The electric field integral equation (EFIE) combined with the multilevel fast multipole algorithm (MLFMA) is applied to analyze the radiation and impedance properties of wire antennas mounted on complex conducting pla...The electric field integral equation (EFIE) combined with the multilevel fast multipole algorithm (MLFMA) is applied to analyze the radiation and impedance properties of wire antennas mounted on complex conducting platforms to realize fast, accurate solutions. Wire, surface and junction basis functions are used to model the current distribution on the object. Application of MLFMA reduces memory requirement and computing time compared to conventional methods, such as method of moment (MOM), especially for the antenna on a large-sized platform. Generalized minimal residual (GMRES) solver with incomplete LU factorization preconditioner using a dual dropping strategy (ILUT) is applied to reduce the iterative number. Several typical numerical examples are presented to validate this algorithm and show the accuracy and computational efficiency.展开更多
This paper provides a conceptual and non-rigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions.Both the non-oscillatory and the oscillatory kernels ar...This paper provides a conceptual and non-rigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions.Both the non-oscillatory and the oscillatory kernels are considered.For non-oscillatory kernel,we outline the main ideas of the classical fast multipole method proposed by Greengard and Rokhlin.In the oscillatory case,the directional fast multipole method developed recently by Engquist and Ying is presented.展开更多
In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced...In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced. Taking advantage of the relationship between Euler-Maclaurin formula and trapezoidal quadrature rule,and the relationship between trapezoidal and square quadrature rule,sharp computable bound with analytical form on the error of numerical integration of Bessel integral identity by square quadrature rule is derived in this paper. Numerical experiments are presented at the end to demonstrate the accuracy of the sharp computable bound on the numerical integration error.展开更多
The detection of a missile target in heavy sea clutter is a significantly challenging problem due to the clutter effects. In this paper, the radar cross sections(RCS) of a pre-assumed generic missile model is computed...The detection of a missile target in heavy sea clutter is a significantly challenging problem due to the clutter effects. In this paper, the radar cross sections(RCS) of a pre-assumed generic missile model is computed with multilevel fast multi-pole algorithm(MLFMA), while the RCS of ocean surface is computed by a more reduced form of the fractional Weierstrass scattering model proposed here. At last, the computed RCS of missile model is compared with that of sea surface, and then the comparisons of missile-to-ocean RCS ratios of different incident angles, incident frequencies, and polarization patterns are also presented. The discussion and comparisons of RCS of the missile and ocean surface can help us to plan and design a radar system in the application of detection of a missile target or other analogous weaker targets in the strong sea clutter background.展开更多
We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements...We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements are solved efficiently. This is an extension of the fast multipole BEM for two-dimensional (2D) acoustic problems developed by authors recently. Some new improvements are obtained. In this new technique, the improved Burton-Miller formulation is employed to over-come non-uniqueness difficulties in the conventional BEM for exterior acoustic problems. The computational efficiency is further improved by adopting the FMM and the block diagonal preconditioner used in the generalized minimum residual method (GMRES) iterative solver to solve the system matrix equation. Numerical results clearly demonstrate the complete reliability and efficiency of the proposed algorithm. It is potentially useful for solving large-scale engineering acoustic scattering problems.展开更多
基金This project was supported by the National Natural Science Foundation of China (60431010).
文摘The electric field integral equation (EFIE) combined with the multilevel fast multipole algorithm (MLFMA) is applied to analyze the radiation and impedance properties of wire antennas mounted on complex conducting platforms to realize fast, accurate solutions. Wire, surface and junction basis functions are used to model the current distribution on the object. Application of MLFMA reduces memory requirement and computing time compared to conventional methods, such as method of moment (MOM), especially for the antenna on a large-sized platform. Generalized minimal residual (GMRES) solver with incomplete LU factorization preconditioner using a dual dropping strategy (ILUT) is applied to reduce the iterative number. Several typical numerical examples are presented to validate this algorithm and show the accuracy and computational efficiency.
基金supported by the Sloan Foundation and the National Science Foundation of USA (CAREER Award DMS-0846501)
文摘This paper provides a conceptual and non-rigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions.Both the non-oscillatory and the oscillatory kernels are considered.For non-oscillatory kernel,we outline the main ideas of the classical fast multipole method proposed by Greengard and Rokhlin.In the oscillatory case,the directional fast multipole method developed recently by Engquist and Ying is presented.
基金the National Natural Science Foundation of China (No. 11074170)the Independent Research Program of State Key Laboratory of Machinery System and Vibration (SKLMSV) (No. MSV-MS-2008-05)the Visiting Scholar Program of SKLMSV (No. MSV-2009-06)
文摘In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced. Taking advantage of the relationship between Euler-Maclaurin formula and trapezoidal quadrature rule,and the relationship between trapezoidal and square quadrature rule,sharp computable bound with analytical form on the error of numerical integration of Bessel integral identity by square quadrature rule is derived in this paper. Numerical experiments are presented at the end to demonstrate the accuracy of the sharp computable bound on the numerical integration error.
基金supported by the PLA General Armament Department Pre-Research Foundation of China(Grant No.102060302)
文摘The detection of a missile target in heavy sea clutter is a significantly challenging problem due to the clutter effects. In this paper, the radar cross sections(RCS) of a pre-assumed generic missile model is computed with multilevel fast multi-pole algorithm(MLFMA), while the RCS of ocean surface is computed by a more reduced form of the fractional Weierstrass scattering model proposed here. At last, the computed RCS of missile model is compared with that of sea surface, and then the comparisons of missile-to-ocean RCS ratios of different incident angles, incident frequencies, and polarization patterns are also presented. The discussion and comparisons of RCS of the missile and ocean surface can help us to plan and design a radar system in the application of detection of a missile target or other analogous weaker targets in the strong sea clutter background.
基金supported by the Fundamental Research Funds for the Central Universities (Grant No. 2010MS080)the Research Fund for Doctoral Program of Higher Education of China (Grant No. 20070487403)
文摘We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements are solved efficiently. This is an extension of the fast multipole BEM for two-dimensional (2D) acoustic problems developed by authors recently. Some new improvements are obtained. In this new technique, the improved Burton-Miller formulation is employed to over-come non-uniqueness difficulties in the conventional BEM for exterior acoustic problems. The computational efficiency is further improved by adopting the FMM and the block diagonal preconditioner used in the generalized minimum residual method (GMRES) iterative solver to solve the system matrix equation. Numerical results clearly demonstrate the complete reliability and efficiency of the proposed algorithm. It is potentially useful for solving large-scale engineering acoustic scattering problems.
