Parallel Iterative FEM Solver with Initial Guess for Frequency Domain Electromagnetic Analysis

The finite element method is a key player in computational electromag-netics for designing RF(Radio Frequency)components such as waveguides.The frequency-domain analysis is fundamental to identify the characteristics of the components.For the conventional frequency-domain electromagnetic analysis using FEM(Finite Element Method),the system matrix is complex-numbered as well as indefinite.The iterative solvers can be faster than the direct solver when the solver convergence is guaranteed and done in a few steps.However,such complex-numbered and indefinite systems are hard to exploit the merit of the iterative solver.It is also hard to benefit from matrix factorization techniques due to varying system matrix parts according to frequency.Overall,it is hard to adopt conventional iterative solvers even though the system matrix is sparse.A new parallel iterative FEM solver for frequency domain analysis is implemented for inhomogeneous waveguide structures in this paper.In this implementation,the previous solution of the iterative solver of Matlab(Matrix Laboratory)employ-ing the preconditioner is used for the initial guess for the next step’s solution process.The overlapped parallel stage using Matlab’s Parallel Computing Toolbox is also proposed to alleviate the cold starting,which ruins the convergence of early steps in each parallel stage.Numerical experiments based on waveguide structures have demonstrated the accuracy and efficiency of the proposed scheme.

Finite element solution based on fast numerical technique for large-scale electromagnetic computation

A numerical technique of the target-region locating （TRL） solver in conjunction with the wave-front method is presented for the application of the finite element method （FEM） for 3-D electromagnetic computation. First, the principle of TRL technique is described. Then, the availability of TRL solver for nonlinear application is particularly discussed demonstrating that this solver can be easily used while still remaining great efficiency. The implementation on how to apply this technique in FEM based on magnetic vector potential （MVP） is also introduced. Finally, a numerical example of 3-D magnetostatic modeling using the TRL solver and FEMLAB is given. It shows that a huge computer resource can be saved by employing the new solver.

HIGHER-ORDER NODE-BASED TDFEM FOR TRANSIENT ELECTROMAGNETIC ANALYSIS IN RECTANGULAR WAVEGUIDE

Higher-order Time Domain Finite Element Method (TDFEM) based on the nodal inter- polation is proposed for two-dimensional electromagnetic analysis. The detailed algorithms of the method are presented firstly, and then the accuracy, CPU time and memory consumption of the higher-order node-based TDFEM are investigated. The high performance of the presented approach is validated by numerical results of the transient responses of Transverse Electric (TE) field and Transverse Magnetic (TM) field in a rectangular waveguide.

Calculation of angular glint in near field utilizing graphical electromagnetic computing

The angular glint in the near field plays an important role on radar tracking errors. To predict it more efficiently for electrically large targets, a new method based on graphical electromagnetic computing （GRECO） is proposed. With the benefit of the graphic card, the GRECO prediction method is faster and more accurate than other methods. The proposed method at the first time considers the special case that the targets cannot be completely covered by radar beams, which makes the prediction of radar tracking errors more self-contained in practical circumstances. On the other hand, the process of the scattering center extraction is omitted, resulting in possible angular glint prediction in real time. Comparisons between the simulation results and the theoretical ones validate its correctness and value to academic research and engineering applications.

RCS Reduction of Airborne Dispenser

The radar cross section (RCS) of dispenser and its components is computed by graphical electromagnetic computing (GRECO) method, which bases on physical optics (PO) method. A satisfied agreement is gotten between computed and measured results outdoor. The results show that the main scattering source of the dispenser is the mirror reflecting of the body; in the most crucial nose-on region, the nose mirror reflecting plays important role; the corner reflecting is important to the fins' RCS. The corresponding measures to reduce dispenser's RCS are proposed. It is indicated that to reduce RCS, shaping should be adopts first, while aerodynamic characteristics and stealth characteristics should be considered synthetically during the design of dispenser.

Implementation of Computational Electromagnetic on Distributed Systems

Now the new generation of technology could raise the bar for distributedcomputing. It seems to be a trend to solve computational electromagnetic work on a distributedsystem with parallel computing techniques. In this paper, we analyze the parallel characteristics ofthe distributed system and the possibility of setting up a tightly coupled distributed system byusing LAN in our lab . The analysis of the performance of different computational methods, such asFEM, MOM, FDTD and finite difference method, are given. Our work on setting up a distributed systemand the performance of the test bed is also included . At last, we mention the implementation of oneof our computational electromagnetic codes.

PARALLEL HIERARCHICAL MATRIX PRECONDITIONERS FOR THE CURL-CURL OPERATOR

This paper deals with the preconditioning of the curl-curl operator. We use H（curl）- conforming finite elements for the discretization of our corresponding magnetostatic model problem. Jumps in the material parameters influence the condition of the problem. We will demonstrate by theoretical estimates and numerical experiments that hierarchical matrices are well suited to construct efficient parallel preconditioners for the fast and robust iterative solution of such problems.

STABILITY ANALYSIS OF YEE SCHEMES TO PML AND UPML FOR MAXWELL EQUATIONS

We utilize Fourier methods to analyze the stability of the Yee difference schemes for Berenger PML （perfectly matched layer） as well as the UPML （uniaxial perfectly matched layer） systems of two-dimensional Maxwell equations. Using a practical spectrum stability concept, we find that the two schemes are spectrum stable under the same conditions for mesh sizes. Besides, we prove that the UPML schemes with the same damping in both directions are stable. Numerical examples are given to confirm the stability analysis for the PML method.

Geometric Optimization Design System Incorporating Hybrid GRECO-WM Scheme and Genetic Algorithm

This article seeks to outline an integrated and practical geometric optimization design system （GODS） incorporating hybrid graphical electromagnetic computing-wedge modeling （GRECO-WM） scheme and the genetic algorithm （GA） for calculating the radar cross section （RCS） and optimizing the geometric parameters of a large and complex target respectively. A new wedge modeling （WM） scheme is presented for calculating the high-frequency RCS of wedge with only one visible facet based on the method of equivalent currents （MEC）. The applications of GODS to 2D cross-section and 3D surface are respectively implemented by choosing an average of monostatic RCS values corresponding to a series of incident angles over a frequency band as the optimum objective function. And the results demonstrate that the RCS can be effectively and conveniently reduced by the GODS presented in this article.

Cohomology in 3D Magneto-Quasistatics Modeling

Electromagnetic modeling provides an interesting context to present a link between physical phenomena and homology and cohomology theories.Over the past twenty-five years,a considerable effort has been invested by the computational electromagnetics community to develop fast and general techniques for defining potentials.When magneto-quasi-static discrete formulations based on magnetic scalar potential are employed in problems which involve conductive regions with holes,cuts are needed to make the boundary value problem well defined.While an intimate connection with homology theory has been quickly recognized,heuristic definitions of cuts are surprisingly still dominant in the literature.The aim of this paper is first to survey several definitions of cuts together with their shortcomings.Then,cuts are defined as generators of the first cohomology group over integers of a finite CW-complex.This provably general definition has also the virtue of providing an automatic,general and efficient algorithm for the computation of cuts.Some counter-examples show that heuristic definitions of cuts should be abandoned.The use of cohomology theory is not an option but the invaluable tool expressly needed to solve this problem.