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 methods for computational electromagnetics: B-spline and T-spline discretizations
TL;DR: In this paper, the authors introduce methods for electromagnetic wave propagation, based on splines and on T-splines, which can be extended to the case of meshes with T-junctions.
Posted Content
Isogeometric Methods for Computational Electromagnetics: B-spline and T-spline discretizations
TL;DR: Methods for electromagnetic wave propagation, based on splines and on T-splines are introduced, and the theory is extended to the case of meshes with T-junctions, leveraging on the recent theory of T- Splines.
Journal ArticleDOI
Approximation in eigenvalue problems for holomorphic fredholm operator functions I
TL;DR: In this paper, the authors present a construction by which the derivation of the asymptotic error estimations for the approximate eigenvalues of the Fredholm operator functions can be reduced to the derived estimations of these estimations in the case of matrix functions.
Journal ArticleDOI
Coercive space-time finite element methods for initial boundary value problems
Olaf Steinbach,Marco Zank +1 more
TL;DR: In this article, a space-time Galerkin-Bubnov-type finite element formulation of parabolic and hyperbolic second-order partial differential equations in finite time intervals is proposed.
Book
Mapped Vector Basis Functions for Electromagnetic Integral Equations
TL;DR: The method-of-moments solution of the electric field and magnetic field integral equations (EFIE and MFIE) is extended to conducting objects modeled with curved cells, important for electromagnetic scattering, antenna, radar signature, and wireless communication applications.