Wolf, Felix (2020):
Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism.
Darmstadt, Technische Universität,
DOI: 10.25534/tuprints-00011317,
[Ph.D. Thesis]
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Item Type: | Ph.D. Thesis | ||||
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Title: | Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism | ||||
Language: | English | ||||
Abstract: | This thesis is concerned with the analysis and implementation of an isogeometric boundary element method for electromagnetic problems. After an introduction of fundamental notions, we will introduce the electric field integral equation (EFIE), which is a variational problem for the solution of the electric wave equation under the assumption of constant coefficients. Afterwards, we will review the notion of isogeometric analysis, a technique to conduct higher-order simulations efficiently and without the introduction of geometrical errors. We prove quasi-optimal approximation properties for all trace spaces of the de Rham sequence and show inf-sup stability of the isogeometric discretisation of the EFIE. Following the analysis of the theoretical properties, we discuss algorithmic details. This includes not only a scheme for matrix assembly but also a compression technique tailored to the isogeometric EFIE, which yields dense matrices. The algorithmic approach is then verified through a series of numerical experiments concerned with electromagnetic scattering problems. These behave as theoretically predicted. In the last part, the boundary element method is combined with an eigenvalue solver, a so-called contour integral method. We introduce the algorithm and solve electromagnetic resonance problems numerically, where we will observe that the eigenvalue solver benefits from the high orders of convergence offered by the boundary element approach. |
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Place of Publication: | Darmstadt | ||||
Classification DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften |
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Divisions: | 18 Department of Electrical Engineering and Information Technology > Institute for Accelerator Science and Electromagnetic Fields > Computational Electromagnetics Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE) |
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Date Deposited: | 13 Jan 2020 09:13 | ||||
Last Modified: | 13 Jan 2020 09:13 | ||||
DOI: | 10.25534/tuprints-00011317 | ||||
URN: | urn:nbn:de:tuda-tuprints-113179 | ||||
Referees: | Kurz, Prof. Dr. Stefan ; Schöps, Prof. Dr. Sebastian ; Costabel, Prof. Dr. Martin | ||||
Date of oral examination: | 19 December 2019 | ||||
URI: | https://tuprints.ulb.tu-darmstadt.de/id/eprint/11317 | ||||
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