In this paper, the characteristic basis function method (CBFM) is applied to instead of conventional MOM for MLFMA implementations. CBFM includes the mutual coupling effects among different subdomains directly by ...
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ISBN:
(纸本)9781424438631;9781424438624
In this paper, the characteristic basis function method (CBFM) is applied to instead of conventional MOM for MLFMA implementations. CBFM includes the mutual coupling effects among different subdomains directly by constructing the high level basis functions, Use of these basis functions leads to a significant reduction in the number of unknowns, and results in a substantial size reduction of the coupling matrix;This reduces matrix size improves the convergence properties. The MLFMA is introduced to speed up the matrix-vector multiplications. The advantages of applying the CBFM with MLFMA are illustrated with numerical simulation. The results demonstrate the efficiency and accuracy of the proposed method.
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.
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.
In this paper, an updated equivalence principle algorithm (EPA) is presented. Compared with previous work by the authors, the high-order point sampling scheme is used to reduce the high-frequency noise in field projec...
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In this paper, an updated equivalence principle algorithm (EPA) is presented. Compared with previous work by the authors, the high-order point sampling scheme is used to reduce the high-frequency noise in field projection. An updated tap basis scheme is introduced to simplify the formulation. With these schemes, the equivalence principle algorithm can be used to solve multiscale problems by substituting the oversampled region with a proper equivalence surface. Moreover, EPA can also be accelerated using attached unknown accelerations and multilevel fast multipole algorithm so that large multiscale problems can be solved efficiently.
For efficiently solving large dense complex linear systems that arise in the electric field integral equation (EFIE) formulation of electromagnetic wave scattering problems, the multilevel fast multipole algorithm (ML...
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For efficiently solving large dense complex linear systems that arise in the electric field integral equation (EFIE) formulation of electromagnetic wave scattering problems, the multilevel fast multipole algorithm (MLFMA) is used to speed up the matrix vector product operations, and the sparse approximate inverse (SAI) preconditioning technique is employed to accelerate the convergence rate of the generalized minimal residual (GMRES) iterative method. We show that the convergence rate can be greatly improved by augmenting to the GMRES method a few eigenvectors associated with the smallest eigenvalues of the preconditioned system. Numerical experiments indicate that this new variant GMRES method is very effective with the MLFMA and can reduce both the iteration number and the computational time significantly. (C) 2008 Wiley Periodicals, Inc.
In this letter, we consider iterative solutions of the three-dimensional electromagnetic scattering problems formulated by surface integral equations. We show that solutions of the electric-field integral equation (EF...
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In this letter, we consider iterative solutions of the three-dimensional electromagnetic scattering problems formulated by surface integral equations. We show that solutions of the electric-field integral equation (EFIE) can be improved by employing an iterative least-squares QR (LSQR) algorithm. Compared to many other Krylov subspace methods, LSQR provides faster convergence and it becomes an alternative choice to the time-efficient no-restart generalized minimal residual (GMRES) algorithm that requires large amounts of memory. Improvements obtained with the LSQR algorithm become significant for the solution of large-scale problems involving open surfaces that must be formulated using EFIE, which leads to matrix equations that are usually difficult to solve iteratively, even when the matrix-vector multiplications are accelerated via the multilevel fast multipole algorithm.
The development of the MLFMA for realistic targets is currently at the stage where clever implementation, using a series of tricks based on the characteristics of the MLFMA and current computer technology, is required...
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The development of the MLFMA for realistic targets is currently at the stage where clever implementation, using a series of tricks based on the characteristics of the MLFMA and current computer technology, is required. A sophisticated parallel MLFMA for use on distributed-memory computers is presented as a whole picture of developing the program using a style of multilevel development in this paper. A series of implementation tricks for the parallel MLFMA are analyzed and compared. Particularly, a novel trick for reducing the truncation numbers is presented for extremely large targets, in the paper. These tricks are integrated into a sophisticated parallel MLFMA. The memory requirement and the CPU time for each part in each level are analyzed numerically by typical numerical experiments. The capability of this sophisticated parallel MLFMA is demonstrated by computing scattering by a sphere with a diameter of 480 wavelengths, containing around 130 million unknowns, and for a plane model with a fuselage of more than 1000 wavelengths, containing more than 72 million unknowns. These are the largest scattering problems ever solved by full-wave numerical methods, to our knowledge.
In solving systems of linear equations arising from practical scientific and engineering modelling and simulations such as electromagnetics applications, it is important to choose a fast and robust solver. Due to the ...
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In solving systems of linear equations arising from practical scientific and engineering modelling and simulations such as electromagnetics applications, it is important to choose a fast and robust solver. Due to the large scale of those problems, preconditioned Krylov subspace methods are most suitable. In electromagnetics simulations, the use of preconditioned Krylov subspace methods in the context of multilevel fast multipole algorithms (MLFMA) is particularly attractive. In this paper, we present a short survey of a few preconditioning techniques in this application. We also compare several preconditioning techniques combined with the Krylov subspace methods to solve large dense linear systems arising from electromagnetic scattering problems and present some numerical results.
We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering...
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We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving closed conductors. We consider the solutions of relatively large scattering problems by employing the multilevel fast multipole algorithm. Accuracy problems of MFIE and CFIE arising from their implementations with the conventional Rao-Wilton-Glisson (RWG) basis functions can be mitigated by using the LL functions for discretization. This is achieved without increasing the computational requirements and with only minor modifications in the existing codes based on the RWG functions.
To further expedite solution of electromagnetic scattering from conducting structures with slots, a novel improved electric field integral equation (IEFIE) is developed to reduce the iteration time in multilevelfast ...
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ISBN:
(纸本)9781424407484
To further expedite solution of electromagnetic scattering from conducting structures with slots, a novel improved electric field integral equation (IEFIE) is developed to reduce the iteration time in multilevel fast multipole algorithm(MLFMA) By adding the principal value term of magnetic field integral equation (MFIE) operator on the both sides of the EFIE operator, a well-conditioned improved EFIE operator is constructed. To achieve a reasonable accuracy, only several update steps for the unknown current is required. Numerical results demonstrate the validity of the present method.
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