Kezhong Zhao

The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems

This paper presents the adaptive cross approximation (ACA) algorithm to reduce memory and CPU time overhead in the method of moments (MoM) solution of surface integral equations. The present algorithm is purely algebraic; hence, its formulation and implementation are integral equation kernel (Greens function) independent. The algorithm starts with a multilevel partitioning of the computational domain. The interactions of well-separated partitioning clusters are accounted through a rank-revealing LU decomposition. The acceleration and memory savings of ACA come from the partial assembly of the rank-deficient interaction submatrices. It has been demonstrated that the ACA algorithm results in O(NlogN) complexity (where N is the number of unknowns) when applied to static and electrically small electromagnetic problems. In this paper the ACA algorithm is extended to electromagnetic compatibility-related problems of moderate electrical size. Specifically, the ACA algorithm is used to study compact-range ground planes and electromagnetic interference and shielding in vehicles. Through numerical experiments, it is concluded that for moderate electrical size problems the memory and CPU time requirements for the ACA algorithm scale as N/sup 4/3/logN.

A Domain Decomposition Method for Electromagnetic Radiation and Scattering Analysis of Multi-Target Problems

A domain decomposition method is presented for analyzing electromagnetic problems involving multiple separable scatterers. The method first decomposes the original problem into several disjoint subregions. In each subregion, the domain decomposition method is further applied by decomposing the region into smaller, possibly repeated, subdomains. The domain decomposition method is general enough for arbitrary geometries, but is also capable of exploiting repetitions. This renders geometrically complicated and electrically large subregion problems tractable. The subregions communicate through the near-field Greens function. To overcome the vast computational costs required in exchanging information between electrically large subregions, the adaptive cross approximation algorithm is adopted to expedite the process. The method is applied to study radiation characteristics of a reflector antenna system and an antenna array in the presence of a frequency selective surface to demonstrate the utility of the present approach.

Solving electromagnetic problems using a novel symmetric FEM-BEM approach

This paper presents a novel symmetric finite element method-boundary element method (FEM-BEM) formulation for solving unbounded electromagnetic problems. The proposed method offers two very attractive features: 1) it is variational, leading to a symmetric system of equations and 2) the meshes for the computations of FEM and BEM can be nonconformal, leading to decoupled computations of FEM and BEM. The accuracy and efficiency of the method are studied for both electromagnetic radiation and scattering problems

Hybrid domain decomposition method and boundary element method for the solution of large array problems

The non-overlapping domain decomposition method (DDM) has emerged as a powerful and attractive technique for numerically-rigorous solution of Maxwells equations due to its inherent parallelism and its beauty as an efficient and effective preconditioner. DDM is based on a divide-and-conquer philosophy. Instead of tackling a large and complex problem directly as a whole, the original problem is partitioned into smaller, possibly repetitive, and easier to solve sub-domains. Some suitable boundary conditions called transmission conditions are prescribed at the interfaces between adjacent sub-domains to enforce the continuity of electromagnetic fields. However in the existing approaches, the radiation condition is approximated by the first order absorbing boundary condition (ABC), producing the unwanted spurious reflection from the truncation boundary. In order to minimize such unphysical reflection, the truncation boundary must be placed sufficiently far away from the object, resulting a large number of sub-domains. In this paper, the unbounded exterior space will be treated as an additional domain. This domain is formulated by a boundary element method (BEM) which incorporates the radiation condition through its Greens function.

Modeling large almost periodic structures using a non-overlapping domain decomposition method

Domain decomposition is a tool that is introduced artificially to ease large scale computation or that is natural in some situations. Domain decomposition methods are a very natural way to exploit the possibilities of multiprocessor computers, but such algorithms are very useful even when used on single process PC environment. The idea is to decompose the computational domain into smaller subdomains. The equations are solved on each subdomain. We first describe a domain decomposition method, a non-overlapping Schwarz algorithm, for solving large almost periodic electromagnetic problems. For large almost periodic structures, when using domain decomposition approach, the FEM matrix only needs to be evaluated once for all domains that are of the same building block. The solving process of domain decomposition is iterative and can become prohibitively slow. We describe a procedure that results in superior speed-up of the solving process.

Modeling of Environmental Effects by Numerical Green's Function in Electromagnetic Applications

The finite-element boundary element method has been successfully used to provide proper truncation for numerical computation in an unbounded region. The information of the exterior environment can be incorporated whenever the corresponding Greens function is available. In this paper, we extend the method by computing Greens functions numerically so that general exterior environments can also be incorporated into the boundary element computation. Once the numerical Greens function is computed for a given environmental configuration, it can be reused for other instances of electromagnetic devices. This method is especially beneficial if a small portion of geometry needs to be repeatedly changed.

A hybrid FEM-DDM-PO method for electrically large objects

This paper has an emphasis on the HF part; we use physical-optics (PO) method [1] with large-dimension curvilinear elements [2]. On the LF side, the hybrid method proposed here employs the FEM domain decomposition method (DDM) [3-4]. In addition, an iterative Multi-Region procedure is developed to make the information between sub-regions fully exchanged.

Application of DP-FETI domain decomposition method for the negative index of refraction materials

In this paper, NIM are modeled by a fast nonconforming dual primal-finite element tearing interconnecting (DP-FETI) domain decomposition method (DDM). We apply the DP-FETI-DDM method to model both positive and negative index materials, refer to as PIM and NIM. Since NIM are generally periodic in nature, the proposed method is capable of taking advantage of such periodicity and only requires small amount of memory.

Implementing Higher Order Absorbing Boundary Conditions in Vector Finite Element Methods

It is vital to use appropriate mesh truncation schemes and accurate absorbing boundary conditions (ABC) on the truncation surfaces to achieve reliable computational results while solving electromagnetic radiation and scattering problems in unbounded regions with the finite element method (FEM). Previously derived higher order ABCs had difficulties in implementation which lead either to destruction of sparsity and symmetry of the FEM matrix or reduction of accuracy. The ABC proposed in this paper is not only capable of producing credible numerical results but also can easily be formulated and implemented via introduction of a cement variable on the surface it is imposed. In addition it is possible theoretically to extend the ABC to higher orders in a hierarchical way by improving the quality of approximation employed

Hybridization of Finite Elements, Boundary Elements, and Physical Optics for Reflector Antenna Systems

This paper presents a hybrid approach to model the reflector antenna system. A DDM approach is used to model the feed region, and an efficient IE-FFT EFIE algorithm is employed for modeling the sub-reflector, and finally the main reflector is treated using a simple curvilinear PO technique.