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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TL;DR: In this paper, asymptotic error estimations for the difference of eigenvalues of a holomorphic operator function and its approximations are derived by transforming of an appropriately chosen identity.
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A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems
TL;DR: In this article, an indirect higher order boundary element method using NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity is presented.
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Nonlinear eigenvalue problems and contour integrals
Marc Van Barel,Peter Kravanja +1 more
TL;DR: Beyn's algorithm for solving nonlinear eigenvalue problems is given a new interpretation and a variant is designed in which the required information is extracted via the canonical polyadic decomposition of a Hankel tensor.
Journal ArticleDOI
Triangular discretization method for the evaluation of RF-fields in cylindrically symmetric cavities
U. van Rienen,Thomas Weiland +1 more
TL;DR: In this paper, the authors describe a discretization method using an "orthogonal triangular double grid" to solve for fields with azimuthal variation in cavities with dielectric and/or permeable insertions.
Journal ArticleDOI
Relationships among contour integral-based methods for solving generalized eigenvalue problems
TL;DR: All contour integral-based eigensolvers can be regarded as projection methods and can be categorized based on their subspace used, the type of projection and the problem to which they are applied implicitly.