Costs and cost scaling in time-domain integral-equation analysis of electromagnetic scattering

Abstract

Computation of scattering from multi-wavelength bodies is expensive, and costs scale with up to the sixth power of incident frequency. Conventional integral-equation time-domain methods have costs scaling with the fifth power. Here are described modifications to the IETD approach that offer the prospect of a reduction in cost scaling, to possibly the third power of frequency, and an associated large reduction in cost. The approach exploits the pulsed nature of the illumination, which results in surface fields that are small most of the time over most of the body, on bodies that are electrically large. Neglect of these produces some modest increase in error, but allows large reductions in cost and storage requirements. In the examples shown, cost reductions by amounts approaching two orders of magnitude are obtained, with the factor by which costs are reduced itself increasing with roughly the square of the body size; storage requirements are rendered essentially negligible. Introductionomputation of scattering from multi-wavelength bodies is costly (at least until sizes at which optical methods become applicable are reached). The cost of such analyses scales with some power of the incident frequency [ 11. For frequency-domain integral-equation methods, this power is six. For FDTD it is nominally four, but in practice it is rather higher, given a frequency-depend-(IETD) methods, the cost scales with the fifth power of incident frequency. The issue is complicated somewhat by the ability of time-domain approaches to provide answers at multiple frequencies, and of frequency-domain integral approaches to provide monostatic characterization for not much more than the cost of a single run. Much as does the operation count, storage needs also scale quite severely with frequency. It varies between methods, but scaling is typically with about the fourth power of frequency. ant "nodes per wavelength" [ 2 ] . For integral-equation time-domainThere is considerable effort presently being aimed at reducing such costs: the matrix-localization and associated techniques applied to frequency-domain integral-methods [3] are examples. We will, in this paper, concentrate on the IETD approach, and will describe modifications to the usual algorithm that, at the price of some loss in accuracy, offer marked reductions in both cost and cost scaling. The modifications are applicable only to bodies that are electrically large, but these are, of course, those where high cost is an issue.In Section 3, we will outline the IETD approach, in part to allow the origin of the usual fifth-power cost scaling to be described, and to provide a platform from which we will describe the physical basis of the reduced-cost algorithm. In Section 4, we will discuss the implementation of the reduced-cost algorithm, explaining the means by which operations may be caused to scale with about the third power of frequency, and storage needs with the second power. Results of the approach, both relating to the accuracy loss and to the reductions in operations ...

Fresnel's Formulas in Time Domain

“…The various terms in (14) give an expansion for the transformed field into a pure transverse component and a mixed one. It follows from the discussion above that the coefficients characterize the scattering of the component of the original field perpendicular to the x axis (the transverse component), whereas characterizes the formation of the transverse component as well as that normal to the interface.…”

“…The field is defined completely by the presence of the plane boundary between the media with different properties and it is expressed by the more complicated formula (14) where the differential matrices are equal to (15) and is the unit matrix of order 2. The vector functions are defined by integrating the initial field (16) where the functions have the form (17) with is the Bessel function, and…”

Time domain wake field computation with boundary element method

“…Many discussions have been done mainly for numerical instabilities [11]- [13] and computation cost of calculation and memory [14], [15]. At the first part of this section, we briefly summarize these problems.…”

Extending integral equation time domain acoustic scattering analysis to larger problems

“…In this paper we will describe a modi"cation to the usual integral equation time domain technique which reduces its cost and cost scaling sharply, and extends considerably the range of problem size tractable. Recently, an approach was presented [4,5] which was able to reduce cost scaling by one power of frequency; the present one, based on work recently presented in electromagnetic scattering [6] applications, improves on this, reducing the cost scaling by approaching two powers.…”