Surface Integral Equation With Multibranch RWG Basis Functions for Electromagnetic Scattering From Dielectric Objects

A discontinuous Galerkin (DG) surface integral equation method is proposed for electromagnetic scattering from targets with the impedance boundary condition (IBC). We present electric field integral equation (EFIE), magnetic field integral equation (MFIE), and self‐dual integral equation formulations for the problem and study their numerical performance. On the basis of the results of these experiments, DG is developed for EFIE and MFIE (DG‐EFIE and DG‐MFIE). The convergence of the iterative solutions and the solution accuracy of DG‐EFIE and DG‐MFIE are further investigated for a wide range of surface impedances. The numerical performance of these formulations is found to be nearly complementary with respect to the surface impedance. The capability of the proposed DG solution strategy for calculating scattering from large multiscale IBC targets is demonstrated.

The surface integral equation method is one of the most popular numerical methods for the electromagnetic analysis of composite metallic and dielectric structures. In this paper, the authors seek the "optimal" surface integral equation formulations for closed metallic, homogeneous and piecewise homogeneous dielectric and composite objects by studying the properties of the integral equations. The goal is to develop formulations in which all unknown quantities are well tested in the Galerkin method and the discretized matrix equation has good spectral properties leading to rapidly converging iterative solutions. The results show that by deriving the equations so that they map the currents onto itself and are directly tested in the same space as the unknowns are expanded can significantly improve conditioning of the matrix equation.

Recently, scattering from 3D composite conducting and dielectric object receives much attention. Traditionally, FEM-BI method is applied to solve the problem. But absorption boundary condition (ABC) is needed in FEM-BI method. In this paper, we use two combinations of surface integral equation to solve the RCS of 3D composite conducting and dielectric object. Fast multipole method (FMM) is used. The problem is formulated in terms of a set of coupled integral equations involving equivalent electric and magnetic surface currents based on the equivalence theorem. The conducting structures and the dielectric materials are modeled by planar triangular patches, RWG basis and Galerkin method are used. The fast multipole method is applied to accelerate the computation of matrix-vector multiplication. The computational complexity and storage requirement is O(N/sup 1.5/), respectively. Numerical results are given for various structures and compared with other available data. The numerical results show that the present method has satisfying accuracy.

Surface integral equations (SIEs) are commonly used to formulate scattering and radiation problems involving three-dimensional metallic and homogeneous dielectric objects with arbitrary shapes [1]–[3]. For numerical solutions, equivalent electric and/or magnetic currents defined on surfaces are discretized and expanded in a series of basis functions, such as the Rao-Wilton-Glisson (RWG) functions on planar triangles. Then, the boundary conditions are tested on surfaces via a set of testing functions. Solutions of the resulting dense matrix equations provide the expansion coefficients of the equivalent currents, which can be used to compute the scattered or radiated electromagnetic fields. In general, SIEs involve three basic operators, i.e., integro-differential K and T operators, and the identity operator I{X}(r) = X(r). Depending on the testing scheme and the boundary conditions used, there are four basic SIEs [2],[3], namely, the tangential electric-field integral equation (T-EFIE), the normal electric-field integral equation (N-EFIE), the tangential magnetic-field integral equation (T-MFIE), and the normal magnetic-field integral equation (N-MFIE). In the tangential equations, boundary conditions are tested directly by sampling the tangential components of the electric and magnetic fields on the surface. In the normal equations, however, electromagnetic fields are tested after they are projected onto the surface via a cross-product operation with the outward normal vector.

Conference of 42nd Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2015, Incorporating the 6th European-American Workshop on Reliability of NDE ; Conference Date: 26 July 2015 Through 31 July 2015; Conference Code:119404

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.

The single-source integral equation (SSIE) technique is presented to analyze electromagnetic scattering from an arbitrarily shaped three-dimensional conducting object coated by a homogeneous dielectric body. The external and interior surface equivalence principles combined with the continuity of the tangential components of the total electric and magnetic fields on the surface of the dielectric and zero tangential component of the total electric field on the surface of the conductor are used to formulate the single-source electric and magnetic field integral equations. With a localization procedure, the Calderon preconditioned single-source electric field integral equation (SSEFIE) is constructed and combined with single-source magnetic field integral equation (SSMFIE) to produce a single-source combined field integral equation (SSCFIE), which is free from spurious resonance and dense-mesh breakdown. Numerical results validate the good performance of the proposed algorithm.

The “conventional” finite element‐boundary integral (FE‐BI) method suffers from two major drawbacks, one is the huge computer resources required by the dense BI submatrix; the other is the slow convergence rate of the resulting linear system of equations. In this article, both the drawbacks are investigated. First, the integral equation fast Fourier transform (IE‐FFT) algorithm with a Gaussian interpolation scheme is employed to deal with the BI part. Second, an effective and simple preconditioner is developed for solving the matrix equation obtained from FE‐BI method. Numerical results show that the proposed preconditioner can dramatically speed up the convergence of the FE‐BI system, whatever the combined field integral equation (CFIE), the electric field integral equation (EFIE), and the magnetic field integral equation (MFIE) are employed on the truncation boundary. Some examples are given to demonstrate the accuracy and efficiency of the method. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2065–2071, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24538

In this paper, we present four different formulations for the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional (3-D) homogeneous dielectric body in the frequency domain. The four integral equations treated here are the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), the combined field integral equation (CFIE), and the PMCHW (Poggio, Miller, Chang, Harrington, and Wu) formulation. For the CFIE case, we propose eight separate formulations with different combinations of expansion and testing functions that result in sixteen different formulations of CFIE. One of the objectives of this paper is to illustrate that not all CFIE are valid methodologies in removing defects, which occur at a frequency corresponding to an internal resonance of the structure. Numerical results involving the equivalent electric and magnetic currents, far scattered fields, and radar cross section (RCS) are presented for three canonical dielectric scatterers, viz. a sphere, a cube, and a finite circular cylinder, to illustrate which formulation works and which does not.

Characteristic mode (CM) analysis of multi-scale and complex targets has attracted much attention in computational electromagnetics. However, it is hard to calculate the multi-scale problems in terms of desired accuracy and stability by using conventional methods. What is more, it is a challenging work to generate a good quality mesh for the multi-scale structures including very fine features. In this paper, we present Discontinuous Galerkin (DG) surface integral equations-based theory to analyze the CMs. The multi-scale objects are firstly divided into several subdomains, and we generate the meshes of every parts independently. HRWG basis functions are adopted in our work and the characteristic currents are expanded by HRWG basis functions. In many applications, only characteristic currents with small eigenvalues are desired because they are corresponding to the modes that radiate efficiently and have large modal coefficients. Special singularity extraction schemes are chosen to treat the infinite term in the resulting integral equations since HRWG basis functions are not divergence-conforming and there is divergence operator in electric field integral equation (EFIF) and magnetic field integral equation (MFIE). In DG method, they are no requirements for normal continuity of currents across the contour of between every two subdomains, hence, the proposed method can handle both non-conformal mesh and conformal mesh. Numerical results are presented to validate the propose formulation. This work may offer great flexibility to CM analysis of multi-scale and complex structures.

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.

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.

This article introduces a new method for discretizing and solving integral equation formulations of Maxwell's equations, which achieves spectral accuracy for smooth surfaces. The approach is based on a hybrid Nyström-collocation method using Chebyshev polynomials to expand the unknown current densities over curvilinear quadrilateral surface patches. As an example, the proposed strategy is applied to the magnetic field integral equation (MFIE) and the N-Müller formulation for scattering from metallic and dielectric objects, respectively. The convergence is studied for several different geometries, including spheres, cubes, and complex NURBS geometries imported from CAD software, and the results are compared against a commercial Method-of-Moments solver using RWG basis functions.

The detection of concealed objects in the baggage by non-invasive methods has become a very important issue in the border control process. This paper is concerned with the multiple inverse scattering of the plane wave on various objects or scatterrers by using µ-diff MATLAB open-source toolbox. The acquired information is corelated with the material nature (i.e. steel, salt, neoprene and PVC) for different measured orientation of the scatterers. The non-invasive detection of concealed objects represents a huge challenge, which has attracted particular attention due to a heightened threat of terrorism. The Fourier series and on four integral equations, i.e. Electric Field Integral Equation (EFIE), Magnetic Field Integral Equation (MFIE), Combined Field Integral Equation (CFIE) and Brakhage-Werner Integral Equation (BWIE) generate the approximation framework able to solve the multiple scattering problems. A multi-frequency scattering data approach is adopted and a low frequency domain is proposed for detecting concealed objects in the luggage.

A new acceleration method is proposed for efficiently solving the problem of electromagnetic scattering from metal targets in half-space. The analysis of electromagnetic problems in any structure can be settled by the electric field integral equation. But the generated matrix condition number is large and the iterative solution has poor convergence. The number of the matrix condition generated by the magnetic field integral equation is small and iterative convergence is good. But only the closed structure problems can be worked out. The combined field integral equation is adopted because of the universality of the electric field integral equation and the convergence of the magnetic field integral equation. The gradient term of Green's function is involved in the integral equation of the mixed field. In order to further enhance the calculation efficiency, an efficient four-dimensional spatial interpolation method is introduced for half-space Green's function. Tabulation and lagrange interpolations are performed in the Sommerfeld integrals for the half-space Green's function. The improved efficiency can be 7.5 times higher than that of the traditional combined field integral equation(CFIE). Numerical results show that the computational time can be reduced significantly by the proposed method with encouraging accuracy.