Computations of electromagnetic fields by the multiple multipole method (generalized multipole technique) (original) (raw)
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Fast multipole method based solution of electrostatic and magnetostatic field problems
Computing and Visualization in Science, 2005
Applications of boundary element methods (BEM) to the solution of static field problems in electrical engineering are considered in this paper. The choice of a suitable BEM formulation for electrostatics, steady current flow fields or magnetostatics is discussed from user's point of view. The dense BEM matrix is compressed with an enhanced fast multipole method (FMM) which combines well-known BEM techniques with the FMM approach. An adaptive grouping scheme for problem oriented meshes is presented along with a discussion on the influence of the mesh to the efficiency of the FMM. The computational costs of the FMM algorithm are analyzed for typical problems in practice. Finally, some electrostatic and magnetostatic numerical examples demonstrate the simple usability and the efficiency of the FMM. 1 Introduction By today, numerical field simulations have become accepted tools in science and industry. Engineers demand fast and accurate numerical solutions along with an easy handling of the software tool. Of course, these points are mainly influenced by the implementation of a numerical method and its user interface. But the underlying numerical method is very important, too. That's why boundary element methods are very attractive for practical applications. Only the surfaces of the considered bodies must be modeled and discretized, since the surrounding air is implicitly taken into account. This fact makes the pre-processing clear and simple. Experienced users can easily control the mesh quality as well as accuracy and processing time. Users of numerical simulation Dedicated to George C. Hsiao on the occasion of his 70th birthday.
A parallel version of the fast multipole method
1990
Abstract This paper presents a parallel version of the fast multipole method (FMM). The FMM is a recently developed scheme for the evaluation of the potential and force fields in systems of particles whose interactions are Coulombic or gravitational in nature. The sequential method requires O (N) operations to obtain the fields due to N charges, rather than the O (N 2) operations required by the direct calculation.
On the location and number of expansion centers for the generalized multipole technique
Electromagnetic Compatibility, IEEE …, 1996
The generalized multipole technique is investigated here from the perspective of determining a scheme for placing the multipole sources. The multipole technique is described using only the monopole current filament model. A limiting process is developed to determine the location and number of sources correlated to the radius of curvature of the scatterer. The ideas presented are verified by analyzing the convergence of the method using circular and elliptical cylinders. It is shown that ellipses with major to minor axis ratios up to 5:l converge in a fashion comparable to the circular case.
Progress In Electromagnetics Research M, 2019
In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The goal of this study is to investigate the similarities and differences between the spectral domain analysis and conventional FMM formulation. The benefit of the spectral domain analysis such as transforming the convolutional form of the Green's function to a multiplicative form is incorporated in the SD-FMM method. The study focuses on the application of SD-FMM to one-, two-, and three-dimensional electric field integral equation (EFIE). The cases of perfectly electric conducting (PEC) strips, circular perfectly conducting cylinders, and perfectly conductor spheres are analyzed. The results from the SD-FMM method are compared with the results from the conventional FMM and the direct application of Method of Moments (MoM). The SD-FMM results agree well with results from the direct application of MoM.
A simple numerical experiment of GREEN's function expansion in the Fast Multipole Method
In this paper the theoretical foundation of the fast multipole method (FMM) applied to electromagnetic scattering problems is briefly presented, the truncation of the GREEN's function expansion is revisited, and the well established truncation criteria, in terms of the relative accuracy of the solutions of the electric field integral equation, is revised from a numerical experiment. From this numerical procedure an interesting result for the number L of poles is reported. In FMM L is the number of terms in the GREEN's function expansion and it determines the precision of such an expansion. In our experiment a lesser value of L is obtained compared to previous studies.
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Applied Optics, 1995
The potency and versatility of a numerical procedure based on the generalized multipole technique 1GMT2 are demonstrated in the context of full-vector electromagnetic interactions for general incidence on arbitrarily shaped, geometrically composite, highly elongated, axisymmetric perfectly conducting or dielectric objects of large size parameters and arbitrary constitutive parameters. Representative computations that verify the accuracy of the technique are given for a large category of problems that have not been considered previously by the use of the GMT, to our knowledge. These problems involve spheroids of axial ratios as high as 20 and with the largest dimension of the dielectric object along the symmetry axis equal to 75 wavelengths; sphere-cone-sphere geometries; peanut-shaped scatterers; and finite-length cylinders with hemispherical, spherical, and flat end caps. Whenever possible, the extended boundary-condition method has been used in the process of examining the applicability of the suggested solution, with excellent agreement being achieved in all cases considered. It is believed that the numerical-scattering results presented here represent the largest detailed three-dimensional precise modeling ever verified as far as expansion functions that fulfill Maxwell's equations throughout the relevant domain of interest are concerned.