A study on the parameters of an approach that combines the characteristic basis function method and the multilevel fast multipole algorithm is presented. This approach is a very efficient scheme for the rigorous compu...
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A study on the parameters of an approach that combines the characteristic basis function method and the multilevel fast multipole algorithm is presented. This approach is a very efficient scheme for the rigorous computation of electrically large problems. An analysis of the configuration parameters of the method to obtain accurate results reducing CPU time is shown. Non-uniform rational B-splines surfaces are employed for the representation of the geometry and the characteristic basis functions are described in terms of curved rooftops generated in the parametric space. The associated macro-testing functions are defined as aggregations of curved razor-blade functions.
The multilevel fast multipole algorithm (MLFMA) based on the Nystrom discretization of surface integral equations (SIEs) is developed for solving electromagnetic (EM) scattering by large composite objects. Traditional...
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The multilevel fast multipole algorithm (MLFMA) based on the Nystrom discretization of surface integral equations (SIEs) is developed for solving electromagnetic (EM) scattering by large composite objects. Traditionally, the MLFMA is based on the method of moments (MoM) discretization for the SIEs and it usually works well when the robust Rao-Wilton- Glisson (RWG) basis function is enough to represent unknown currents. However, the RWG basis function may not represent both the electric and magnetic current in solving the electric field integral equation (EFIE) and magnetic field integral equation (MFIE) for penetrable objects, and how one represents another current could be a problem in the MoM. In this work, we use the Nystrm method as a tool to discretize the SIEs and incorporate the MLFMA to accelerate the solutions for electrically large problems. The advantages of the Nystrm discretization include the simple mechanism of implementation, lower requirements on mesh quality, and no use of basis and testing functions. These benefits are particularly desired in the MLFMA because the solved problems are very large and complex in general. Numerical examples are presented to demonstrate the effectiveness of the proposed scheme.
As the fastest integral equation solver to date, the multilevel fast multipole algorithm （MLFMA） has been applied successfully to solve electromagnetic scattering and radiation from 3D electrically large objects. Bu...
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As the fastest integral equation solver to date, the multilevel fast multipole algorithm （MLFMA） has been applied successfully to solve electromagnetic scattering and radiation from 3D electrically large objects. But for very large-scale problems, the storage and CPU time required in MLFMA are still expensive. fast 3D electromagnetic scattering and radiation solvers are introduced based on MLFMA. A brief review of MLFMA is first given. Then, four fast methods including higher-order MLFMA （HO-MLFMA）, fast far field approximation combined with adaptive ray propagation MLFMA （FAFFA-ARP-MLFMA）, local MLFMA and parallel MLFMA are introduced. Some typical numerical results demonstrate the efficiency of these fast methods.
In this paper, a hybrid Integral Equation-Domain Decomposition Method-multilevel fast multipole algorithm (IE-DDMMLFMA) with Gauss-Seidel iterative technique is proposed to calculate the scattering from perfectly elec...
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In this paper, a hybrid Integral Equation-Domain Decomposition Method-multilevel fast multipole algorithm (IE-DDMMLFMA) with Gauss-Seidel iterative technique is proposed to calculate the scattering from perfectly electric conducting Body of Translation (BoT). The BoT can be partitioned into translational nonoverlapping sub-domains. A hybrid local/global MLFMA framework is adopted to realize efficient matrix-vector multiplication in sub-domains and between sub-domains by utilizing the feature of translational invariance of BoT. To reduce the number of interactions between sub-domains, Gaussian-Seidel iterative technique is applied. Numerical examples are presented to demonstrate the efficiency of the present method.
An efficient hybrid method is proposed to analyze the electromagnetic scattering from the composite structures comprising PEC and inhomogeneous high-contrast dielectric materials with the volume-surface integral equat...
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An efficient hybrid method is proposed to analyze the electromagnetic scattering from the composite structures comprising PEC and inhomogeneous high-contrast dielectric materials with the volume-surface integral equation (VSIE) approach, which uses the main framework of the multilevel fast multipole algorithm (MLFMA) but adopts the multilevel adaptive cross approximation algorithm (MLACA) and the equivalent dipole-moment (EDM) to deal with part of the "strong" interaction of MLFMA. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed scheme.
Calderon 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 s...
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Calderon 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 Calderon preconditioner are singular at resonant frequencies. In this paper, the resonance problem of the Calderon preconditioner is removed by using a complex wavenumber, and that of the EFIE is eliminated by enforcing the boundary condition (n) over cap . D = rho(s) to the EFIE, resulting in the so-called augmented EFIE (AEFIE). It is shown that the proposed Calderon 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.
We present design and simulation of three-dimensional (3D) shell structures, which generate directional radiation patterns from isotropic sources thanks to their near-zero-index (NZI) characteristics, as well as reali...
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We present design and simulation of three-dimensional (3D) shell structures, which generate directional radiation patterns from isotropic sources thanks to their near-zero-index (NZI) characteristics, as well as realizations of these shells via low-cost 3D printing. Throughout the design process of NZI beam generators, both homogenized structures, for which near-zero relative permittivity and/or permeability values are enforced, and actual models involving periodic arrangements of dielectric rods are considered. Solutions of the electromagnetic problems are obtained by using rigorous implementations of the state-of-the-art surface-integral-equation (SIE) formulations in frequency domain. Iterative solutions of matrix equations derived from SIEs are accelerated by different forms of the multilevel fast multipole algorithm (MLFMA) and suitable preconditioners, when necessary. In the design process of NZI shells, alternative strategies are employed to obtain customized radiation patterns. In this context, various cavities with strong resonance behaviors are designed as source regions. At the same time, outer surfaces are modified to either enhance or suppress outgoing electromagnetic fields. In addition to comprehensive simulations and analyses of NZI beam generators, their capabilities are verified by measurements, specifically at 10.3 GHz, on different prototypes fabricated via 3D printing. Measurements of diverse NZI shell structures are presented to demonstrate that NZI properties can successfully be achieved by well-designed arrangements of dielectric rods with proper materials. The results demonstrate the feasibility of efficient, effective, low-cost, and reconfigurable NZI shells to generate alternative beam configurations that can be useful in a plethora of microwave applications.
We present a novel stabilization procedure for accurate surface formulations of electromagnetic scattering problems involving three-dimensional dielectric objects with arbitrarily low contrasts. Conventional surface i...
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We present a novel stabilization procedure for accurate surface formulations of electromagnetic scattering problems involving three-dimensional dielectric objects with arbitrarily low contrasts. Conventional surface integral equations provide inaccurate results for the scattered fields when the contrast of the object is low, i.e., when the electromagnetic material parameters of the scatterer and the host medium are close to each other. We propose a stabilization procedure involving the extraction of nonradiating currents and rearrangement of the right-hand side of the equations using fictitious incident fields. Then, only the radiating currents are solved to calculate the scattered fields accurately. This technique can easily be applied to the existing implementations of conventional formulations, it requires negligible extra computational cost, and it is also appropriate for the solution of large problems with the multilevel fast multipole algorithm. We show that the stabilization leads to robust formulations that are valid even for the solutions of extremely low-contrast objects. (C) 2008 Elsevier Inc. All rights reserved.
A generalized hybrid scheme combining finite element method (FEM) and the method of moments (MOM) is first presented to investigate scattering from a 3-D dielectric object above a 2-D dielectric rough surface. The hyb...
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A generalized hybrid scheme combining finite element method (FEM) and the method of moments (MOM) is first presented to investigate scattering from a 3-D dielectric object above a 2-D dielectric rough surface. The hybrid FEM/MOM scheme is divided into the FEM region for the object based on Helmholtz's equation and the MOM region for the rough surface based on coupled integral function, which can greatly reduce the computed region. With the rough surface getting larger, the unknowns of the rough surface get more. So MLFMA is employed to reduce computation complexity of MOM region itself and coupling interaction matrices between MOM region and FEM region. Consequently, the iterative process can be greatly accelerated. This generalized hybrid FEM/MOM is very suitable for investigating scattering from composite model of a complex material object and electrically large dielectric rough surface. Some examples verify this generalized hybrid FEM/MOM in high efficiency, low storage requirement, high precision and generality.
In practical applications, frequency-selective surfaces (FSSs) are finite, and sometimes even curved. In this paper, we present a hybrid volume-surface integral-equation approach to analyze the transmission and reflec...
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In practical applications, frequency-selective surfaces (FSSs) are finite, and sometimes even curved. In this paper, we present a hybrid volume-surface integral-equation approach to analyze the transmission and reflection characteristics of finite and curved FFS structures. The hybrid integral equations are established using the surface- and volume-equivalent principles. This approach has two advantages. One is the capability of modeling arbitrarily shaped FSS structures in detail, the other one allows its to easily apply the multilevelfast multiple algorithm to speed up the solution process. The scattering characteristics and frequency responses of several FSSs are analyzed. The simulation results show that for a finite-sized FSS, reducing the radius of curvature causes amplitude variation, frequency shift, and bandwidth change in the reflection and transmission responses. (c) 2005 Wiley Periodicals, Inc.
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