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In nowadays, two dimensional integral equations are frequently used in various different engineering and scientific studies. In solving these equations using numerical and analytical methods along wide frequency spectrums; the electrical dimensions of the objects and the complexity of their geometric structures are considered as critical computational aspects. This article offers an effective solution to solve some integral equations. Various problems of the theory of diffraction realized by perfectly conductive metal plates are reduced to these integral equations. Thus, a method for solving integral equations is proposed to understand arbitrary values of frequency parameters and strip sizes. Diffraction theory, defines the diffraction processes that occur when waves such as in the form of light, encounter different obstacles in multiples of their wavelengths with dimensions. A certain bending and deflection of waves around these barriers is characterized by diffraction theory. In dealing with diffraction theory, advanced numerical and matrix-based solutions such as the moment method and the T-matrix method are used. On the other hand, the integralbased solutions proposed in this study are used effectively. The integral-based solution obtained from this study is simulated according to the different medium permeability which is calculated with the electrical dimension varying depending on the frequency of the wave, and a graphical representation is provided. It is seen that the normalized current value at the ends of the strip is maximum for two different cases where the medium permeability is 20 and 30. [ABSTRACT FROM AUTHOR]

The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as ω → 0 in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nyström discretization of a one-dimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples. • Efficient solver for wideband electromagnetic scattering from bodies of revolution. • Thorough discussion of the evaluation of modal Green's functions. • Computation of high-fidelity radar cross sections. • Numerical examples demonstrating that high-order accuracy is basically required for high-frequency calculations. [ABSTRACT FROM AUTHOR]

Resonances, i.e., extrema of the eigenvalues of characteristic modes for closed perfectly conducting objects are investigated. The characteristic modal solutions based on the electric, magnetic, and combined field integral operators (EFIO, MFIO, and CFIO) are studied and compared with analytical solutions for a sphere. All these formulations are found to capture both external (radiating) and internal (cavity) resonances predicted by the analytical expressions. At the internal resonances, the eigenvalues obtained with the EFIO- and MFIO-based approaches are not correct, and the corresponding modes are nonunique. These solutions also exhibit a strong duality between the electric (TM) and magnetic (TE) type modes. A connection is found between the external and internal resonances and the condition numbers of the matrices. The modal expansion of the CFIO-based solution is correct, even though it also experiences the nonuniqueness of the EFIO- and MFIO-based solutions. [ABSTRACT FROM PUBLISHER]

Calderón preconditioned electric-field integral equation (CP-EFIE) is very efficient in analyzing electromagnetic problems with a moderate electrical size. For the analysis of electrically large problems with closed surfaces, the CP-EFIE, however, suffers from the well-known spurious internal resonance problem because both the EFIE and the Calderón preconditioner are singular at resonant frequencies. In this paper, the resonance problem of the Calderón preconditioner is removed by using a complex wavenumber, and that of the EFIE is eliminated by enforcing the boundary condition n̂ · D = ρs to the EFIE, resulting in the so-called augmented EFIE (AEFIE). It is shown that the proposed Calderón preconditioned AEFIE is a resonant-free formulation, and has a fast convergence rate for an iterative solution. Numerical examples are given to demonstrate the good accuracy and fast convergence of the proposed approach for the analysis of electrically large problems. The multilevel fast multipole algorithm (MLFMA) is employed to reduce the computational and storage complexities of the iterative solution. [ABSTRACT FROM PUBLISHER]