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A Study on the Fast Degenerated Kemel Algorithm for Solving Magnetic Field Integral Equation from Conducting Bodies

Author: XuXiuMing
Tutor: BaoYaMing
School: Nanjing University of Posts and Telecommunications
Course: Electromagnetic Field and Microwave Technology
Keywords: Magnetic Field Integral Equation Method of Moment Degenerated KernelFunction Low-rank Approximation Hierarchical Matrix
CLC: O441.4
Type: Master's thesis
Year: 2012
Downloads: 44
Quote: 1
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Abstract


Many fast algorithms based on Method of moment (MoM) for solving electromagnetic fieldproblems attract much attention and have been employed to a lot of applications. Green’s function,as a kernel function of integral equation, accurately describes the electromagnetic fieldpropagation, and will result in a dense matrix if the equation is discredited. Inhierarchical-matrix-based method, the idea of the degenerated kernel function with separated thesource and field variables are employed for coefficient matrix element storage and computationaltime saving, so the fast iterative solving can be obtained. .Firstly, electromagnetic scattering problems in three-dimensional from smooth conductingbodies can be analyzed by using magnetic field integral equation (MFIE). For fast solving theMFIE, a fast algorithm is proposed for finding common each edge of a pair of adjacentlytriangular patches in the pre-process before the solving, the fast algorithm is based on theconcepts of adjacent matrix and incidence matrix for the topology of the discrete element of thesurface. The computational complexity of the algorithm for finding the common edges is O(N ) .All the common edges are reordered by linear Octree address code (Morton code). Secondly, theLagrange interpolation is employed to decompose the Kernel Function of MFIE (the gradient ofGreen function). The matrix precision approach the original one can be controlled by interpolationpoints, thus, the original kernel function is transformed into a precision-controllable degeneratedkernel function. The corresponding programs are implemented. Finally, some numerical examplesare obtained, which show that less memory space and the CPU time are required by using theH-matrix-based method. The complexities are proportional toO(N log N ).In conclusion, the fast algorithm based on the degenerated kernel is researched and appliedfor scattering problems. Some typical three-dimensional conducting scatterers are analyzed bymeans of MFIE, MOM and the proposed method. These may be further developed and applied.

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