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2021 | Buch

Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism

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Über dieses Buch

This book presents a comprehensive mathematical and computational approach for solving electromagnetic problems of practical relevance, such as electromagnetic scattering and the cavity problems. After an in-depth introduction to the mathematical foundations of isogeometric analysis, which discusses how to conduct higher-order simulations efficiently and without the introduction of geometrical errors, the book proves quasi-optimal approximation properties for all trace spaces of the de Rham sequence, and demonstrates inf-sup stability of the isogeometric discretisation of the electric field integral equation (EFIE). Theoretical properties and algorithms are described in detail. The algorithmic approach is, in turn, validated through a series of numerical experiments aimed at solving a set of electromagnetic scattering problems. In the last part of the book, the boundary element method is combined with a novel eigenvalue solver, a so-called contour integral method. An algorithm is presented, together with a set of successful numerical experiments, showing that the eigenvalue solver benefits from the high orders of convergence offered by the boundary element approach. Last, the resulting software, called BEMBEL (Boundary Element Method Based Engineering Library), is reviewed: the user interface is presented, while the underlying design considerations are explained in detail. Given its scope, this book bridges an important gap between numerical analysis and engineering design of electromagnetic devices.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Motivation: The Cavity Problem
Abstract
This chapter gives a brief overview of the historircal context and the state-of-the-art relevant for the development of isogeometric boundary element methods for electromagnetic problems.
Felix Wolf
Chapter 2. Foundations
Abstract
This chapter introduces essential notions of functional analysis, function approximation and electromagnetism.
Felix Wolf
Chapter 3. Isogeometric Boundary Elements
Abstract
This chapter introduces isogeometric discretisations and discusses analytical properties of the corresponding discrete spaces with boundary element methods in mind.
Felix Wolf
Chapter 4. Algorithmic Considerations for Matrix Assembly
Abstract
In this chapter, we will review the algorithmic approach to the matrix assembly of the linear system induced by the isogeometric discretisation of the EFIE.
Felix Wolf
Chapter 5. Numerical Examples: Electromagnetic Scattering
Abstract
This chapter is devoted to the presentation of multiple numerical examples. These are designed to verify the behaviour predicted in Theorem 3.​48 and Corollary 3.​49, and to benchmark the method.
Felix Wolf
Chapter 6. The Discrete Eigenvalue Problem
Abstract
This chapter is devoted to the discussion of the solution of Problem 2.​32, i.e., the computation of resonant frequencies within perfectly conducting structures.
Felix Wolf
Chapter 7. Final Remarks
Abstract
As closing remarks, we will summarise the results of this thesis and mention some closely related open problems.
Felix Wolf
Backmatter
Metadaten
Titel
Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism
verfasst von
Felix Wolf
Copyright-Jahr
2021
Electronic ISBN
978-3-030-61939-8
Print ISBN
978-3-030-61938-1
DOI
https://doi.org/10.1007/978-3-030-61939-8

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