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A novel marching on in time and Poggio-Miller- Chang-Harrington-Wu-Tsai (PMCHWT)-based time domain integral equation solver for analyzing transient scattering from composite multiregion structures comprising homogeneous penetrable volumes and perfectly conducting surfaces is presented. To render the marching on in time procedure stable, observer and source integrals are approximated via multipoint collocation and evaluated in closed form. The proposed scheme avoids the costly evaluation of five dimensional integrals required in full space-time Galerkin schemes, and proves to be stable for all targets investigated, including coated perfect electrically conducting surfaces and multiregion penetrable volumes. [ABSTRACT FROM AUTHOR]

The primary impediment to analyzing two-dimensional transient scattering phenomena using classical marching-on-in-time-based integral equation solvers is these schemes' high computational complexity that scales as O (N s 2 N t 2 , where N s and N t denote the number of spatial and temporal degrees of freedom of the current on the scatterer. Here, three schemes that reduce this cost by permitting the rapid evaluation of the temporal convolution of a bandlimited transient source signature with the two-dimensional wave equation Green function are studied; these three methods rely on (i) blocked fast Fourier transforms, (ii) truncated singular value decompositions, and (iii) multiresolution concepts. The computational cost of all three proposed algorithms scales as O(N s 2 N t log α N t ) with α ≤ 2. The three schemes are compared on their respective multiplicative constants inherent in this cost estimate, their memory requirements, and their ease of implementation. [ABSTRACT FROM AUTHOR]

A new algorithm is presented for analyzing scattering from two-dimensional (2-D) nonlinear penetrable objects that are illuminated by transient transverse magnetic (TM) polarized fields. The proposed scheme solves a time-domain volume-integral inequation (TDVIE) using a marching-on-in-time (MOT) technique. Numerical results obtained using this technique and the finite-difference-time-domain (FDTD) method are in excellent agreement. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 26: 419–423, 2000. [ABSTRACT FROM AUTHOR]

The development of time-domain integral equation solvers with robust late-time stability properties has been a long-standing quest. Among the many methods that have been investigated, those leveraging quasi-exact integration techniques appear to be most successful. This article presents stable and accurate marching-on-in-time (MOT) solvers for time-domain electric, magnetic, and combined field integral equations (EFIE, MFIE, and CFIE) based on quasi-exact integration techniques. The novel MOT solvers exhibit excellent stability while yielding highly accurate results, as demonstrated by various numerical examples. In addition, the solvers’ excellent stability and accuracy properties are used to examine spurious modes encountered when time-domain integral equations are applied to closed surfaces. It is demonstrated that MOT solutions to the time domain EFIE and MFIE often are polluted by spurious modes at the cavity’s resonant frequencies whereas those of the CFIE solver are devoid of such contamination. [ABSTRACT FROM AUTHOR]

The interior resonance problem of time domain integral equations (TDIEs) formulated to analyze acoustic field interactions on penetrable objects is investigated. Two types of TDIEs are considered: The first equation, which is termed the time domain potential integral equation (TDPIE), suffers from the interior resonance problem, i.e., its solution is replete with spurious modes that are excited at the resonance frequencies of the acoustic cavity in the shape of the scatterer. Numerical experiments demonstrate that, unlike the frequency-domain integral equations, the amplitude of these modes in the time domain could be suppressed to a level that does not significantly affect the solution. This is achieved by increasing the numerical solution accuracy through the use of a higher-order discretization in space and the band limited approximate prolate spheroidal wave function with high interpolation accuracy as basis function in time. The second equation is obtained by linearly combining TDPIE with its normal derivative. The solution of this equation, which is termed the time domain combined potential integral equation (TDCPIE), does not involve any spurious interior resonance modes but it is not as accurate as the TDPIE solution at non-resonance frequencies. In addition, TDCPIE's discretization calls for treatment of hypersingular integrals. [ABSTRACT FROM AUTHOR]

Internal resonant modes are always observed in the marching-on-in-time (MOT) solution of the time domain electric field integral equation (EFIE), although “relaxed initial conditions,” which are enforced at the beginning of time marching, should in theory prevent these spurious modes from appearing. It has been conjectured that, numerical errors built up during time marching establish the necessary initial conditions and induce the internal resonant modes. However, this conjecture has never been proved by systematic numerical experiments. Our numerical results in this communication demonstrate that, the internal resonant modes' amplitudes are indeed dictated by the numerical errors. Additionally, it is shown that in a few cases, the internal resonant modes can be made “invisible” by significantly suppressing the numerical errors. These tests prove the conjecture that the internal resonant modes are induced by numerical errors when the time domain EFIE is solved by the MOT method. [ABSTRACT FROM PUBLISHER]

A method for modeling singular electric currents near conducting edges within marching-on-in-time (MOT) simulators is presented. The use of singular basis functions in MOT simulators presents unique challenges not encountered in frequency-domain implementations. Numerical results demonstrate that the proposed expansion results in accelerated convergence for scatterers with sharp features. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 327–332, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10452 [ABSTRACT FROM AUTHOR]

Electromagnetic scattering from electrically large objects with multiscale features is an increasingly important problem in computational electromagnetics. A conventional approach is to use an integral equation-based solver that is then augmented with an accelerator, a popular choice being a parallel multilevel fast multipole algorithm (MLFMA). One consequence of multiscale features is locally dense discretization, which leads to low-frequency breakdown and requires nonuniform trees. To the authors’ knowledge, the literature on parallel MLFMA for such multiscale distributions capable of arbitrary accuracy is sparse; this paper aims to fill this niche. We prescribe an algorithm that overcomes this bottleneck. We demonstrate the accuracy (with respect to analytical data) and performance of the algorithm for both PEC scatterers and point clouds as large as $755{\lambda }$ with several hundred million unknowns and nonuniform trees as deep as 16 levels. [ABSTRACT FROM AUTHOR]

Prior theoretical studies and experience confirm that the stability of marching-on-in-time (MOT) solvers pertinent to the analysis of scattering from free-standing three-dimensional perfect electrically conducting surfaces hinges on the accurate evaluation of MOT matrix elements resulting from a Galerkin discretization of the underlying time domain integral equation (TDIE). Unfortunately, the accurate evaluation of the four-dimensional spatial integrals involved in the expressions for these matrix elements is prohibitively expensive when performed by computational means. Here, a method that permits the quasi-exact evaluation of MOT matrix elements is presented. Specifically, the proposed method permits the analytical evaluation of three out of the four spatial integrations, leaving only one integral to be evaluated numerically. Since the latter has finite range and a piecewise smooth integrand, it can be evaluated to very high accuracy using standard quadrature rules. As a result, the proposed method permits the fast evaluation of MOT matrix elements with arbitrary (user-specified) accuracy. Extensive numerical experiments show that an MOT solver for the electric field TDIE that uses the proposed quasi-exact method is stable for a very wide range of time step sizes and yields solutions that decay exponentially after the excitation vanishes. [ABSTRACT FROM AUTHOR]