A nonconformal scheme for scattering analysis from PEC objects

This work presents a new formulation for conducting bodies of revolution (BOR) in layered media. It is derived using magnetic field integral equation (MFIE). The discrete complex image method is used to transform the Sommerfeld integrals into closed form solutions. For large closed objects, the use of the magnetic field formulation is shown to be more advantageous than the electric field integral equation (EFIE) concerning the convergence of the solution. The obtained formulation is applied to the contiguous half-spaces case. Results of both the magnetic and electric field integral equation formulations are presented.

Efficient analysis of electromagnetic-wave responses from electrically large complex objects is a crucial but difficult topic in many applications of electromagnetic engineering. Among various numerical methods, the Method of Moments (MoM) solves for surface- or volume-distributed equivalent currents, which are expanded in terms of basis functions. In this paper, the traveling-wave phase variation has been incorporated into the basis functions to enhance their capability of describing the equivalent surface currents induced over surfaces of perfect electric conductors (PECs). A rigorous derivation is first given as physical insight, to show that the induced surface current is composed of a traveling-wave term and several standing-wave terms. A phase-extracted basis function (PEBF) is then proposed to describe the traveling current wave, and is applied in solving the electromagnetic scattering from three-dimensional (3D) PEC objects with smooth surfaces. By hybridizing the phase-extracted basis function with higher-order hierarchical basis functions, a moving standing-wave (MSW) basis function is further introduced to describe both the traveling-wave and the standing-wave terms in the induced surface current. It is shown from several numerical examples that the moving standing-wave basis function has excellent performance for solving electromagnetic scattering from three-dimensional PEC objects with both smooth and non-smooth surfaces, as well as for three-dimensional PEC cavities. After that, the unique properties of the phase-extracted basis function are utilized in the “sparsification” of the MoM matrix, and in the fast calculation of wideband responses. With the aid of the phase-extracted basis function and the moving standing-wave basis functions, the total memory requirements and the computational time can be significantly reduced, while numerical solutions can be obtained with good accuracy. The advantages of the phase-extracted basis functions and the moving standing-wave basis functions in predicting electromagnetic scattering from electrically large complex objects are summarized before the conclusions are drawn.

Electromagnetic (EM) scattering from perfect electric conductor (PEC) object embedded between two rough interfaces is investigated utilizing method of moments (MoM) for both TE and TM polarizations. Theoretical formulations of EM scattering model considered in this paper is presented and the total fields and their derivatives are solved numerically by employing MoM. The rough surfaces are modeled as realizations of a Gaussian random process with the Gaussian spectrum, while the tapered incident wave is chosen to reduce the truncation error. The influences of characteristic parameters of the rough surfaces, the relative permittivity of the medium, as well as the average height between the two rough surfaces, on the bistatic scattering coefficient (BSC) are discussed.

In modeling scattering from lossy surfaces, the surface is often approximated as a perfect electric conductor (PEC). However, when loss and wave penetration become important, the IBC model is typically employed and is adequate for many numerical simulations. However, the IBC's range of validity is considered unclear and an accurate quantification of its error is difficult. Consequently, other more exact implementations are necessary, such as integral equation methods. In this paper, a novel numerical implementation of the exact dielectric integral equations has been developed for scattering from a two-dimensional (2D), lossy dielectric interface. The formulation presented herein combines the coupled integral equations to form a single equation. This equation is easily interpreted as the magnetic field integral equation (MFIE) for a 2D, PEC surface with a perturbative term related to the finite conductivity of the surface. The advantage of this perturbation approach is that for ocean and other high loss surfaces, the solution is expected to be rapidly convergent with respect to other approaches and will reproduce the correct result even for surfaces with small curvature radii. Test cases demonstrate increased convergence with increased loss and increased contrast for perpendicular polarization. However with parallel polarization, convergence problems are uncovered and are associated with the Brewster angle effect.

An alternative method of moments discretization of the magnetic field integral equation (MFIE) uses testing functions inside the target and in a plane normal to the target surface. This approach is adapted to targets modeled with flat-faceted patches. A comparison with traditional numerical solutions of the MFIE that use testing functions on the target surface shows that the normally-integrated MFIE formulation produce far fields that are more accurate than those obtained from the traditional MFIE. The alternate approach can be made free from internal resonances and that approach is often more accurate than the combined field integral equation.

The adaptive integral method (AIM) is applied to the solution of the combined field integral equation (CFIE) of scattering by a three-dimensional (3-D) perfect electric conductor (PEC). The employment of CFIE eliminates the interior resonance problem suffered by both the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE). Furthermore, it significantly improves the efficiency of AIM by reducing the number of iterations for convergence. It is shown that the memory requirement and computational complexity per iteration of the AIM solution of CFIE are O(N1.5) and O(N1.5log N), respectively, for 3-D PEC surface scattering problems. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 321–328, 1998.

Formulas that provide an efficient and reliable numerical evaluation of the magnetic field integral equation (MFIE) with the use of vector triangular basis functions are developed. The MFIE integrals for the three basis functions on a triangular facet are converted from three vector integrals to three scalar integrals, which are evaluated simultaneously. The 1/R2 singular behavior is extracted from the integral, and closed-form expressions are given for the singular terms. Consequently, the formulas are valid for all observation points and are suitable for general-purpose modeling. © 1997 John Wiley & Sons, Inc.

In this paper, radar absorbing material (RAM) is utilized to reduce the scattered field of metal beams in all directions. Equivalence principle is used to divide the primal question into two, and then the electric field and magnetic field integral equation can be built according to boundary condition. When the equivalent electric current and magnetic current on outer surface are obtained by moments method, the scattered field and bistatic scattering cross section can be predicted in a single frequency. The forward scattering cross section over a frequency band can be simulated by using moments method in conjunction with asymptotic waveform evaluation (AWE) technique. The numerical result agrees with the result simulated by CST very well, hence the correctness of the methods adopted in this paper.

A novel numerical technique is presented for electromagnetic scattering analysis for coated flat strips. The computational formula is derived from a coupled system of electric- and magnetic-field integral equations and solved using an adaptive multiscale moment method. In this method, the unknowns are expanded in terms of local-supported triangular functions on different scales which are similar to wavelet-like basis functions. The procedure of solving the problem from a V-scale to a (V+1) -scale has four steps. The first step is to predict the solutions on (V +1) -scale from the known solution on a V-scale using interpolation. The second step is to eliminate the smaller coefficients of the basis functions of the solution and omit the corresponding rows and columns of the system matrix obtained from the moment method so as to reduce the size of the linear equations. The third step is to solve the matrix equation by the conjugate gradient (CG) method. The final step is to obtain the solution on the (V +1) -scale by adding some zero-terms corresponding to the coefficient whose value is zero. Many numerical examples are presented. The results have shown that the novel numerical technique is an efficient, stable and adaptive algorithm.

A time-domain discontinuous Galerkin method is presented to analyze transient scattering from perfect electrically conducting (PEC) objects. As mono-polar RWG functions are chosen for spatial functions, it is possible to analyze complex structures with either conformai or non-conformal discretization. Numerical results are included to demonstrate the accuracy and efficiency of this method.

The Method of Moments (MoM) is one of the most popular techniques for solving electromagnetic scattering problems. Its main advantage is that, when used to discretise a Boundary Integral Equation (BIE), only the surface of the objects needs to be discretised. Many other techniques require discretisation of the volume as well, leading to an increase of unknowns and requiring an artificial boundary to emulate infinity. The downside of the MoM is that the resulting linear system is dense, due to the Green's function, and often ill-conditioned. The density of the impedance matrix would lead to a prohibitive O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) complexity for both the CPU time and the memory. A number of techniques have been developed in the past, reducing this complexity. Among the most succesful are the Fast Multipole Methods (FMM), which reduce the complexity for a matrix-vector product to O (N log N). This matrix-vector product is the bottleneck of an iterative solution of the linear system. However, an iterative solution can only be efficient if the problem is sufficiently well-conditioned. The choice of BIE influences the conditioning number of the impedance matrix. The Electric Field Integral Equation (EFIE) leads to a highly accurate solution but is notoriously ill-conditioned. In comparison, the Magnetic Field Integral Equation (MFIE) is less accurate (for the same level of discretisation) but is well-posed. Also, on open surfaces the MFIE is not applicable. In order to alleviate the problems with the EFIE, a powerful preconditioner is required to stabilise the breakdown, which occurs in particular at low frequencies (LF). Recently, an approach has been proposed, allowing multiplication of the EFIE impedance matrix with itself, leading to a well-conditioned problem. In the next section, this approach will be briefly revisited. In order to maintain the O (N log N) complexity for the global solution, we employ FMM to accelerate the Calderon Preconditioner as well. A number of difficulties occur, but these can all be overcome. This combination of FMM and Calderon Preconditioning will be dealt with in the remaining sections. At the time of the conference, examples will be shown to illustrate the novel techniques.

We analyze the error in typical moment method scattering solutions for smooth cylindrical geometries and TM-polarized fields. We consider the magnetic field integral equation (MFIE), electric field integral equation (EFIE), and combined field integral equation. To quantify the impact of mesh element size, approximate integration of moment matrix elements, and geometrical discretization error on the accuracy of computed surface currents and scattering amplitudes, we derive error estimates analytically for the circular cylinder. For pulse functions and point testing, current and scattering amplitude errors are generally second order in the mesh element width. The convergence rate worsens to first order if low-order numerical quadrature is used to evaluate moment matrix elements with the EFIE formulation, or if a flat-facet mesh is employed with the MFIE formulation. Third-order convergence is also possible in some special cases. These results for the circular cylinder are empirically compared to computed error values for other smooth scatterer geometries. Convergence rates with respect to mesh refinement agree, but scatterers with regions of high curvature exhibit increased absolute error.

A coaxial line flush mounted on an infinite perfectly conducting ground plane and covered by a dielectric hemisphere is investigated. Green's functions for the region above the ground plane are derived with separated homogeneous and particular solution parts so as to be compatible with numerical analysis techniques. A magnetic field integral equation is obtained in terms of the unknown annular aperture tangential electric field and is solved by the method of moments. A comparison between the present case and that of a flush-mounted coaxial line with an infinite homogeneous region above the ground plane is presented in terms of the tangential aperture electric field, the coaxial line apparent input impedance and the far radiated field.

A superlens is a slab of metal sandwiched between two dielectric layers. This structure can produce the image of an object in close vicinity without suffering from diffraction limit. Better resolution can be achieved by using a multilayer structure of metal and dielectric. In this paper, a new numerically accurate and efficient method is proposed to analyze a multilayer superlens structure. A Method of Moment (MoM) solution of the Magnetic Field Integral Equation (MFIE) formulation of the problem using Complex Images (CI) representation of the required Green's function is employed. First a single slab of silver as a superlens at 356nm and 633nm wavelengths will be analyzed, next a multilayer structure will be designed to overcome the diffraction limit of the single layer structure in the visible light frequency range.

The investigation of the heating mechanism of a material sample in an energized electromagnetic cavity requires the understanding of the interaction of the electromagnetic fields with the material sample in a cavity. The key step for this understanding is to quantify the distribution of the induced electric field by solving an Electric Field Integral Equation (EFIE) or a Magnetic Field Integral Equation (MFIE) inside the material sample placed in the cavity. In this study, a complete set of vector wave functions which include both solenoidal and irrotational functions are employed. EFIE and MFIE are derived based on the expansion of these vector wave functions. Due to the slow convergence of the dyadic Green's function, some schemes were developed to improve the convergence rate of the numerical calculation in order to save computation time. Numerical results of some material samples agree well with theoretical estimations.