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Study on model order reduction for Maxwell's equations based on Krylov subspace methods

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Please use this identifier to cite or link to this item:https://doi.org/10.14943/doctoral.k14580
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Title: Study on model order reduction for Maxwell's equations based on Krylov subspace methods
Other Titles: クリロフ部分空間法によるマクスウェル方程式のモデル縮約法に関する研究
Authors: 比留間, 真悟 Browse this author
Keywords: Cauer circuit
complex permeability
Darwin model
homogenization method
Krylov subspace methods
Lanczos process
Maxwell’s equations
model order reduction (MOR)
Stieltjes continued fraction
Issue Date: 25-Mar-2021
Publisher: Hokkaido University
Abstract: With the recent development of the power electronics devices, the evaluation of the eddy current losses in the electromagnetic apparatuses has become significant for the designers because the high-frequency components in the power supply induce non-negligible losses. Although the finite element method (FEM) is useful to evaluate the eddy current losses,it is sometimes difficult to perform the FE analysis (FEA) when we consider the highfrequency component. Since the skin depth becomes significantly small at high-frequency, we have to subdivide the conducting domains into fine elements. As a result, we have an unsolvable size of the FE equation. To circumvent this problem, model order reduction (MOR) techniques are developed to reduce the computational costs and time in the eddy current analysis. In this paper, new MOR techniques are presented to 1. generate a reduced-order model that is equivalent to the Cauer circuit of the electric apparatuses, 2. accelerate the homogenization method by educing the unknowns, 3. consider the inductive and capacitive effects simultaneously. Chapter 3 discusses a new MOR technique that allows us to obtain a Cauer circuit from a given system. Chapter 4 discusses the use of the proposed method in the homogenization method. We apply it to the FE equation of a unit cell, Dowell's equation, and homogenization FEA. Chapter 5 discusses the application of the proposed method to the Darwin model of Maxwell’s equations.
Conffering University: 北海道大学
Degree Report Number: 甲第14580号
Degree Level: 博士
Degree Discipline: 情報科学
Examination Committee Members: (主査) 教授 五十嵐 一, 教授 山下 裕, 教授 北 裕幸, 准教授 野口 聡
Degree Affiliation: 情報科学院(情報科学専攻)
Type: theses (doctoral)
URI: http://hdl.handle.net/2115/84643
Appears in Collections:課程博士 (Doctorate by way of Advanced Course) > 情報科学院(Graduate School of Information Science and Technology)
学位論文 (Theses) > 博士 (情報科学)

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