Quasi-periodic electromagnetic surfaces have similar planar elements located on periodic lattices. Because the elements are different, the periodic boundary condition is not accurate for full wave modeling of quasi-pe...
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ISBN:
(纸本)9780996007849
Quasi-periodic electromagnetic surfaces have similar planar elements located on periodic lattices. Because the elements are different, the periodic boundary condition is not accurate for full wave modeling of quasi-periodic electromagnetic surfaces. In order to utilize the periodicity of elements to accelerate the full wave simulation, this work applies the idea of equivalence principle algorithm and projects the current of different elements onto periodic equivalence surfaces. The projection process can be written in matrix operators. For unknowns on the equivalence surfaces, the reduced basis method can be applied to reduced the number of unknowns. After extracting the periodicity or the translational invariance of the element alignment, the fast Fourier transform can be used to accelerate matrix vector production in iterative solvers for method of moments. It can reduce the computational complexity of matrix vector production from O(N-2) to O(N logN), where N is the number of elements. Numerical examples show the algorithm can accelerate iterative solvers and has potential to solve large quasi-periodic electromagnetic surfaces.
In this thesis, a domain decomposition method based on the Huygens' principle for integral equations is studied. Step-by-step development of equivalenceprinciple al- gorithm (EPA) is described for solving arbitra...
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In this thesis, a domain decomposition method based on the Huygens' principle for integral equations is studied. Step-by-step development of equivalenceprinciple al- gorithm (EPA) is described for solving arbitrary shaped perfect electric conductor (PEC) and penetrable objects. The main advantage of EPA is its efficiency thanks to the enhanced conditioning hence accelerated iterative solutions of the matrix equa- tions derived from discretizations. For further enhancing the efficiency, the multilevel fast multipole algorithm (MLFMA) is used to speed up the matrix-vector multiplica- tions (MVMs) in EPA. Following standard implementations, a novel implementation of EPA using potential integral equations (PIEs) is further presented. EPA is general- ized to be compatible with PIEs used to formulate inner problems inside equivalence surfaces. Based on the stability of PIEs at low frequencies, the resulting EPA-PIE im- plementation is suitable for low-frequency problems involving dense discretizations with respect to wavelength. Along with the formulation and demonstration of the EPA-PIE scheme, high accuracy and stability of the implementation are presented on canonical problems.
A new domain decomposition scheme based on equivalence principle algorithm (EPA) is proposed for analyzing electromagnetic scattering from connected structures. The EPA transforms the unknown of inside scatterers to t...
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A new domain decomposition scheme based on equivalence principle algorithm (EPA) is proposed for analyzing electromagnetic scattering from connected structures. The EPA transforms the unknown of inside scatterers to the unknown on the equivalence surfaces which enclose the scatterers. The challenge arises when the equivalence surface intercepts the connected scatterers, because the current will be singular at the connection that is hard to model. In this paper, a new scheme based on source reconstruction method (SRM) is introduced to deal with the connected problems. This scheme can avoid the current singularity and keep the good convergence of EPA equations. Furthermore, generalized EPA (GEPA) is proposed to improve the theory of EPA and the ability to solve real life problems. Numerical results demonstrate the accuracy and efficiency of the proposed method.
In the solution of a radiation problem on a large-scale antenna array with a large perfect electrically conducting object, the equivalence principle algorithm hybridized with physical optics has been used to accelerat...
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In the solution of a radiation problem on a large-scale antenna array with a large perfect electrically conducting object, the equivalence principle algorithm hybridized with physical optics has been used to accelerate the calculation. However, the efficiency of this hybridization will be low if the number of elements in the antenna array is large. This article proposes a novel method to speed up the equivalence principle algorithm hybridized with physical optics by introducing the periodic equivalence principle algorithm. The calculation of the couplings among the elements will be simplified, and the elapsed time will decrease. At the same time, the total memory required will be saved.
The conventional equivalence principle algorithm (EPA) exploits cubical surfaces to support equivalent sources. However, it introduces strong discontinuities due to sharp edges and corners. In this letter, a spherical...
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The conventional equivalence principle algorithm (EPA) exploits cubical surfaces to support equivalent sources. However, it introduces strong discontinuities due to sharp edges and corners. In this letter, a spherical surface is employed as the equivalence surface to avoid singularities from nonsmoothness. To achieve better accuracy, the meshless sampling scheme is used for integral operators on the spherical equivalence surface. The numerical examples are provided to validate the performance enhancement of EPA through the proposed method.
Conventional equivalence principle algorithm (EPA) employs cubical boxes to support equivalence sources. However, it introduces strong discontinuities. In this work, a spherical surface is employed as the equivalence ...
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ISBN:
(纸本)9781479962815
Conventional equivalence principle algorithm (EPA) employs cubical boxes to support equivalence sources. However, it introduces strong discontinuities. In this work, a spherical surface is employed as the equivalence surface in EPA to avoid singularities from non-smooth surfaces. Further to achieve high order accuracy, meshless samples are used for the integrals on the spherical surface to avoid the equivalence surface mesh discretization. Theoretically the accuracy of EPA can be significantly improved, which was further benchmarked though numerical examples. Various meshless schemes are also discussed to achieve the optimal solution based on the spherical equivalence surface.
It is common that spherical scatterers are used to represent air bubbles or brine inclusions embedded in the snow or sea ice layer. This physical configuration is then solved using radiative transfer theory to obtain ...
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ISBN:
(纸本)9781467372183
It is common that spherical scatterers are used to represent air bubbles or brine inclusions embedded in the snow or sea ice layer. This physical configuration is then solved using radiative transfer theory to obtain backscattering coefficient from the snow or sea ice layer. With the advent of new techniques in computational electromagnetics, the typical theoretical model of single layer of snow or sea ice can be easily extended to consider types of scatterers which are of other shapes or irregular shapes. A computational electromagnetic method based on equivalence principle algorithm can be incorporated into existing theoretical model to calculate the backscattering coefficient of layers using radiative transfer theory. Averaging over different orientation angles of the scatterers in the medium is also needed in the calculation of phase matric and extinction matrix of scatterers when the scatterers are no longer limited in spherical shape. Theoretical analysis of the developed model is presented for this extension work.
An equivalence principle algorithm (EPA) method is extended to analyze the electromagnetic scattering from multiple bodies of revolution (MBoR) with the axes arbitrarily oriented. equivalence spheres are used to enclo...
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An equivalence principle algorithm (EPA) method is extended to analyze the electromagnetic scattering from multiple bodies of revolution (MBoR) with the axes arbitrarily oriented. equivalence spheres are used to enclose each BoR and the equivalence currents are expanded by the basis functions of bodies of revolution (BoR). To obtain the scattering operators and translation operators of EPA for Fourier modes independently, the rotational symmetry systems are established in local BoR coordinate systems. The origin of the local BoR coordinate system is located at the center of the equivalence sphere and the z-axis coincides with the axis of the enclosed BoR to obtain the scattering operator of each equivalence sphere, whereas the origin is located at the observation sphere and z-axis passes through the center of the source sphere to obtain the translation operator of each pair of equivalence spheres. The current coefficient transformation algorithm is used to transform the equivalence currents among local BoR coordinate systems. The total equation is iteratively solved in the global coordinate system. The proposed scheme is especially efficient for the analysis of scattering from MBoR randomly distributed in electrically large scale region. Numerical results are given to demonstrate the efficiency.
In this paper, equivalence principle algorithm (EPA) with grid-robust higher order vector basis (GRHOVB) is proposed to solve the multiscale problems. The EPA is a kind of domain decomposition method which transforms ...
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In this paper, equivalence principle algorithm (EPA) with grid-robust higher order vector basis (GRHOVB) is proposed to solve the multiscale problems. The EPA is a kind of domain decomposition method which transforms the interaction of objects into the interaction between virtual equivalence surfaces. Compared with traditional Curvilinear Rao-Wilton-Glisson function, GRHOVB can be used on the equivalence surface to reduce the number of unknowns and also to improve the accuracy. The tap basis is utilized to deal with current continuity when the object is intercepted by an equivalence surface. The equations are simplified further to improve the tap basis scheme. Moreover, to accelerate the solution, multilevel fast multipole algorithm is utilized in EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed method.
A hybrid method combining the equivalence principle algorithm (EPA) with physical optics (PO) is proposed to solve electromagnetic radiation of an antenna array with perfectly electrically conducting (PEC) object of a...
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A hybrid method combining the equivalence principle algorithm (EPA) with physical optics (PO) is proposed to solve electromagnetic radiation of an antenna array with perfectly electrically conducting (PEC) object of arbitrary shape. The main idea of this approach is based on the domain decomposition method which is a scheme for multi-scale problems. An EPA can simulate antenna array accurately, and PO is an asymptotical method to obtain current distribution on a PEC object of arbitrary shape as an electrically large problem. For an antenna array with identical elements, the equivalenceprinciple operator only needs to be calculated and be stored once. Compared with the original EPA, this approach performs with higher efficiency and fewer iterations with acceptable accuracy. Numerical results demonstrate the feasibility of the hybrid method.
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