A special higher order finite-element method is presented for the analysis of electromagnetic scattering from a large, deep, and arbitrarily shaped open cavity. This method exploits the unique features of the finite-element equations and, more importantly, the unique features of the problem of scattering by a large and deep cavity. It is designed in such a manner that it uses minimal memory, which is proportional to the maximum cross section of the cavity and independent of the depth of the cavity, and its computation time increases only linearly with the depth of the cavity. Furthermore, it computes the scattered fields for all angles of incidence without requiring significant additional time. The technique is implemented with higher order tetrahedral and mixed-order prism elements, both having curved sides to allow for accurate modeling of arbitrary geometries. Numerical results show that higher order elements yield a remarkably more accurate and efficient solution for scattering by three-dimensional (3-D) cavities. Of the two kinds of element, the mixed-order prism is optimal for the proposed special solver.

A special higher order finite-element method for scattering by deep cavities

This paper is a review of all methods that have been used in the literature for the solution of a very important and challenging set of problems, namely electromagnetic scattering from inlets, cavities, and open ducts. The techniques examined have been grouped together according to their fundamental principles, so that easy and direct comparisons among them are facilitated. The complexity and difficulty of the problems are clearly inferred from the very long list of references, which includes several very recent articles. The purpose of the paper is to highlight the advantages and limitations of the techniques invoked, draw useful conclusions, and trigger initiatives for future improved approaches to the topic.

A review of electromagnetic scattering analysis for inlets, cavities, and open ducts

The forward-backward methodology is combined with the iterative physical optics (IPO) algorithm to improve convergence for cavity scattering problems. Wave propagation inside elongated cavities, such as jet engine inlet ducts, follows a predominant down-and-back path. The forward-backward method allows the IPO currents on the cavity walls to be updated sequentially (forward) and reverse-sequentially (backward) along the waveguide axis. A relaxation parameter is introduced to help control the convergence characteristics, making the new algorithm mathematically equivalent to the classical iterative method of symmetric successive over-relaxation. The fast far-field approximation (FaFFA) accelerates the matrix-vector products in the IPO formulation, and an equivalent surface impedance is used to characterize thin material linings in the cavity.

Forward-backward iterative physical optics algorithm for computing the RCS of open-ended cavities

A fully high-order finite element algorithm is presented for simulating electromagnetic scattering by a deep cavity using curvilinear tetrahedral elements. Unlike the previously developed algorithm based on mixed-order triangular prism elements, this new algorithm can significantly suppress numerical dispersion errors in all directions, thus resulting in a more accurate and efficient simulation of complex wave propagation inside a deep cavity. Moreover, the use of tetrahedral elements removes limitations on the modeling of complex cavities imposed by the use of triangular prism elements. Numerical examples and experimental results are presented to demonstrate the advantages of the new algorithm.

A fully high-order finite-element simulation of scattering by deep cavities

In a previous paper (see ibid., vol.41, p.1560-1569, no.11, 1993), we presented the hybrid ray-FDTD method for analyzing the electromagnetic scattering from two-dimensional cavities with complex terminations. In this paper, we present three hybrid methods for analyzing the scattering from three-dimensional (3-D) inlet cavities. In these hybrid methods, the finite-difference time-domain (FDTD) method is used to determine the reflection matrix associated with the termination. Modal analysis, physical optics (PO), or rays are used to analyze the remaining front section of the cavity. Representative results are presented. >

The application of FDTD in hybrid methods for cavity scattering analysis

A formulation based on the high frequency asymptotic principles of physical optics is developed for analyzing the scattering by relatively arbitrary open-ended waveguide cavities containing complex interior terminations. A magnetic field integral equation (MFIE) is obtained for the equivalent currents on the interior cavity walls and is solved using an iterative physical optics (IPO) algorithm which iteratively applies physical optics to account for multiple reflections inside the cavity. The number of iterations required for convergence is related to the expected number of important reflections. The IPO method is more approximate than a matrix solution of the MFIE, but it is quite accurate for electrically large cavities and is much more efficient. Numerical results are presented which demonstrate the convergence and accuracy of the method by comparison with modal reference solutions. >

J. Luis Rodriguez

Papers

An iterative physical optics approach for analyzing the electromagnetic scattering by large open-ended cavities