_k(t) = w(t+s_k)f(t+s_k)$ is slowly oscillatory with respect to $\omega$.
• Figure 2: Scattering of an incident acoustic field with center-frequency $\omega = 15$ off of a simple aircraft structure using the FHM. A total of $250$ frequency domain integral equation solutions were used in this simulation.
• Figure 3: Demonstration of the FHM for the Maxwell equations: scattering of a time-domain signal by a hemispherical concavity. Upper time sequence: real part of the $y$-component of the total electric field. Lower time sequence: magnitude of the total electric field. Credit: Bruno, Tanushev and Voss, unpublished.
• Figure 4: Electromagnetic time domain resonances in a slotted cube---an idealized cavity structure of the type arising in field-concentration test cases in areas such as, e.g., electromagnetic compatibility. Upper left: open cavity structure considered. Remaining images: time sequence of events as an incident field impinges on the cavity entrance. As a result of the propagation and scattering events the field is split into two portions, one within the cavity and one outside the cavity, that eventually passes the structure completely. The interior resonant modes continue to operate for long periods of time, allowing for the release of electromagnetic energy on every period of the interior modal field. Credit: Bruno, Tanushev and Voss, unpublished.
• Figure 5: Left and Center: Scattering of a point source from an aircraft nacelle model. The wideband point source is located at a point $\mathbf{r}_0$ within the cavity at distance $\delta$ (equal to $5\%$ of the radius of the opening) above and to the right of the nacelle centerline, and approximately 1/3 of the way along the centerline from the opening of the cavity, with frequency content given by a Gaussian amplitude function distribution. Left: Scattered field along a horizontal plane with center frequency for which the nacelle opening is 16 wavelengths in diameter. Center: Observed decay rates of the maximum magnitude of the scattered field in a cylindrical region of radius equal to double the nacelle opening diameter around the centerline and for center frequencies corresponding to wavelengths equal to $0.7854$, $0.3927$, $0.1963$, $0.0982$ and $0.0654$ nacelle-opening diameters, respectively. Right: "Tracking Error" (equal to the absolute-value quantity on the left-hand side of equation \ref{['eq:eq:ptwise_error']}), for a nacelle scattering experiment under an incident chirp field of long duration and with frequencies in the range $1\leq \omega \leq 25$, for various values of the numbers $M = m_f - m_i$ of active windows used.