A. Arif Ergin

The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena

This article describes a plane-wave time-domain (PWTD) algorithm that facilitates the fast evaluation of transient wave fields produced by surface scattering. The algorithm presented relies on a Whittaker-type expansion of transient fields in terms of propagating plane waves. The incorporation of the PWTD scheme into existing matching-on-in-time- (MOT-) based integral-equation solvers is elucidated. It is shown that the computational cost of performing a surface-scattering analysis, using two-level and multilevel PWTD-enhanced MOT schemes, scales as O(N/sub t/N/sub s//sup 1.5/ log N/sub s/) and O(N/sub t/N/sub s/log/sup 2/N/sub s/), respectively, when the surface source density is represented by N/sub s/ spatial and N/sub t/ temporal samples. Hence, the computational cost of the proposed algorithms scales much more favorably than that of classical MOT schemes, which scale as O(N/sub t/N/sub s//sup 2/). Therefore, PWTD-enhanced MOT schemes make possible the analysis of broadband scattering from structures of unprecedented dimensions.

Analysis of transient electromagnetic scattering from closed surfaces using a combined field integral equation

In the past, both the time-domain electric and magnetic field integral equations have been applied to the analysis of transient scattering from closed structures. Unfortunately, the solutions to both these equations are often corrupted by the presence of spurious interior cavity modes. In this article, a time-domain combined field integral equation is derived and shown to offer solutions devoid of any resonant components. It is anticipated that stable marching-on-in-time schemes for solving this combined field integral equation supplemented by fast transient evaluation schemes such as the plane wave time-domain algorithm will enable the analysis of scattering from electrically large closed bodies capable of supporting resonant modes.

Fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm

The computational complexity of classical marching-on-in-time (MOT) methods for solving time domain integral equations (TDIEs) pertinent to the analysis of transient scattering phenomena involving perfectly conducting targets grows as O(N/sub t/N/sub s//sup 2/) (N/sub t/ and N/sub s/ denote the number of temporal and spatial degrees of freedom (DOF) of the electric current on the target). This scaling law impedes the application of these schemes to the analysis of large-scale scattering phenomena. The recently developed plane wave time domain (PWTD) algorithm permits the rapid evaluation of transient wave fields generated by temporally bandlimited sources and hence the acceleration of marching on in time based TDIE solvers. Previously, we described a two-level PWTD enhanced TDIE solver for analyzing electromagnetic scattering from perfectly conducting targets; the computational complexity of this algorithm scales as O(N/sub t/N/sub s//sup 1.5/logN/sub s/). Here, a multilevel PWTD scheme for rapidly evaluating electric fields due to temporally bandlimited electric current sources is described. In addition, a multilevel PWTD enhanced TDIE solver for analyzing electromagnetic scattering from perfectly conducting scatterers using O(N/sub t/N/sub s/log/sup 2/N/sub s/) CPU resources is outlined. Last, the accuracy and CPU/memory efficiency of this solver are demonstrated by analyzing transient scattering from electrically large bodies.

Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time-domain algorithm

A fast algorithm is presented for solving electric, magnetic, and combined field time-domain integral equations pertinent to the analysis of surface scattering phenomena. The proposed two-level plane wave time-domain (PWTD) algorithm permits a numerically rigorous reconstruction of transient near-fields from their far-field expansion and augments classical marching-on in-time (MOT) based solvers. The computational cost of analyzing surface scattering phenomena using PWTD-enhanced MOT schemes scales as O(N/sub i/N/sub s//sup 2/3/ log N/sub s/) as opposed to /spl Oscr/(N/sub t/N/sub s//sup 2/) for classical MOT methods, where N/sub t/ and N/sub s/ are the numbers of temporal and spatial basis functions discretizing the scatterer current. Numerical results that demonstrate the efficacy of the proposed solver in analyzing transient scattering from electrically large structures and that confirm the above complexity estimate are presented.

Analysis of transient wave scattering from rigid bodies using a Burton–Miller approach

Transient scattering from closed rigid bodies can be analyzed using a variety of time domain integral equations, e.g., the Kirchhoff integral equation and its normal derivative. Unfortunately, when the spectrum of the incident field includes one or more of the resonance frequencies of the corresponding interior problem, the solutions to these time domain integral equations become corrupted with spurious interior modes. In this article, this phenomenon is demonstrated via numerical experiments, and a Burton–Miller-type time domain combined field integral equation is proposed as a remedy. To verify that the solutions to this Burton–Miller-type equation are not corrupted by interior modes, various numerical results are presented. It is anticipated that this equation, when used in conjunction with fast time domain integral equation solvers (e.g., plane wave time domain algorithms), will enable the accurate analysis of transient wave scattering from acoustically large bodies.

Volume‐integral‐equation‐based analysis of transient electromagnetic scattering from three‐dimensional inhomogeneous dielectric objects

A novel technique for analyzing transient electromagnetic scattering from three-dimensional inhomogeneous dielectric targets is proposed. An integral equation for the electric flux density throughout the scatterer is constructed by invoking the electromagnetic volume equivalence principle. This equation is solved using a marching-on-in-time scheme in which the electric flux density is expanded in space by volumetric rooftop basis functions defined on a tetrahedral mesh and in time by piecewise polynomials. The proposed method is validated for representative dielectric structures by comparison via Fourier transformation of scattering data obtained with this method and various frequency domain techniques.

Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm

The analysis of transient wave scattering from rigid bodies using integral equation-based techniques is computationally intensive: if carried out using classical schemes, the evaluation of the velocity potential on the surface of a three-dimensional scatterer, represented in terms of Ns spatial basis functions for Nt time steps, requires O(NtNs2) operations. The recently developed plane wave time domain (PWTD) algorithm permits the rapid evaluation of transient fields that are generated by bandlimited source distributions. It has been shown that incorporation of the PWTD algorithm into integral equation-based solvers in a two-level setting reduces the computational complexity of a transient analysis to O(NtNs1.5 logNs). In this paper, it is shown that casting the PWTD scheme into a multilevel framework permits the analysis of transient acoustic surface scattering phenomena in O(NtNslog2Ns) operations using O(NtNs) memory. Numerical examples that demonstrate the efficacy of the multilevel implementation are also presented.

Plane-wave–time-domain-enhanced marching-on-in-time scheme for analyzing scattering from homogeneous dielectric structures

A novel and fast integral-equation-based scheme is presented for analyzing transient electromagnetic scattering from homogeneous, isotropic, and nondispersive bodies. The computational complexity of classical marching-on-in-time (MOT) methods for solving time-domain integral equations governing electromagnetic scattering phenomena involving homogeneous penetrable bodies scales as O(NtNs2). Here, Nt represents the number of time steps in the analysis, and Ns denotes the number of spatial degrees of freedom of the discretized electric and magnetic currents on the bodys surface. In contrast, the computational complexity of the proposed plane-wave-time-domain-enhanced MOT solver scales as O(NtNs log2Ns). Numerical results that demonstrate the accuracy and the efficacy of the scheme are presented.

Transient analysis of multielement wire antennas mounted on arbitrarily shaped perfectly conducting bodies

This paper presents a novel algorithm for analyzing transient radiation from multielement wire systems mounted on arbitrarily shaped, three-dimensional, perfectly conducting bodies. The algorithm simultaneously characterizes the transient radiation properties of the antenna and the performance of the feed network via a hybrid integral-equation/finite difference scheme. Numerical examples that validate and demonstrate the efficacy of the proposed scheme are presented.

Fast transient analysis of acoustic wave scattering from rigid bodies using a two-level plane wave time domain algorithm

It is well known that the computational cost associated with the application of classical time domain integral equation methods to the analysis of scattering from acoustical targets scales unfavorably with problem size. Indeed, performing a three-dimensional scattering analysis using these methods requires O(NtNs2) operations, where Ns denotes the number of basis functions that model the spatial field distribution over the surface of the scatterer and Nt is the number of time steps in the analysis. Recently, novel plane wave time domain algorithms that augment these classical methods and thereby reduce their high computational cost have been introduced. This paper describes such a plane wave time domain algorithm within the context of the analysis of acoustic scattering from rigid bodies and outlines its incorporation into a time domain integral equation solver in a two-level setting. It is shown that the resulting scheme has a computational complexity of O(NtNs1.5 log Ns). Examples comparing the accuracy...