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Song J. Cai-Cheng Lu Weng Cho Chew 《Antennas and Propagation, IEEE Transactions on》1997,45(10):1488-1493
The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are reviewed. The number of modes required, block-diagonal preconditioner, near singularity extraction, and the choice of initial guesses are discussed to apply the MLFMA to calculating electromagnetic scattering by large complex objects. Using these techniques, we can solve the problem of electromagnetic scattering by large complex three-dimensional (3-D) objects such as an aircraft (VFY218) on a small computer 相似文献
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An efficient static fast-multipole-method (FMM)-based algorithm is presented in this paper for the evaluation of the parasitic capacitance of three-dimensional microstrip signal lines above stratified dielectric media. The effect of dielectric interfaces on the capacitance matrix is included in the stage of FMM when outgoing multipole expansions are used to form local multipole expansions by the use of interpolated image outgoing-to-local multipole translation functions. The increase in computation time and memory usage, compared to the free-space case, is, therefore, small. The algorithm retains O(N) computational and memory complexity of the free-space FMM, where N is the number of conductor patches 相似文献
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Vande Ginste D. Michielssen E. Olyslager F. De Zutter D. 《Antennas and Propagation, IEEE Transactions on》2006,54(5):1538-1548
An efficient multilevel fast multipole algorithm (MLFMA) formalism to model radiation and scattering by/from large planar microwave structures is presented. The technique relies on an electric field integral equation (EFIE) formulation and a series expansion for the Green dyadic, based on the use of perfectly matched layers (PML). In this way, a new PML-MLFMA is developed to efficiently evaluate matrix-vector multiplications arising in the iterative solution of the scattering problem. The computational complexity of the new algorithm scales down to O(N) for electrically large structures. The theory is validated by means of several illustrative, numerical examples. 相似文献
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The fast multipole method (FMM) was originally developed for perfect electric conductors (PECs) in free space, through exploitation of the spectral properties of the free-space Green's function. In the work reported here, the FMM is modified, for scattering from an arbitrary three-dimensional (3-D) PEC target above or buried in a lossy half space. The “near” terms in the FMM are handled via the original method-of-moments (MoM) analysis, wherein the half-space Green's function is evaluated efficiently and rigorously through application of the method of complex images. The “far” FMM interactions, which employ a clustering of expansion and testing functions, utilize an approximation to the Green's function dyadic via real image sources and far-field reflection dyadics. The half-space FMM algorithm is validated through comparison with results computed via a rigorous MoM analysis. Further, a detailed comparison is performed on the memory and computational requirements of the MoM and FMM algorithms for a target in the vicinity of a half-space interface 相似文献
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An acceleration technique to the fast multipole method (FMM) has been proposed to handle large-scale problems of periodic structures in free space with finite sizes based on the accurate sub-entire-domain basis functions. In the proposed algorithm, only nine (or 27) elements in the whole impedance matrix are required to be computed and stored for a two-dimensional (or three-dimensional) periodic structure, and the matrix-vector multiply can be performed efficiently using the combination of fast Fourier transform and FMM. The theoretical analysis and numerical results show that both the memory requirement and computational complexity are only of the order of O(N) with small constants, where N is the total number of unknowns 相似文献
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By virtue of its low operation count, the application of the fast multipole method (FMM) results in a substantial speed-up of the boundary-integral (BI) portion of the hybrid finite-element/boundary-integral technique, independent of the shape of the BI contour. Previously, various versions of the fast multipole method have been proposed, each introducing a different approximation to the implementation of the boundary integral. The main goal of this paper is to provide a comparison of the various FMM approaches on the basis of implementation, CPU time, and accuracy. To gain an appreciation of the differences among the various FMM methodologies, a large portion of the paper is devoted to a discussion of the algorithms at a tutorial level. Flow charts and pseudo-code are also given, at sufficient detail to facilitate their implementation. We present quantitative CPU and memory requirements, using the scattering by a groove as the basis for comparison, and conclude that the FMM can accelerate the BI computation without any significant deterioration in accuracy. A simpler FMM-based algorithm results in a much smaller execution time but has a larger error. However, it turns out that a third algorithm, designated the “windowed” FMM, provides a very good compromise with respect to error and execution time. The paper concludes with the presentation of some three-dimensional applications for which a hybrid FE-BI technique, in conjunction with a fast-integral algorithm, is well suited 相似文献
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Wagner R.L. Jiming Song Chew W.C. 《Antennas and Propagation, IEEE Transactions on》1997,45(2):235-245
The fast multipole method fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional (2-D) rough surface. The resulting algorithm computes a matrix-vector multiply in O(N log N) operations. This algorithm is shown to be more efficient than another O(N log N) algorithm, the multilevel fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more efficient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2-D random rough surfaces using a workstation. For the rougher surface, backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient. For the smoother surface, the Monte Carlo results compare well with the results of the approximate Kirchhoff theory 相似文献
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Jiang D. Meleis W. El-Shenawee M. Mizan E. Ashouei M. Rappaport C. 《Microwave and Wireless Components Letters, IEEE》2002,12(1):24-26
We present the parallel, MPI-based implementation of the SDFMM computer code using a thirty-two node Intel Pentium-based Beowulf cluster. The SDFMM is a fast algorithm that is a hybridization of the method of moments (MoMs), the fast multipole method (FMM), and the steepest descent integration path (SDP), which is used to solve large-scale linear systems of equations produced in electromagnetic scattering problems. An overall speedup of 7.2 has been achieved on the 32-processor Beowulf cluster and a significant reduced runtime is achieved on the 4-processor 667 MHz Alpha workstation 相似文献
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Efficient MLFMA, RPFMA, and FAFFA algorithms for EM scattering by very large structures 总被引:2,自引:0,他引:2
Tie Jun Cui Weng Cho Chew Guang Chen Song J. 《Antennas and Propagation, IEEE Transactions on》2004,52(3):759-770
Based on the addition theorem, the principle of a multilevel ray-propagation fast multipole algorithm (RPFMA) and fast far-field approximation (FAFFA) has been demonstrated for three-dimensional (3-D) electromagnetic scattering problems. From a rigorous mathematical derivation, the relation among RPFMA, FAFFA, and a conventional multilevel fast multipole algorithm (MLFMA) has been clearly stated. For very large-scale problems, the translation between groups in the conventional MLFMA is expensive because the translator is defined on an Ewald sphere with many sampling k/spl circ/ directions. When two groups are well separated, the translation can be simplified using RPFMA, where only a few sampling k/spl circ/ directions are required within a cone zone on the Ewald sphere. When two groups are in the far-field region, the translation can be further simplified by using FAFFA where only a single k/spl circ/ is involved in the translator along the ray-propagation direction. Combining RPFMA and FAFFA with MLFMA, three algorithms RPFMA-MLFMA, FAFFA-MLFMA, and RPFMA-FAFFA-MLFMA have been developed, which are more efficient than the conventional MLFMA in 3-D electromagnetic scattering and radiation for very large structures. Numerical results are given to verify the efficiency of the algorithms. 相似文献
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Fast Solution of Scattering From Conducting Structures by Local MLFMA Based on Improved Electric Field Integral Equation 总被引:1,自引:0,他引:1
《Electromagnetic Compatibility, IEEE Transactions on》2008,50(4):940-945
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快速多极子在任意截面均匀介质柱散射中的应用 总被引:2,自引:1,他引:1
采用快速多极子法(FMM)加速后的矩量法(MoM)求解由电磁场等效原理导出的关于均匀介质柱表面等铲电磁流的积分方程,进而计算其电磁散射特性,FMM的引入使计算时间和内存开销都从O(N^2)降到O(N^3/2),且并不增加多少复杂度。最后给出了一些介质柱体RCS的算例。 相似文献
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A diagonalized multilevel fast multipole method with spherical harmonics expansion of the k-space Integrals 总被引:3,自引:0,他引:3
Diagonalization of the fast multipole method (FMM) for the Helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves. The resulting k-space integral over the Ewald sphere is numerically evaluated. Storing the k-space quadrature samples of the method of moments (MoM) basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems. In this paper, it is proposed to expand the k-space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules. Aggregations, plane wave translations, and disaggregations in the realized multilevel fast multipole method (MLFMM) are carried out using the k-space samples of a numerical quadrature rule. However, the incoming plane waves on the finest MLFMM level are expanded in spherical harmonics again. Thus, due to the orthonormality of spherical harmonics, the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients. Overall, the resulting MLFMM can save a considerable amount of memory without compromising accuracy and numerical speed. 相似文献
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迭代物理光学法结合快速多极子(IPO+FMM)方法,可以快速计算电大腔体的电磁散射特性。传统的快速多极子(FMM)方法需要计算两组的转移因子以及转移过程的全部角谱分量,计算开销是非常大的。随着组间距离的增大,转移过程可以用射线多极子(RPFMM)简化计算,为了充分利用射线多极子方法中参与计算的有效角谱分量随着组间距离增大而变少的特性,采用一种随着组间距离增大自适应调整参与计算的角谱分量的锥形区域的射线多极子方法(RPFMM),当两组距离足够大而位于远场时,用远场近似方法(FaFFA)进一步简化计算。结果表明该方法能在保持计算精度的同时并能较IPO+FMM方法进一步减少计算资源占用、提高计算速度。 相似文献