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A Reduced Matrix Construction Method for Accelerating Iterative Solution of Eigenbasis Function Method

A technology of eigenbasis function and iterative solution, which is applied in the field of reduced matrix construction to speed up the iterative solution of eigenbasis function method, can solve problems such as slow convergence of equations, achieve condition number optimization of reduced matrix, speed up iterative solution, and improve electromagnetic scattering problems The effect of the ability

Active Publication Date: 2021-11-05
ANHUI UNIV OF SCI & TECH
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Problems solved by technology

[0004] The purpose of the present invention is to solve the problem of slow convergence of the iterative solution of the reduced matrix equation in the analysis of the electric large target by the eigenbasis function method, and propose a method for constructing the reduced matrix to speed up the iterative solution of the eigenbasis function method

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  • A Reduced Matrix Construction Method for Accelerating Iterative Solution of Eigenbasis Function Method
  • A Reduced Matrix Construction Method for Accelerating Iterative Solution of Eigenbasis Function Method
  • A Reduced Matrix Construction Method for Accelerating Iterative Solution of Eigenbasis Function Method

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[0013] The schematic diagram of the present invention's reduced matrix structure is as follows: figure 1 Shown, below in conjunction with accompanying drawing the implementation of technical scheme is described in further detail:

[0014] Step 1: First divide the target into M adjacent sub-domains, and then divide each sub-domain into N i units (i=1,2,...M). In order to obtain a set of CBFs containing multi-angle current information, CBFM uses excitations of different incident directions and polarizations to irradiate each subfield, assuming that the total number of excitations is N pws =2N θ N φ , N θ , N φ Denote the number of excitations in the θ and φ directions respectively, define E i is the excitation matrix for each subdomain, and the dimension is is the unknown number of extended subfield i. Apply the singular value decomposition technique to compress the excitation matrix:

[0015] E. i =U i W i V i T (1)

[0016] In the formula, U i and V i are a...

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Abstract

The invention discloses a reduced matrix construction method for accelerating the iterative solution of the characteristic basis function method, which can effectively accelerate the iterative solution speed of the characteristic basis function method. Firstly, the excitation source is compressed using the singular value decomposition technique, and the compressed new excitation source is obtained, which is defined as voltage basis functions (VBFs); secondly, under the new excitation source, the characteristic basis function of each subdomain ( CBFs); Finally, VCBFs and CBFs are used as test functions and basis functions to construct a reduced matrix, and the main diagonal sub-matrixes of the obtained reduced matrix are unit matrices, and the condition number of the reduced matrix is ​​optimized, which can speed up the iterative solution of the reduced matrix equation. The invention provides a new method for the iterative solution of the eigenbasis function method. At the same time, the invention can be combined with algorithms such as multi-layer fast multipole method, adaptive integration method, pre-correction-fast Fourier transform method, etc. Efficiency of function method in analyzing electromagnetic scattering characteristics of electrically large targets.

Description

technical field [0001] The invention relates to a high-efficiency method for quickly analyzing the electromagnetic scattering characteristics of an electrically large-size target, in particular to a reduction matrix construction method for accelerating the iterative solution of the characteristic basis function method. Background technique [0002] The characteristic basis function method (CBFM) is based on the principle of area partitioning, divides the target into multiple subdomains and constructs a cluster of characteristic basis functions (CBFs) independent of the angle of incidence for each subdomain, and finally constructs a reduced order reduction matrix, usually It can be solved by direct method. However, with the increase of the electrical size of the target, the number of CBFs increases continuously, and the dimension of the reduced matrix becomes larger and larger. It is very difficult to solve the reduced matrix equation by the direct method. [0003] The exist...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F30/20G06F17/15G06F17/16
CPCG06F17/15G06F17/16G06F30/20
Inventor 王仲根聂文艳
Owner ANHUI UNIV OF SCI & TECH
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