fastmultipole method (FMM) in computational physics and its multilevel ver- sion, i. e., multilevel fast multipole algorithm (MLFMA) in computational elec- tromagnetics are among the best known methods to solve integ...
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fastmultipole method (FMM) in computational physics and its multilevel ver- sion, i. e., multilevel fast multipole algorithm (MLFMA) in computational elec- tromagnetics are among the best known methods to solve integral equations (IEs) in the frequency-domain. MLFMA is well-accepted in the computational electromagnetic (CEM) society since it provides a full-wave solution regarding Helmholtz-type electromagnetics problems. This is done by discretizing proper integral equations based on a predetermined formulation and solving them nu- merically with O(N log N) complexity, where N is the number of unknowns. In this dissertation, we present two broadband and efficient methods in the context of MLFMA, one for surface integral equations (SIEs) and another for volume integral equations (VIEs), both of which are capable of handling large multiscale electromagnetics problems with a wide dynamic range of mesh sizes. By invoking a novel concept of incomplete-leaf tree structures, where only the overcrowded boxes are divided into smaller ones for a given population threshold, a versatile method for both types of IEs has been achieved. Regarding SIEs, for geometries containing highly overmeshed local regions, the proposed method is always more efficient than the conventional MLFMA for the same accuracy, while it is always more accurate if the efficiency is comparable. Regarding VIEs, for inhomoge- neous dielectric objects possessing variable mesh sizes due to different electrical properties, in addition to obtaining similar results from the proposed method, a reduction in the storage is also achieved. Several canonical and also real-life examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison to the conventional MLFMA.
Integral equations provide full-wave (accurate) solutions of Helmholtz-type elec- tromagnetics problems. The multilevel fast multipole algorithm (MLFMA) dis- cretizes the equations and solves them numerically with O(N...
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Integral equations provide full-wave (accurate) solutions of Helmholtz-type elec- tromagnetics problems. The multilevel fast multipole algorithm (MLFMA) dis- cretizes the equations and solves them numerically with O(NLogN) complexity, where N is the number of unknowns. For solving large-scale problems, MLFMA is parallelized on distributed-memory architectures. Despite the low complexity and parallelization, the computational requirements of MLFMA solutions grow immensely in terms of CPU time and memory when extremely-large geometries (in wavelengths) are involved. The thesis provides computational and theoreti- cal techniques for solving large-scale electromagnetics problems with lower com- putational requirements. One technique is the out-of-core implementation for reducing the required memory via employing disk space for storing large data. Additionally, a pre-processing parallelization strategy, which eliminates mem- ory bottlenecks, is presented. Another technique, MPI+OpenMP paralleliza- tion, uses distributed-memory and shared-memory schemes together in order to maintain the parallelization efficiency with high number of processes/threads. The thesis also includes the out-of-core implementation in conjunction with the MPI+OpenMP parallelization. With the applied techniques, full-wave solutions involving up to 1.3 billion unknowns are achieved with 2 TB memory. Physical optics is a high-frequency approximation, which provides fast solutions of scat- tering problems with O(N) complexity. A parallel physical optics algorithm is presented in order to achieve fast and approximate solutions. Finally, a hybrid integral-equation and physical-optics solution methodology is introduced.
Electromagnetic(EM) problems with complex media are formulated by volume integral equations(VIEs) in the integral equation approach. The VIEs are usually solved by the method of moments(Mo M) with the Schaubert-Wilton...
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Electromagnetic(EM) problems with complex media are formulated by volume integral equations(VIEs) in the integral equation approach. The VIEs are usually solved by the method of moments(Mo M) with the Schaubert-WiltonGlisson(SWG) basis function, but the solution requires highquality conforming meshes, resulting in a high cost in geometric discretization. In this work, a point-matching meshless method is proposed to discretize the VIEs and it uses discrete points instead of meshes to represent an object domain. Also, the method chooses the current densities as the unknown functions to be solved so that the integral kernels are free of material parameters. For electrically large problems, we incorporate it with the multilevel fast multipole algorithm(MLFMA) to accelerate the solving process. Numerical examples are presented to demonstrate the method and good results have been observed
A parallel scheme that combines the OpenMP and the vector arithmetic logic unit (VALU) hardware acceleration is presented to speed up the multilevel fast multipole algorithm (MLFMA) on shared-memory computers. Perform...
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A parallel scheme that combines the OpenMP and the vector arithmetic logic unit (VALU) hardware acceleration is presented to speed up the multilevel fast multipole algorithm (MLFMA) on shared-memory computers. Performance of the hybrid parallel OpenMP-VALU MLFMA is investigated and several strategies are employed to improve the overall speedup and parallel efficiency. Effectiveness of the hybrid parallel scheme is verified by numerical results of the electromagnetic (EM) scattering examples, and related numerical stability issue is discussed as well.
A new, improved version of a global interpolator utilizing trigonometric polynomials is presented for the high-frequency multilevel fast multipole algorithm. The number of required points to sample the outgoing and in...
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A new, improved version of a global interpolator utilizing trigonometric polynomials is presented for the high-frequency multilevel fast multipole algorithm. The number of required points to sample the outgoing and incoming field patterns is low, almost half in some levels, compared with the earlier published versions. Compared with local interpolators based on Lagrange interpolating polynomials, the proposed technique performs even more favorably and reduces the number of sample points by a factor of eight. The numerical examples demonstrate that the interpolator allows full numerical accuracy control during the aggregation and disaggregation phases, regardless of the number of the levels in the octree.
A multi-GPU implementation of the multilevel fast multipole algorithm (MLFMA) based on the hybrid OpenMP-CUDA parallel programming model (OpenMP-CUDA-MLFMA) is presented for computing electromagnetic scattering of a t...
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A multi-GPU implementation of the multilevel fast multipole algorithm (MLFMA) based on the hybrid OpenMP-CUDA parallel programming model (OpenMP-CUDA-MLFMA) is presented for computing electromagnetic scattering of a three-dimensional conducting object. The proposed hierarchical parallelization strategy ensures a high computational throughput for the GPU calculation. The resulting OpenMP-based multi-GPU implementation is capable of solving real-life problems with over one million unknowns with a remarkable speed-up. The radar cross sections of a few benchmark objects are calculated to demonstrate the accuracy of the solution. The results are compared with those from the CPU-based MLFMA and measurements. The capability and efficiency of the presented method are analyzed through the examples of a sphere, an aerocraft, and a missile-like object. Compared with the 8-threaded CPU-based MLFMA, the OpenMP-CUDA-MLFMA method can achieve from 5 to 20 total speed-up ratios.
The potential of the interpolative decomposition multilevel fast multipole algorithm (ID-MLFMA) on developing an effective preconditioning technique for multiscale, dynamic electromagnetic problems are analyzed. The p...
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The potential of the interpolative decomposition multilevel fast multipole algorithm (ID-MLFMA) on developing an effective preconditioning technique for multiscale, dynamic electromagnetic problems are analyzed. The preconditioner based on multilevel inverse-based ILU is developed for ID-MLFMA. The proposed preconditioning technique is investigated by numerical experiments on complex targets.
A parallel implementation of the multilevel fast multipole algorithm (MLFMA) is developed for fast and accurate solutions of electromagnetics problems involving complex plasmonic metamaterial structures. Composite obj...
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ISBN:
(纸本)9781479933433
A parallel implementation of the multilevel fast multipole algorithm (MLFMA) is developed for fast and accurate solutions of electromagnetics problems involving complex plasmonic metamaterial structures. Composite objects that consist of multiple penetrable regions, such as dielectric, lossy, and plasmonic parts, are formulated rigorously with surface integral equations and solved iteratively via MLFMA. Using the hierarchical strategy for the parallelization, the developed implementation is capable of simulating realistic structures discretized with millions of unknowns.
A fast and efficient method is proposed to analyze electromagnetic (EM) scattering of multiscale objects with impedance boundary condition (IBC). The self-dual integral equation (SDIE) in combination with the mixed-po...
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A fast and efficient method is proposed to analyze electromagnetic (EM) scattering of multiscale objects with impedance boundary condition (IBC). The self-dual integral equation (SDIE) in combination with the mixed-potential (MiP) multilevel fast multipole algorithm (MLFMA) is used to calculate EM scattering from the IBC targets, in which the incomplete-leaf (ICL) tree structure and interpolative-decomposition (InDe) based skeletonization technique is utilized to reduce excessive memory usage imposed by multiscale IBC targets meshed with large multiscale factor (MSF). A difference matrix generated from the near-field interactions by two grouping schemes is supplemented in the sparse approximate inverse (SAI) preconditioner to speed up the convergence of the iterative solvers. Numerical experiments demonstrate the effectiveness of the presented method.
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.
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