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1.
伍刚 《微计算机信息》2006,22(36):166-167
矩量法是将连续方程离散为代数方程组的方法,此法对于求解微分方程和积分方程均适用,本文以半波振子天线为例,系统的阐述了半波振子天线的海伦积分方程的建立,利用矩量法求解海伦积分方程而得半波振子天线上的电流分布,已知电流分布求解半波振子天线在远区的电场表达式和方向图。  相似文献   

2.
We numerically study the nonlocal Gross–Pitaevskii equation (NGPE) which describes the dynamics of Bose–Einstein condensates (BEC) with dipole–dipole interaction at extremely low temperature. In preparation for the numerics, first we reformulate the dimensionless NGPE into a Schrödinger–Poisson system. Then, we discretize the three-dimensional Schrödinger–Poisson system in space by a sixth-order compact finite difference method and in time by a splitting technique. By means of three-dimensional discrete fast Sine transform, we develop a fast solver for the resulting discretized system. Finally, we present numerical examples in three dimensions to demonstrate the power of the numerical methods and to discuss some physics of dipolar BEC. The merits of the proposed method for the NGPE are that it is fast and unconditionally stable. Moreover, the method is of spectral-like accuracy in space, and conserves the particle number and the energy of the system in the discretized level.  相似文献   

3.
The equivalent dipole moment method, which was used to model the isotropic media, is extended and applied to the analysis of the electromagnetic scattering characteristics of arbitrarily shaped multilayer electric anisotropic media in this work. The initial motivation to put forward this method is based on the intrinsic physical properties of the electric anisotropic media whose constitutive parameter permittivity is a tensor matrix that can be modeled as equivalent electric dipole moment. This method employs the method of moments to solve the electric field volume integral equation (VIE) formulated by discretizing the scattering body into tetrahedral volume elements, in which the electrical parameters are assumed constant in each element. Then the VIE is solved directly to obtain the scattered field. Numerical results are given to validate the accuracy and efficiency of this method. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.  相似文献   

4.
This article presents a fast solution to the volume–surface integral equation for electromagnetic scattering from three‐dimensional (3D) targets comprising both conductors and dielectric materials by using the multilevel fast dipole method (MLFDM). This scheme is based on the concept of equivalent dipole‐moment method (EDM) that views the Rao–Wilton–Glisson and the Schaubert–Wilton–Glisson basis functions as dipole models with equivalent dipole moments. In the MLFDM, a simple Taylor's series expansion of the terms Rα (α = 1, ?1, ?2, ?3) and R? R? in the formulation of the EDM transforms the interaction between two equivalent dipoles into an aggregation–translation–disaggregation form naturally. Furthermore, benefiting from the multilevel grouping scheme, the matrix‐vector product can be accelerated and the memory cost is reduced remarkably. Simulation results are presented to demonstrate the efficiency and accuracy of this method. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.  相似文献   

5.
In this paper we study the convergence of the Galerkin approximation method applied to the generalized Hamilton-Jacobi-Bellman (GHJB) equation over a compact set containing the origin. The GHJB equation gives the cost of an arbitrary control law and can be used to improve the performance of this control. The GHJB equation can also be used to successively approximate the Hamilton-Jacobi-Bellman equation. We state sufficient conditions that guarantee that the Galerkin approximation converges to the solution of the GHJB equation and that the resulting approximate control is stabilizing on the same region as the initial control. The method is demonstrated on a simple nonlinear system and is compared to a result obtained by using exact feedback linearization in conjunction with the LQR design method.  相似文献   

6.
The nature of the quantum trajectories, described by stochastic master equations, may be jump-like or diffusive, depending upon different measurement processes. There are many different unravelings corresponding to different types of stochastic master equations for a given master equation. In this paper, we study the relationship between the quantum stochastic master equations and the quantum master equations in the Markovian case under feedback control. We show that the corresponding unraveling no longer exists when we further consider feedback control besides measurement. It is due to the fact that the information gained by the measurement plays an important role in the control process. The master equation governing the evolution of ensemble average cannot be restored simply by eliminating the noise term unlike the case without a control term. By establishing a fundamental limit on performance of the master equation with feedback control, we demonstrate the differences between the stochastic master equation and the master equation via theoretical proof and simulation, and show the superiority of the stochastic master equation for feedback control.  相似文献   

7.
In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation (HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.   相似文献   

8.
In this paper, the unified frame of alternating direction method of multipliers (ADMM) is proposed for solving three classes of matrix equations arising in control theory including the linear matrix equation, the generalized Sylvester matrix equation and the quadratic matrix equation. The convergence properties of ADMM and numerical results are presented. The numerical results show that ADMM tends to deliver higher quality solutions with less computing time on the tested problems.  相似文献   

9.
In the optimal linear regulator problem the control vector is usually determined by solving the algebraic matrix Riccati equation using successive substitutions. This, however, can be rather inefficient from a computational point of view. A nonrecursive method which requires that the transition matrix is nonsingular has been proposed by Vaughan (1970). In the present paper we present a nonrecursive solution to the matrix Riccati equation for the case that the transition matrix may be singular. We show that this procedure leads to the same numerical results as the standard iteration of the matrix Riccati equation.  相似文献   

10.
The solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method. The ‘feedback’ part of the regulator equation, that is, the feasible controllers for the regulator equation, is studied thoroughly. The concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility. Useful results, such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds, are also obtained.  相似文献   

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