Plane Wave Time Domain Research Articles

Errata to "analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm"

Errata to "analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm"

A fast time-domain finite element-boundary integral method for electromagnetic analysis

A time-domain, finite element-boundary integral (FE-BI) method is presented for analyzing electromagnetic (EM) scattering from two-dimensional (2-D) inhomogeneous objects. The scheme's finite-element component expands transverse fields in terms of a pair of orthogonal vector basis functions and is coupled to its boundary integral component in such a way that the resultant finite element mass matrix is diagonal, and more importantly, the method delivers solutions that are free of spurious modes. The boundary integrals are computed using the multilevel plane-wave time-domain algorithm to enable the simulation of large-scale scattering phenomena. Numerical results demonstrate the capabilities and accuracy of the proposed hybrid scheme.

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.

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.

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.

Fast Evaluation of Two-Dimensional Transient Wave Fields

This paper presents a novel scheme to efficiently evaluate transient linear wave fields that are generated by two-dimensional (2D) source configurations. The scheme, termed the plane wave time domain algorithm (PWTD), realizes a diagonal translation operator for 2D transient wave fields through their representation in terms of Hilbert transformed plane wave expansions. Numerical results are presented that validate the algorithm and demonstrate its convergence properties. The proposed PWTD algorithm can be coupled to classical 2D time domain integral equation solvers in a two-level and multilevel setting. It is shown that analysis of a 2D surface scattering phenomenon, in which sources are represented in terms of Ns spatial and Nt temporal samples, based on two-level and multilevel PWTD augmented integral equation solvers, requires O(N1.5sNt log Nt) and O(NsNt log Ns log Nt) computational resources, respectively (as opposed to O(N2sNt2) for a classical solver). Therefore, these PWTD schemes render feasible the rapid integral equation based analysis of 2D transient scattering phenomena involving large surfaces.

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.

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 and computational efficiency of the conventional and accelerated methods are presented. The proposed two-level scheme renders feasible the broadband analysis of scattering from large and complex bodies.

Acceleration of integral equation based transient analysis of acoustic scattering phenomena using the plane wave time domain algorithm

The numerical analysis of transient scattering from homogeneous bodies residing in an unbounded medium is often performed using integral equation (IE) based methods. The major advantages of these methods over differential equation based techniques are that (i) the radiation condition is implicitly imposed in the formulation, and that (ii) the number of spatial unknowns, Ns, scales as the surface area of the scatterer. However, IE techniques are notoriously costly as their computational complexity scales as O(N2s) per time step. This complexity can be reduced considerably by using the recently introduced plane wave time domain (PWTD) algorithm [A. A. Ergin et al., J. Comput. Phys. 146, 157–180 (1998)]. In this presentation, the PWTD algorithm will be briefly reviewed and its incorporation into an IE-based transient solver for analyzing scattering from rigid bodies will be elucidated. It will be shown that the computational cost of a transient analysis using two-level and multilevel PWTD enhanced solvers scales as O(Ns1.5<th>log<th>Ns) and O(Ns<th>log2<th>Ns) per time step, respectively. Numerical examples that validate these complexity estimates and demonstrate the efficacy of the proposed methods in analyzing scattering from realistic structures will be presented.

Exact global boundary condition with reduced computational complexity for grid truncation in acoustic finite difference time domain simulations

The numerical analysis of transient acoustic radiation by and scattering from inhomogeneous bodies is often carried out using the finite difference time domain (FDTD) method. However, FDTD grids must be truncated with absorbing boundary conditions when the structure of interest resides in an unbounded medium. Local boundary conditions have to be imposed on a convex outer boundary, thereby often inflating the problem size. This drawback is alleviated if the grid is truncated using exact boundary conditions that rely on a retarded-time boundary integral (RTBI) [L. Ting and M. J. Miksis, J. Acoust. Soc. Am. 80, 1825–1827 (1986)]. Unfortunately, for a 3-D computational domain comprising of O(N3) FDTD cells, where N denotes the number of cells per unit length, the evaluation of the RTBI using classical methods requires O(N4) operations per time step, which renders the RTBI approach impractical. In this presentation, it will be shown that this computational bottleneck can be alleviated by employing the plane wave time domain algorithm [A. A. Ergin et al., J. Comput. Phys. 146, 157–180 (1998)] using which the RTBI can be evaluated in O(N2<th>log2<th>N) operations. Numerical results that demonstrate the efficacy and reduced complexity of the method will be presented.

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.

Fast Evaluation of Three-Dimensional Transient Wave Fields Using Diagonal Translation Operators

This paper presents novel plane wave time domain (PWTD) algorithms which accelerate the computational analysis of transient surface scattering phenomena. The proposed PWTD algorithms permit the fast evaluation of transient fields satisfying the wave equation. The cost associated with the computation of fields atNsobservers produced by a surface bound source density represented in terms ofNsspatial samples forNttime steps scales asO(NtN2s) if classical time domain integral-equation-based methods are used. It is shown that this cost can be reduced toO(NtN4/3slogNs) andO(NtNslogNs) using two-level and multilevel PWTD schemes, respectively. These algorithms are the time domain counterparts of frequency domain fast multipole methods and make feasible the practical broadband analysis of scattering from large and complex bodies.

Time-domain sensing of targets buried under a rough air-ground interface

We consider plane wave time-domain scattering from a fixed target in the presence of a rough (random) surface with application to ground penetrating radar. The time-domain scattering data are computed via a two-dimensional (2-D) finite-difference time-domain (FDTD) algorithm. In addition to examining the statistics of the time-domain fields scattered from such a surface, we investigate subsurface target detection by employing a (commonly used) matched-filter detector. The results of such a detector are characterized by their receiver operating characteristic (ROC), which quantifies the probability of detection and probability of false alarm. Such ROC studies allow us to investigate fundamental assumptions in the matched-filter detector: that the target response is deterministic and the clutter signal stochastic, with the two signals treated as additive and independent.