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A Study on Implementation Techniques of the Degenerated Kernel Method for Electromagnetic Integral Equations

Author: YangYang
Tutor: BaoYaMing
School: Nanjing University of Posts and Telecommunications
Course: Electronics and Communication Engineering
Keywords: Method of Moment Hierarchical Matrix Degenerate Kernel Approximation IterativeMethod Preconditioner
CLC: TM15
Type: Master's thesis
Year: 2013
Downloads: 14
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Abstract


In the field of computational electromagnetics, fast algorithms for accelerating solvingprocedures are important for the solutions of electrically large electromagnetic problems. In thedegenerated kernel method, the integral kernel functions is expanded with functions which thesource and field coordinates are separated, to decrease the reqirments of memory space for theimpedance matrix and reduce the computational operations for single iteration in the iterativesolving procedure.In the thesis, according to the principle of high cohesion and low coupling in modular design, aprogram framework for moment-method-based codes is purposed, which can make use of theexisting codes to improve the reusability and replaceability of the program. Firstly, by refining thecalculation process of numerical integration in the method of moments, the integral subroutine isreusable. the codes for singular integration is extracted for the possible replacement if necessary.The independent degenerated kernel module is established for of the far blocks of the matrix, whichcan reduce the coupling between modules and improve the reliability and maintainability of theprogram. Secondly, under the consideration of different solving algorithms, such as direct methodsand iterative methods, the solving modules are implemented, which make the matrix-vectorequation solver can be changed easily. A preconditioner program with low accuracy hierarchicalmatrix approximation is written to improve the convergence speed of iteration.Finally, conducting spheres, cylinders and NASA almonds are analyzed using the implementedprogram. The numerical results verify the reliability and scalability of the program. The numericalexamples show that the required memory space and the CPU time are proportional toΟ N logN by using the hierarchical matrix method. Hierarchical method with proper degenerated kernel maybe more explored for algorithms with higher efficiency.

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CLC: > Industrial Technology > Electrotechnical > Fundamental Theory of Electrical Engineering > The application of electromagnetic theory
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