高阶旋转体时域有限差分法

旋转体时域有限差分法(BOR FDTD)是模拟电磁波与旋转对称目标体相互作用的一种高效算法,但目前的BOR FDTD对时间和空间的差分精度均只有二阶.通过把电磁场各分量作泰勒展开,并结合麦克斯韦方程,提出了BOR FDTD的三种高阶算法.相对于目前的BOR FDTD,三种高阶算法均不增加存储量.通过模拟简谐波与介质球的相互作用并和理论值作比较,证实了高阶算法在提高计算精度方面的有效性.此外还分析了三种高阶算法的优、缺点,给出了关于高阶算法应用的建议.     

Finite-difference technique based on exponential splines for the solution of obstacle problems

In this paper, we introduce a new technique based on cubic exponential spline functions for computing approximations to the solution of a system of fourth-order boundary value problems associated with obstacle, unilateral and contact problems. It is shown that the present method is of order two and four and gives approximations which are better than those produced by other collocation, finite difference and spline methods. Numerical evidence is presented to illustrate the applicability of the new methods.     

Finite-difference time-domain simulation of electromagnetic propagation in magnetized plasma

The electromagnetic propagation through a homogeneous magnetized plasma slab is studied using the finite-difference time-domain method based on Z transforms. The reflection and transmission coefficients of the magnetized plasma layer for the right-hand circularly polarized wave are computed. The comparison of the numerical results of the Z transform and recursive convolution algorithms with analytic values indicates that the Z transform algorithm is more accurate than the recursive convolution algorithm. The dependence of the absorption coefficient on frequency is presented.     

Solution of 2-D nonlinear electromagnetic field problems with adinat

When the magnetic vector potential has but one component the governing field equation is the same as the heat conduction equation. In the case of ferro-magnetic materials the magnetic behavior is nonlinear, the permeability depending on the magnitude of the curl of the vector potential. Because the material property depends on the curl of the vector potential and not on the potential itself certain modifications to ADINAT are required in order to solve such problems. Spatial derivatives of the field variable must be explicitly computed and saved. Also, output is saved on disk for subsequent field line plotting. Once the flux field is calculated, the constitutive law due to Maxwell is used to compute the elements of the Maxwell stress tensor. This information is subsequently used to determine the net forces acting on magnetic structures.     

A new parallel meshing technique integrated into the conformal FDTD method for solving complex electromagnetic problems

A new efficient parallel finite-difference time-domain （FDTD） meshing algorithm, based on the ray tracing technique, is proposed in this paper. This algorithm can be applied to construct various FDTD meshes, such as regular and conformal ones. The Microsoft F# language is used for the algorithm coding, where all variables are unchangeable with its parallelization advantage being fully exploited. An improved conformal FDTD algorithm, also integrated with an improved surface current algorithm, is presented to simulate some complex 3D models, such as a sphere ball made of eight different materials, a tank, a J-10 aircraft, and an aircraft carrier with 20 aircrafts. Both efficiency and capability of the developed parallel FDTD algorithm are validated. The algorithm is applied to characterize the induced surface current distribution on an aircraft or a warship.     

电磁综合问题的混合遗传算法求解

综合问题是电磁领域中经常遇到的问题,本文给出了一种混合遗传算法,可以很好的处理综合问题.该方法采用带有最优个体保存策略的遗传算法,并结合柔性约束技术和自适应搜索技术.柔性约束可以极大地压缩搜索空间,自适应搜索可以使搜索区的跟踪位移始终保持最优状态.通过线天线阵和滤波器的综合问题,展现了该方法的效能,进而证实该方法是实现多自变量综合问题的强有力手段.     

Numerical solution of non-linear elliptic boundary-value problems by isomorphic iterative methods

New implicit iterative methods are presented for the efficient numerical solution of non-linear elliptic boundary-value problems. Isomorphic iterative schemes in conjunction with preconditioning techniques are used for solving non-linear elliptic equations in two and three-space dimensions. The application of the derived methods on characteristic 2D and 3D non-linear boundary-value problems is discussed and numerical results are given.     

A new approach to the solution of electromagnetic problems with the impedance method

We propose a new approach based on the use of interpolation which provides a significant increase in the accuracy of electric potential calculation using the impedance method. In a rectangular three-dimensional grid, we use a first order interpolation function to describe the distribution of electric potential within each voxel of the mesh. The electric field obtained analytically from this function is used as a solution of the continuity equation applied to each node of the mesh. The system of node equations is then solved to obtain the potential distribution. The obtained results show that this technique provides better accuracy than the conventional impedance method. This approach is exemplified in this article in problems involving high dielectric constant and low conductivity media similar to biological materials.     

A codimension-zero approach to discretizing and solving field problems

Computational science and engineering are dominated by field problems. Traditionally, engineering practice involves repeated iterations of shape design (i.e., shaping and modeling of material properties), simulation of the physical field, evaluation of the result, and re-design. In this paper, we propose a specific interpretation of the algebraic-topological formulation of field problems, which is conceptually simple, physically sound, computational effective and comprehensive. In the proposed approach, physical information is attached to an adaptive, full-dimensional decomposition of the domain of interest. Giving preeminence to the cells of highest dimension allows us to generate the geometry and to simulate the physics simultaneously. We will also demonstrate that our formulation removes artificial constraints on the shape of discrete elements and unifies commonly unrelated methods in a single computational framework. This framework, by using an efficient graph-representation of the domain of interest, unifies several geometric and physical finite formulations, and supports local progressive refinement (and coarsening) effected only where and when required.     

Fast multipole method based solution of electrostatic and magnetostatic field problems

Abstact Applications of boundary element methods (BEM) to the solution of static field problems in electrical engineering are considered in this paper. The choice of a suitable BEM formulation for electrostatics, steady current flow fields or magnetostatics is discussed from user's point of view. The dense BEM matrix is compressed with an enhanced fast multipole method (FMM) which combines well-known BEM techniques with the FMM approach. An adaptive grouping scheme for problem oriented meshes is presented along with a discussion on the influence of the mesh to the efficiency of the FMM. The computational costs of the FMM algorithm are analyzed for typical problems in practice. Finally, some electrostatic and magnetostatic numerical examples demonstrate the simple usability and the efficiency of the FMM. Communicated by: U. Langer     

The direct solution of periodic parabolic problems by boundary-value techniques

In this paper fast direct methods are presented for the solution of the parabolic boundary value problem. The algorithms used are block variants of the cyclic factorisation algorithm previously presented in Evans [1]     

Parallel algorithms for the iterative solution of sparse least-squares problems

In this paper, we are concerned with a generalized Gauss-Seidel approach to sparse linear least-squares problems. Two algorithms, related to those given by Schechter (1959), for the solution of linear systems are presented and their parallel implementation is discussed. In these procedures, which can be viewed as an alternative ordering of the variables in the SOR methods, the variables are divided into nondisjoint groups. Numerical results, obtained on CRAY X-MP/48, are presented and discussed.     

Double ultraspherical solution of eigenvalue problems for partial differential equations

Particular spectral method based on an expansion in double ultraspherical polynomials is proposed to solve a number of eigenvalue problems defined by partial differential equations with constant and variable coefficients.We obtain comparable results with those computed by Liu and Oritz [14] by using Tau-Lines method, El-Hawary [8] by using El-Gendi-Lines method, El-Hawary [7] by using double Chebyshev approximation and Brandt et al.[1] by using multigrid method.     

An operator splitting-radial basis function method for the solution of transient nonlinear Poisson problems

This paper presents an operator splitting-radial basis function (OS-RBF) method as a generic solution procedure for transient nonlinear Poisson problems by combining the concepts of operator splitting, radial basis function interpolation, particular solutions, and the method of fundamental solutions. The application of the operator splitting permits the isolation of the nonlinear part of the equation that is solved by explicit Adams-Bashforth time marching for half the time step. This leaves a nonhomogeneous, modified Helmholtz type of differential equation for the elliptic part of the operator to be solved at each time step. The resulting equation is solved by an approximate particular solution and by using the method of fundamental solution for the fitting of the boundary conditions. Radial basis functions are used to construct approximate particular solutions, and a grid-free, dimension-independent method with high computational efficiency is obtained. This method is demonstrated for some prototypical nonlinear Poisson problems in heat and mass transfer and for a problem of transient convection with diffusion. The results obtained by the OS-RBF method compare very well with those obtained by other traditional techniques that are computationally more expensive. The new OS-RBF method is useful for both general (irregular) two- and three-dimensional geometry and provides a mesh-free technique with many mathematical flexibilities, and can be used in a variety of engineering applications.     

非介质材料物体的电磁时域特征的摄取

阐述了应用电磁场的时域和频域性质对非介质材料进行无损检测和识别。通过理论分析和实验证明用不同的激励源和激励方式激励同一对象,可得到不同的响应结果;用相同的激励源和激励方式激励不同的对象,也可得到不同的响应结果。通过分析和选择针对问题的激励来取得一个特异性尽可能强的特征向量空间,从而进行模式识别。     

A unified framework for the numerical solution of optimal control problems using pseudospectral methods

A unified framework is presented for the numerical solution of optimal control problems using collocation at Legendre-Gauss (LG), Legendre-Gauss-Radau (LGR), and Legendre-Gauss-Lobatto (LGL) points. It is shown that the LG and LGR differentiation matrices are rectangular and full rank whereas the LGL differentiation matrix is square and singular. Consequently, the LG and LGR schemes can be expressed equivalently in either differential or integral form, while the LGL differential and integral forms are not equivalent. Transformations are developed that relate the Lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem. The LG and LGR discrete costate systems are full rank while the LGL discrete costate system is rank-deficient. The LGL costate approximation is found to have an error that oscillates about the true solution and this error is shown by example to be due to the null space in the LGL discrete costate system. An example is considered to assess the accuracy and features of each collocation scheme.     

Improved iterative algorithm for 3D edge FEM analysis of electromagnetic field boundary value problems

In this article, an improved iterative arithmetic of the symmetric successive over‐relaxation preconditioning biconjugate‐gradient algorithm (ISSOR‐PBCG) is utilized to solve the 3D edge FEM equations derived from the time‐harmonic electromagnetic‐field boundary value problems. Several typical structures have been analyzed, and the computation time is compared with that of other algorithms such as biconjugate‐gradient (BCG) algorithm and the conventional symmetric successive over‐relaxation preconditioning biconjugate‐ gradient algorithm (SSOR‐PBCG). The CPU time saved using the ISSOR‐PBCG algorithm is nearly 27% and 65.5%, as compared with that using the SSOR‐PBCG and the BCG algorithm. It can be seen that the ISSOR‐PBCG algorithm is efficient for edge FEM equation sets derived from large‐scale time‐harmonic electromagnetic‐field problems. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.