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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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
Isogeometric Discrete Differential Forms in Three Dimensions
TL;DR: The key point of the analysis is the definition of suitable projectors that render the diagram commutative, and the theory is then applied to the numerical approximation of Maxwell source problems and eigenproblems.
Journal ArticleDOI
A numerical method for nonlinear eigenvalue problems using contour integrals
TL;DR: A contour integral method is proposed to solve nonlinear eigenvalue problems numerically by reducing the original problem to a linear eigen value problem that has identical eigenvalues in the domain.
Book ChapterDOI
Galerkin Boundary Element Methods for Electromagnetic Scattering
Annalisa Buffa,Ralf Hiptmair +1 more
Abstract: Methods based on boundary integral equations are widely used in die numerical simulation of electromagnetic scattering in the frequency domain This article examines a particular class of these methods, namely the Galerkin boundary element approach, from a theoretical point of view Emphasis is put on the fundamental differences between acoustic and electromagnetic scattering The derivation of various boundary integral equations is presented, properties of their discretised counterparts are discussed, and a-priori convergence estimates for the boundary element solutions are rigorously established
Book
Non-self-adjoint boundary eigenvalue problems
TL;DR: In this article, the authors present expansion theorems for regular boundary eigenvalue problems for first order systems of ordinary differential equations, including Birkhoff regular, Stone regular, and Stone regular boundary value problems.
Journal ArticleDOI
A new design for the implementation of isogeometric analysis in Octave and Matlab
TL;DR: GeoPDEs as mentioned in this paper is an Octave/Matlab package for the solution of partial differential equations with isogeometric analysis, first released in 2010, and it is based on the use of Octave and Matlab classes.