An FFT-Accelerated Integral-Equation Solver for Analyzing Scattering in Rectangular Cavities

Abstract

An efficient integral-equation method is presented for the fast analysis of scattering from arbitrarily shaped 3-D structures in a rectangular cavity. The proposed method employs: 1) the frequency-domain surface-volume electric field integral equation to model scattering from conductors and dielectrics; 2) the rectangular-cavity Green functions to account for the cavity walls; 3) the Ewald method and 3-D spatial interpolation to accelerate the Green function computations; and 4) the adaptive integral method (AIM) to reduce the computational complexity of the iterative method-of-moments solution procedure. The structure of interest is first meshed with arbitrary triangular/tetrahedral elements. The mesh is then enclosed with an auxiliary regular grid. Next, a four-step algorithm is executed: anterpolation (mesh-to-grid), propagation (grid-to-grid), interpolation (grid-to-mesh), and correction (mesh-to-mesh). The computationally dominant propagation step of the AIM is accelerated by decomposing the Green functions into eight components that are in convolution or correlation form in the three Cartesian directions. This results in eight types of propagation matrices; these are in nested Toeplitz or Hankel form and are efficiently multiplied with the necessary vectors using 3-D fast Fourier transforms. Numerical results validate the method, quantify its costs, and demonstrate its utility. Index Terms-Cavity Green functions, fast Fourier transform (FFT), integral equations. 0018-9480

Finite Element Based Eigenanalysis for the Study of Electrically Large Lossy Cavities and Reverberation Chambers

“…The finite wall conductivity can be considered as a perturbation of the corresponding PEC situation, and the respective eigenfunctions can be utilized as fair approximations. But again to evaluate losses from (13) we need both the electric and the magnetic fields tangential to the wall, where (3) should apply. Recall now that the required tangential electric field was enforced to vanish across the PEC wall, hence it is not available.…”

“…Most of the effort in the analysis and design of reverberation chambers is directed toward the solution of the deterministic electromagnetic problem (in the presence of specific sources). Method of Moments (MoM) is one of the most frequently used techniques for this type of problem in its simple form or extended by other techniques in a hybrid scheme [6][7][8][9][10][11][12][13][14][15][16]. Maybe the most complete work in this area is that of Bruns' [6,7].…”

“…Maybe the most complete work in this area is that of Bruns' [6,7]. In [8][9][10][11][12][13], MoM is used with the aid of several techniques (spectral domain techniques [8], discrete singular convolution in a two dimensional analysis [9,10], finite element boundary integral technique [12], MoM accelerated with Ewald and adaptive integral method [13]). However, in all these cases, the Perfect Electric Conductor (PEC) cavity Green's function is adopted, which is proved to be inaccurate, since it fails to account for the walls finite conductivity losses, neither can produce results for large objects in the cavity, and it is unable to model in detail a reverberation chambers (cables, screws, etc.).…”

THE UNIFED-FFT GRID TOTALIZING ALGORITHM FOR FAST O(N LOG N) METHOD OF MOMENTS ELECTROMAGNETIC ANALYSIS WITH ACCURACY TO MACHINE PRECISION (Invited Paper)

“…The MoM interactions are decomposed into four 2D convolution/correlation terms accounting for the walls of the rectangular enclosure and allowing for the use of FFT for their O(N log N ) evaluation. Analogous formulations have been previously developed only for the FFT-based fast algorithms involving pre-corrections [5,9]. Such formulations introduce additional error compared to the direct MoM solution making accurate resolution of weak but important interactions inaccurate.…”

“…Additionally, speedenhanced direct solvers have been extended to finite-element analysis in a deterministic fashion [13]. Further, [9] has extended a similar FFT-based approach to cavities for scattering problems. Figure 1.…”