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Integral equations of electromagnetic scattering problems complicated key technology research

Author: MaLianFeng
Tutor: NieZaiPing
School: University of Electronic Science and Technology
Course: Electromagnetic Field and Microwave Technology
Keywords: Adaptive cross approximation method multilevel fast multipole method LDL decomposition integral equation accuracy
CLC: O441.4
Type: Master's thesis
Year: 2011
Downloads: 131
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Abstract


Now target stealth, microwave imaging, target identification and the continuous development of engineering requirements on the electromagnetic properties of complex analysis appears promising important. In order to calculate target scattering and radiation characteristics, the field of computational electromagnetics has seen a considerable surge in the research on the accurate and efficient numerical method. This paper focuses on adaptive cross approximation based on direct methods - low-rank LDL decomposition, combined multilevel adaptive cross approximation method and the multilevel fast multipole algorithm for solving electrically large complex targets, and the convergence and accuracy of the analysis of integral equations for numerical method.This paper describes the electromagnetic scattering, integral equations and numerical methods for solving such problems—Method of Moments (MoM), the simple method of moments introduced the basic principles and key technologies.Then, the basic mathematical theory and the numerical implementation of the integral equation adaptive cross approximation method are introduced. The error bound of the algorithm is assessed and the heart of the algorithm–compression of low rank matrix is studied as a key point. By using the compression of low rank matrix, the complexity of the algorithm is reduced without affecting the accuracy of the algorithm. Because the low rank matrix compressed by adaptive cross-approximation technique impedance matrix block is recoverable, and therefore in this paper, ACA-LDLT based on low-rank decomposition method for solving matrix equation is given, the Monostatic RCS of targets can be quickly solved without considering the convergence of iterative methods.To improve the ACA-LDLT method of computing power, combining with higher order laminated basis function, the solving capacity of this method is up to 800λ2 in the 64GB workstation.Secondly, based on the dipole radiation theory, the improved adaptive cross approximation method is proposed. The computational complexity can be reduced to 1 / 4. Meanwhile, in order to better deal with the electromagnetic scattering problem with the fine structure or the powerful basis functions defined on a large patch, in this paper, the MLACA-MLFMM hybrid method is proposed.The ACA technique is wording on the region where the computational complexity of MLFMM is high. The computational complexity of hybrid method is lower than O (NlogN).Finally, the integral equation numerical precision problems are studied in this thesis. The accuracy analysis of the Integral equation in numerical methods is an important aspect of the application. Some of the key issues about integral equation accuracy analysis are summarized by numerical methods ACA mentioned in this article and MLFMA developed by the research group to deal with PEC targets. From some numrerical examples, the accuracy of numerical solution and the impact of convergency in integral equation are relationship with other issues in addition to the inherent nature of the integral operator.As a basic research work for electromagnetic scattering characteristics of the 3-D electrically-large objects with arbitrary shape and materials, this research work presented in the dissertation provides the powerful way in rigorous modeling and effective solution.

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CLC: > Mathematical sciences and chemical > Physics > Electromagnetics,electrodynamics > Electricity and Magnetism > Electromagnetic waves and electromagnetic fields
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