Search

In this work, we propose simple and efficient tridiagonal computed sparse preconditioners for improving the condition number for large compressed electric field integral equation (EFIE) method of moment (MoM) matrix. The preconditioner computation is based on the triangle and block triangle interaction and filled tridiagonally. The computed preconditioner is highly sparse and retains the ${O(N)}$ complexity of computation and preconditioner matrix solution time. Numerical results show the efficiency and accuracy of the proposed preconditioner. [ABSTRACT FROM AUTHOR]

In the solution of frequency- and time-domain integral equations, the singularity cancellation transformations are well-known for the treatments of the singular integrals involving Green’s functions and their gradients. The cancellation transformations for strongly near-singular integrals become inaccurate and inefficient for an extremely deformed triangular patch, and this phenomenon is referred to as shape-dependent problem in this article. As the degree of the singularity increases, the shape-dependent problem of strong near-singularity is more severe than that of the weakly near-singular integrals. Furthermore, if the source triangle is deformed, the accuracy of the cancellation methods decreases when no near singularity exists. In this work, we first investigate the reason for these problems via the theoretical analysis with numerical verification. Second, an updated framework of singularity cancellation methods for strongly near-singular integrals is proposed, which has a fast and consistent convergence rate for both regular and irregular triangles. Third, some numerical experiments are presented to illustrate the effectiveness of the theoretical framework and the proposed transformations. [ABSTRACT FROM AUTHOR]

The singularity cancellation transformations are well-known for calculating weakly singular and near-singular integrals in integral equation solutions. However, some singularity cancellation methods suffer from the shape-dependent problem of inaccuracy and inefficiency for deformed triangles. By the theoretical analysis and numerical verification in this article, the relation between the near-singularity and shape-dependence of the singularity cancellation schemes is discussed. Moreover, a novel framework for devising cancellation transformations of weakly near-singular integrals is presented, which results in fast convergence for both regular and irregular triangular domains. Some numerical results are given to illustrate the validity of the theoretical framework and the efficiency of the proposed transformations. [ABSTRACT FROM AUTHOR]

Implementation of max-ortho basis functions is proposed in a method for analysis of axially symmetric metallic antennas based on exact kernel of electric field integral equation in combination with Galerkin testing. High-precision evaluation of matrix elements is enabled by: a) representing them as a linear combination of impedance integrals due to the Legendre polynomials and their first derivatives; b) using the singularity cancelation techniques; and c) evaluating the Legendre polynomials and their first derivatives by well-known recurrent formulas. Applicability of max-ortho bases up to expansion order of $n =128$ is illustrated on a full-wave thick dipole antenna. [ABSTRACT FROM AUTHOR]

Electromagnetic scattering by super-thin conducting objects is formulated by integral equation approach. It could be difficult to obtain accurate solutions for such a problem because the current density changes dramatically near the edges of such objects and many low-quality meshes exist on the side faces of objects when discretized. Traditionally, the electric field integral equation is used to describe the problem and the three-dimensional (3-D) objects are approximated as a two-dimensional (2-D) open structure with a summation of the current density at two opposite sides. In this communication, the magnetic field integral equation (MFIE) is employed to govern the problem and the super-thin objects are strictly treated as 3-D objects. The MFIE is a second-kind integral equation resulting in a better conditioning and can also release the low-frequency breakdown problem, but it has not been applied to very thin structures. In the method of moments solution, a robust near-singularity treatment for its kernel is developed based on the Green’s lemma. The derived formulations are friendly and very suitable for low-quality triangular meshes. Numerical examples are presented to demonstrate the scheme and good results have been obtained. [ABSTRACT FROM PUBLISHER]

A nested complex source beam (NCSB) method based on octree structure is proposed to accelerate the method-of-moments (MoM) solution for three-dimensional (3-D) electromagnetic scattering analysis. At the finest level, the far-field contribution of each basis function is expressed with that of complex source beams (CSBs) distributed on the equivalent sphere surface for every group. Furthermore, the far field radiated by CSBs of the source group at child level can be represented by that radiated by CSBs of the source group at parent level. Similarly, the received field of CSBs for each observation group at the parent level can be expressed with that of CSBs belong to their child level group. An equivalent relationship of CSBs between every two adjacent levels is built to obtain the nested equivalent process for NCSB method, and only the CSBs at the finest level have the direct association with the basis functions in their group. The NCSB method is shown to be O(NlogN) computational complexity for both matrix–vector product (MVP) time and memory storage by numerical examples with appropriate parameters, and numerical results demonstrate the better efficiency of the proposed method than the current multilevel CSB method. [ABSTRACT FROM PUBLISHER]

An efficient methodology is introduced for rapid analysis and design of three-dimensional (3-D) doubly periodic structures over a wide frequency range based on hybrid finite element boundary integral (FEBI) methods. The 3-D doubly periodic structures can be represented as nonorthogonal lattices composed of general inhomogeneous bianisotropic media with arbitrarily-shaped metallic patches. Based on Floquet theory and periodic boundary conditions, the original stated problem that involves infinite periodic structures can be converted into a single unit cell. Using the equivalence principle, the derived BI equation formulation is applied to the top and bottom surfaces of the unit cell, which results in a perfectly reflectionless boundary condition for the FE-based approach. Then, the unit cell was meshed using triangular prismatic volume elements, which provide a great deal of flexibility in modeling complex planar geometries with arbitrary shapes in the transverse direction. The adaptive integral method (AIM) was employed to accelerate the calculation of the matrix-vector product for the BI portion within the iterative solver. Furthermore, a model-based parameter estimation (MBPE) technique was proposed for the wide-band interpolation of the required impedance matrix elements in the BI part for near field components that were used in the AIM procedure. The accuracy and efficiency of the proposed hybrid algorithms are demonstrated by the presented numerical results (e.g., in comparison with analytical solutions). Several simulation results are presented to illustrate the flexibility of the proposed methods for analysis of frequency selective surfaces with arbitrarily-shaped metallic patches, bianisotropic materials, and nonorthogonal lattice configurations. [ABSTRACT FROM PUBLISHER]