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Astudy on Hierarchical-matrix-based Algorithm for Solving Electromagnetic Scattering from Conducting

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Tutor: BaoYaMing
School: Nanjing University of Posts and Telecommunications
Course: Electromagnetic Field and Microwave Technology
Keywords: Method of Moments,H- matrix,Degenerate kernel approximation,Lagrange Interpolati
CLC: O441
Type: Master's thesis
Year:  2012
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Abstract:
In order to solve the Moment Method of storage and computation in the process of excessive , there are a series of fast algorithm , including fast Fourier transform (FFT) - based methods , fast multipole method (FMA) . Which is fast multi- pole method is the use of degenerate kernel approximation this important idea to achieve the purpose of reducing the computing complexity and storage complexity . Fast multipole method can be seen as a specific degradation of nuclear approximation In addition, you can use other methods to degenerate core approximation such as the Taylor expansion , Lagrange interpolation , these methods also can field source separation to approximate the original kernel function, thereby reducing the amount of calculation and memory capacity . This article is on the basis of the H- matrix the the Lagrange Interpolation degradation kernel function to achieve fast calculation . First subdivision of the triangular faces , three-dimensional conductive targets to obtain the public side , the relationship between the use of point , line and surface target surface current basic principle is obtained according to the method of moments . Then surrounded with a tangent to the target model cube this model , block octree in each layer , at the most granular level renumbered . Conditions may allow re-use , discriminant nearly block and far blocks . Which does not meet the conditions of the block may allow for nearly block , whose elements are still the method of moments to fill ; meet the conditions may allow the block as far block , the kernel function using Lagrange Interpolation degradation of low rank approximation matrix filled . Followed by a conjugate gradient method (CG) for solving the matrix-vector equation thinning , the approximate current from the target surface . Finally , the current of the current method of moments are compared to verify the correctness of the H- matrix algorithm , and analysis using computational and storage amount of H- matrix algorithm for solving the three - dimensional conductive targets . The results show that the H- matrix algorithm and combined with the corresponding degenerate core conductor electromagnetic scattering problems can be efficiently solved .
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