Solving Maxwell's Eigenvalue Problem via Isogeometric Boundary Elements and a Contour Integral Method
TLDR
This work solves Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method and discusses the analytic properties of the discretisation, and outlines the implementation.Abstract:
We solve Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method. We discuss the analytic properties of the discretisation, outline the implementation, and showcase numerical examples.read more
Citations
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Journal ArticleDOI
Mixed Spectral-Element Methods for 3-D Maxwell’s Eigenvalue Problems With Bloch Periodic and Open Resonators
TL;DR: In this article, two mixed spectral-element methods (MSEMs) are proposed to solve Maxwell's eigenvalue problems with Bloch (Floquet) periodic and open resonators.
Journal ArticleDOI
Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods
Markus Holzmann,Gerhard Unger +1 more
TL;DR: The self-adjointness of these operators is shown, and equivalent formulations for the eigenvalue problems involving boundary integral operators are derived for the numerical computations of the discrete eigenvalues and the corresponding eigenfunctions by boundary element methods.
Book
Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism
TL;DR: This thesis proves quasi-optimal approximation properties for all trace spaces of the de Rham sequence and shows inf-sup stability of the isogeometric discretisation of the EFIE, which is a variational problem for the solution of the electric wave equation under the assumption of constant coefficients.
Book ChapterDOI
The Discrete Eigenvalue Problem
TL;DR: In this paper, the authors discuss the solution of the problem of computing resonant frequencies within perfectly conducting structures, i.e., the computation of frequencies within a perfectly conducting structure.
Journal ArticleDOI
Complex moment-based methods for differential eigenvalue problems
TL;DR: In this paper , the authors proposed operation analogues of Sakurai-Sugiura-type complex moment-based eigensolvers using higher-order complex moments and analyzed the error bound of the proposed methods.
References
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Journal ArticleDOI
A Numerical Comparison of an Isogeometric and a Parametric Higher Order Raviart–Thomas Approach to the Electric Field Integral Equation
TL;DR: In this article, numerical experiments were conducted to compare an isogeometric discretization of the electric field integral equation and a parametric Raviart-Thomas approach, focusing on accuracy with respect to degrees of freedom.
Journal ArticleDOI
Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods
Markus Holzmann,Gerhard Unger +1 more
TL;DR: The self-adjointness of these operators is shown, and equivalent formulations for the eigenvalue problems involving boundary integral operators are derived for the numerical computations of the discrete eigenvalues and the corresponding eigenfunctions by boundary element methods.
Journal ArticleDOI
Shape Optimization of Rotating Electric Machines using Isogeometric Analysis and Harmonic Stator-Rotor Coupling
TL;DR: In this article, a 6-pole permanent magnet synchronous machine is modeled using a multipatch isogeometric approach and rotation of the machine is realized by modeling the stator and rotor domain separately and coupling them at the interface using harmonic basis functions.
Convergence analysis of a Galerkin boundary element method for electromagnetic resonance problems
TL;DR: In this paper, a convergence analysis of a Galerkin boundary element method for resonance problems arising from the time harmonic Maxwell's equations is presented, where boundary integral formulations of the resonance problems are eigenvalue problems for holomorphic Fredholm operator-valued functions, where the operators satisfy a generalized Garding's inequality.
Book ChapterDOI
Operator Functions in Banach Spaces
TL;DR: In this paper, the structure of the resolvent of a holomorphic Fredholm operator function in Banach spaces is discussed in detail, and it is highlighted that on a domain in C, its resolute set is finitely meromorphic if its resolver set is non-empty.