Multilevel Characteristic Basis Function Method Research Articles

Compressive Sensing Enhanced Multilevel Characteristic Basis Function Method for Analyzing Electrically Large Scattering Problems

Compressive Sensing Enhanced Multilevel Characteristic Basis Function Method for Analyzing Electrically Large Scattering Problems

Accelerated Direct Solver With Multiscale Compressed Block Decomposition and Multilevel Characteristic Basis Function Method

In this letter, an accelerated fast direct solver based on the multiscale compressed block decomposition (MSCBD) and the multilevel characteristic basis function method (MLCBFM) is presented to analyze electrically large problems. The MSCBD is used to enhance the efficiency of the characteristic basis functions generation to accelerate the process of linear system solving in the MLCBFM. In addition, the MLCBFM can reduce the number of unknowns and improve the efficiency of MSCBD process. That means the MSCBD and MLCBFM can accelerate each other. The correctness and efficiency of the method are demonstrated with numerical results for several perfect electric conducting objects, by comparing with other methods.

Acceleration of Multilevel Characteristic Basis Function Method by Multilevel Multipole Approach

Multilevel characteristic basis function (CBF) method (MLCBFM) accelerated by multilevel multipoles will be presented in this article. The proposed algorithm starts from the conventional MLCBFM, rearrange CBFs for each level as multilevel aggregated CBFs. The algorithm not only reduces degrees of freedom of problems but also exploits hierarchical characteristics of divided geometries such as different truncation coefficients or sampling rates in each level of multipole expansions, which results in dramatic acceleration in analyzing electrically large structure. The results of the proposed method agree very well with exact solutions.

Fast analysis for large-scale electromagnetic scattering problems by a hybrid approach

In this paper, a fast and accurate hybrid approach based on the multilevel characteristic basis function method (MLCBFM) is presented to analyze the electrically large scattering problems. First, a modified fast dipole method (MFDM) is proposed to improve the accuracy and efficiency of the conventional fast dipole method (FDM). Then, the MFDM is combined with the adaptive cross approximation (ACA) algorithm and the equivalent dipole method (EDM) to enhance the efficiency of the MLCBFM. In the proposed hybrid method, the use of MFDM makes the construction of secondary characteristic basis functions and reduced matrix of the MLCBFM more accurate and efficient. The impedance matrices representing the interactions of the middle-field pairs are efficiently compressed by using the ACA in order to enable the hybrid method to further reduce the time and the memory significantly when the criterion for the far-field pairs becomes stricter to obtain relatively high accurate solutions. The numerical results of one hundred PEC cubes have demonstrated that the MFDM is capable of effectively reducing the CPU time and the relative errors. Furthermore, another results have shown that the proposed hybrid method has reduced the CPU time and the memory requirement by 27 and 32%, respectively, when the same criterion for the far-field pairs are chosen.

Multi-level characteristic basis function method for analysis of scattering from objects embedded in multi-layered media

ABSTRACTThe multi-level characteristic basis function method is adapted to analyze the problem of scattering from objects embedded in layered media. Inhomogeneous plane waves incident upon the layered media are used to construct multiple levels of characteristic basis functions (CBFs). The use of the CBFs helps reduce the size of the impedance matrix of the associated method of moment significantly, enabling us to employ direct solver as opposed to iterative solvers. The process of generating the reduced matrix is shown to be naturally parallel, and the reduced matrix to be well conditioned, which obviates the need of pre-conditioning. Numerical results are included to demonstrate the accuracy and efficiency of the present approach when used for the analysis of scattering from objects embedded in multi-layered media.

Direct solution of electromagnetic scattering from perfect electric conducting targets using multilevel characteristic basis function method with adaptive cross approximation algorithm

The adaptive cross approximation (ACA) enhanced multilevel characteristic basis function method (MLCBFM) is studied in this article. It is well known that the impedance submatrices containing the reaction terms of low-level basis functions such as Rao–Wilton–Glisson basis functions have low-rank property. However, the authors find that the high-level impedance matrices between nonoverlapping high-level blocks are also low rank and can be compressed efficiently. This property is used to efficiently calculate the high-level reduced matrix of the MLCBFM through the ACA algorithm in this study. Furthermore an efficient scheme for the high-level characteristic basis functions (CBFs) generation is given, which reduces the redundant operations in the high-level CBFs generation step without loss of accuracy. Numerical results are given to demonstrate the accuracy and efficiency of the presented method.

Solution of Electrically Large Problems With Multilevel Characteristic Basis Functions

We present a multilevel version to the characteristic basis function method (CBFM). This technique extends the range of applicability of the conventional CBFM and allows a direct solution of problems even when they exceed 250,000 degrees of freedom. In this paper, it is shown how we can use the multilevel CBFM, which is a natural extension of the conventional approach and which saves both time and memory, and yet retains excellent accuracy in the computed far fields. Also, the adaptive cross algorithm is used for fast calculation of the interaction between the blocks in the process of generating the reduced matrix.

Parallelized multilevel characteristic basis function method for solving electromagnetic scattering problems

AbstractParallel implementation of the multilevel characteristic basis function method is discussed in this article. The use of this method enables us to solve very large electromagnetic problems in a direct manner via a recursive application of the characteristic basis function method. Furthermore, we show that, unlike the iterative schemes, the present method is very well suited for parallelization. Examples are presented to show that upto one million unknown problems can be solved on a workstation using the present scheme, and that the results show very good agreement with those derived by using analytical or fast multipole methods. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2963–2969, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24767

SYNTHESIS OF PHASED ARRAYS IN COMPLEX ENVIRONMENTS WITH THE MULTILEVEL CHARACTERISTIC BASIS FUNCTION METHOD

The aim of this paper is to present a method to carry out the synthesis of large phased arrays when they are afiected by complex environments which can in∞uence the radiation pattern. The synthesis is performed with the help of the Multilevel Characteristic Basis Function Method to calculate a matrix relating input voltages and the far fleld pattern samples. The method is illustrated with the synthesis of a Secondary Surveillance Radar antenna on a turret containing multiple obstacles.