A Calderón‐preconditioned single source combined field integral equation for analysis of bi‐isotropic object

In this paper, a Calderón‐preconditoned single source combined field integral equation (SSCFIE) has been developed to analyze electromagnetic scattering from bi‐isotropic objects. The field decomposition method is adopted to split the homogeneous bi‐isotropic media into two uncoupled isotropic media instead of direct calculation of complicated Green's function in bi‐isotropic material. Unlike dual source integral equation, the Calderón‐preconditioned single source electric and magnetic integral equations in the presence of bi‐isotropic media are constructed and combined to make the proposed algorithm free from dense mesh breakdown and spurious resonance. Numerical results show good performance of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Three-dimensional magnetic field analysis by T-Ω method using the finite element method coupled with integral equations

The electromagnetic quantities of the magnetic bodies and conductors are calculated by the Finite Element Method with Integral Equation and it is not necessary to divide the free air space. The field at an arbitrary point in the free air is obtained from the Integral Equation after the FEM-IEM analysis. In this paper, the magnetization is written in the terms of the unknown total scalar potential Ω, and the current vector potential T is added in the conductors. In order to calculate the unknowns defined in only the substances by FEM, it is necessary to establish the boundary condition by IEM. Then the calculation of the boundary condition on the surface of magnetic body requires high technical skills, so the formulation presented in this paper is improved by integration of parts. Results of the standard models specified by the I.E.E. of Japan suggest the validity of our method.     

Optimization of 3-D nonlinear magnetic circuit by using the magnetization integral equation method

To design optimal electrical machines, it is necessary to develop an optimal design method for determining the shapes, sizes, positions of the cores, permanent magnets and windings which produce such specified values as flux distributions and torques. In this paper, a design method for determining the optimal sizes of cores taking into account the nonlinearity of the core has been developed by using the nonlinear programming method and the magnetization integral equation method. The pole shape of an electromagnet which produces the uniform flux distribution is determined by using the design method for determining the optimal sizes of cores. The effectiveness of the method is shown by designing the pole piece of the permanent magnet-type MRI device.     

Laplace方程复位函数半解析方法

为高效快捷地求解电磁场问题,将复位函数方法与半解析方法相结合,求解了二维静电场问题。引入复位函数,对广义多极技术、多极理论和新型等效源方法等几种不同的半解析方法进行了统一描述,简化了半解析解的表述方式,降低了计算量,而且为直接从边值问题出发寻找复位函数解答建立了一条新途径,并进行了数值算例验证。研究表明,复位函数半解析方法思路直观简捷,实施方便,计算量小;在相同计算量情况下,计算精确度明显优于其他各种数值方法。     

Multiscalet basis in Galerkin's method for solving three‐dimensional electromagnetic integral equations

Multiscalets in the multiwavelet family are used as the basis and testing functions in Galerkin's method. Since the multiscalets are orthogonal to their translations under the Sobolev inner product, the resulting Galerkin's method behaves like a collocation method but possesses the ability of derivative tracking for unknown functions in solving integral equations. The former makes the method simple in implementation and the latter allows to use coarse meshes in discretization. These robust features have been demonstrated in solving two‐dimensional (2D) electromagnetic (EM) problems, but have not been exploited in three‐dimensional (3D) scenarios. For 3D problems, the unknown functions in the integral equations are dependent on two coordinate variables. In order to preserve the use of coarse meshes for 3D cases, we realize the omnidirectional derivative tracking by tracking the directional derivatives along two orthogonal directions, or equivalently tracking the gradient. This process yields a nonsquare matrix equation and we use the least‐squares method (LSM) to solve it. Numerical examples show that the multiscalet‐based Galerkin's method is also robust in solving for 3D EM integral equations with a minor cost increase from LSM. Copyright © 2007 John Wiley & Sons, Ltd.     

Laplace方程分域展开方法

针对电磁场分析中有限元法适应能力强,但计算量大,效率低,而解析法计算量小,但适用范围窄的各自优缺点,将有限元方法与解析方法相结合,提出了一种分域展开的半解析方法用以求解工程电磁场问题。依据龙格定理,把复杂的求解场域分割为若干形状简单的子域,在每个子域内利用本征函数构造半解析展开式逼近方程的解,然后通过子域拼接得到整个场域的解。展开式系数用配点法确定。由于采用解析展开式,逼近效率高,减少了未知数个数;同时由于是局域逼近,具有解函数形式简单,计算量小,矩阵是稀疏的,条件数小,易于求解,实施方便等优点。以二维Laplace问题为研究对象,数值算例验证了方法的有效性,表明该方法花费时间短,计算精确度高。     

Efficient hybrid scheme of finite element method of lines for modelling computational electromagnetic problems

A hybrid scheme called finite element method of lines is proposed and described for modelling and analysis of generalized computational electromagnetic problems with emphasis on a number of irregular waveguide examples. This new technique is developed by combining a finite element method with a method of lines so that it can handle not only irregular composite geometry but also maintain high accuracy enjoyed by semi‐analytical procedures. Analytical and numerical algorithmic building blocks of this new scheme are discussed in detail such as geometry discretization, element mapping, element trial functions, reformulation and computational issues of non‐linear ordinary differential equations. Our results show that this new technique is able to efficiently solve complex problems as compared with the conventional method of lines. Copyright © 2004 John Wiley & Sons, Ltd.     

The modified multilevel compressed block decomposition algorithms for analyzing the scattering of objects in half space

The convergence rate of iterative methods can vary in an unpredictable way. It is related to the matrix condition number, which is notoriously bad for the electric field integral equation in the large‐scale electromagnetic problems. Therefore, an efficient direct solution—a multilevel compressed block decomposition (MLCBD) algorithm based on the adaptive cross‐approximation algorithm—is applied to overcome this problem; it is very efficient for the monostatic problems. Simulation results of the objects up and below ground in half space demonstrate that the proposed MLCBD method is efficient for analyzing electromagnetic problems. Copyright © 2013 John Wiley & Sons, Ltd.