Wei-Bin Kong

Analysis of Multiscale Problems Using the MLFMA With the Assistance of the FFT-Based Method

A new method for analysis of multiscale problems using the multilevel fast multipole algorithm (MLFMA) is proposed. In this method, the MLFMA bears the main part of the computation at the macro level, while some FFT-based method is responsible for the computation on the subregion with liner meshes. With this strategy, a reasonable balance between the computational efficiency and storage efficiency can be achieved in the case when the local regions with tiny geometry features are relatively centralized. The new method has been compared with several existing methods, including the hybrid method of the MLFMA and LFFIPWA, the MLFMA equipped with the hybrid tree structure (HTS), and the MLFMA with the near-matrix compression, such as the ID-MLFMA and the MLFMA-ACA. Numerical examples are provided to demonstrate the correctness and efficiency of the proposed method.

The MLFMA Equipped with a Hybrid Tree Structure for the Multiscale EM Scattering

We present an efficient strategy for reducing the memory requirement for the near-field matrix in the multilevel fast multipole algorithm (MLFMA) for solving multiscale electromagnetic (EM) scattering problems. A multiscale problem can obviously lower the storage efficiency of the MLFMA for the near-field matrix. This paper focuses on overcoming this shortcoming to a certain extent. A hybrid tree structure for the MLFMA that possesses two kinds of bottom-layer boxes with different edge sizes will be built to significantly reduce the memory requirement for the near-field matrix in the multiscale case compared with the single-tree-structure technique. Several numerical examples are provided to demonstrate the efficiency of the proposed scheme in the multiscale EM scattering.

An Upgraded ACA Algorithm in Complex Field and Its Statistical Analysis

An upgraded adaptive cross approximation (U-ACA) algorithm in complex field is proposed, including detailed discussion about both relative-error estimator and pivoting threshold. Two new relative-error estimators are constructed, and the range of the pivoting threshold is determined theoretically. Besides, a statistical analysis of the U-ACA algorithm for computational electromagnetics is provided to identify the credibility of existing relative-error estimators and new ones. The statistical experiments show that the U-ACA algorithm with either of the two new relative-error estimators is a more robust algorithm at present for applications in computational electromagnetics, compared with the previous ACA algorithm.

Volume integral equation combined with ODDM for analysis of EM scattering from inhomogeneous anisotropie nonmagnetic dielectric objects

In this paper, the volume integral equation (VIE) combined with overlapping domain decomposition method (ODDM) is presented for analysis of electromagnetic (EM) scattering from inhomogeneous anisotropic nonmagnetic dielectric objects. Discretizing a volumetric domain of electrically large size by using tetrahedra usually produces too many unknowns for the traditional VIE-MoM to accommodate. However, the VIE combined with ODDM (VIE-ODDM) can overcome this difficulty. In the VIE-ODDM, at any time, only one subdomain problem needs to be stored in host memory, significantly reducing memory requirement. Numerical results are provided to demonstrate the validity and efficiency of the proposed method.

FFT-Based Method With Near-Matrix Compression

In this paper, a novel grouping scheme of the basis functions within the framework of the fast Fourier transform (FFT)-based method is proposed for creating a block-sparse structure for the near-matrix, and then FFT-based method with near-matrix compression is established for the efficient analysis of multiscale problems. For a multiscale problem, if an FFT-based method is required to maintain both higher efficiency and higher accuracy at calculating the far interactions, then the near-matrix will be inevitably very large. Compared with the traditional FFT-based method, the proposed method can significantly reduce the near-matrix memory requirement without increasing the time spent. Several numerical examples are provided to demonstrate the correctness and the efficiency of the proposed method.

Fast analysis of EM scattering by joint use of the MLFMA and the FGG-FG-FFT

In this paper, a hybrid algorithm of the MLFMA and the FGG-FG-FFT is proposed for fast analysis of multiscale EM scattering from electrically large PEC objects. For multiscale problems, both the MLFMA and the FGG-FG-FFT have their own disadvantages. However, the hybrid algorithm can more easily deal with multiscale problems, leading to higher efficiency than either of these two algorithms. Numerical examples are provided to demonstrate the validity and efficiency of the proposed method.

An ODDM using the JMCFIE formulation

In this paper, an ODDM using the JMCFIE formulation is built for solving EM scattering from electrically large homogeneous dielectric objects whose MLFMA models are too large for the users computer to accommodate. This ODDM has stronger convergence property than the existing ODDM in the literature for the same purpose. Numerical examples are provided to demonstrate both the correctness and performance of the proposed method.

An IE-ODDM with higher-order hierarchical Legendre basis functions

In this paper, an IE-ODDM with higher-order hierarchical Legendre basis functions is proposed for solving the scattering from an electrically large PEC object. Because higher-order basis functions are employed, the sizes of the meshes can be selected larger. Thence, even though the area of each subdomain is relatively larger, the number of unknowns involved in the subdomain is relatively smaller compared with the case where RWG basis functions are employed. Therefore, compared with the original IE-ODDM, our IE-ODDM requires both lower memory requirement and less time spent of reaching convergence. Two numerical results are provided to verify the validity and efficiency of the proposed method.

Using a hybrid tree structure in the MLFMA in the multi-resolution case

The multilevel fast multipole algorithm (MLFMA) has been used in calculating electromagnetic scatterings from electrically large objects. The octree structure plays an important role in the MLFMA. However, in the multi-resolution case, a single octree structure may produce a larger near-field matrix. In this paper, in order to overcome this shortcoming to a certain extent, a hybrid tree structure scheme is proposed. In this scheme, there are two kinds of bottom-layer cubes with different edge size. With the hybrid tree structure, the memory requirement for the near matrix can be significantly reduced in the multi-resolution case compared with the MLFMA equipped with a single octree structure. Numerical examples are provided to demonstrate the efficiency of the proposed scheme.